Datasets:

nums
listlengths
4
4
target
int64
10
100
solution
listlengths
3
3
optimal_path
stringlengths
282
529
start_size
int64
4
4
search_path
stringlengths
505
16.8k
rating
float64
0
0.99
search_type
stringclasses
5 values
heuristic
stringclasses
2 values
[ 48, 11, 54, 1 ]
18
[ "48-11=37", "54+1=55", "55-37=18" ]
Current State: 18:[48, 11, 54, 1], Operations: [] Exploring Operation: 48-11=37, Resulting Numbers: [54, 1, 37] Generated Node #2: [54, 1, 37] from Operation: 48-11=37 Current State: 18:[54, 1, 37], Operations: ['48-11=37'] Exploring Operation: 54+1=55, Resulting Numbers: [37, 55] Generated Node #3: [37, 55] from Operation: 54+1=55 Current State: 18:[37, 55], Operations: ['48-11=37', '54+1=55'] Exploring Operation: 55-37=18, Resulting Numbers: [18] 18,18 equal: Goal Reached
4
Current State: 18:[48, 11, 54, 1], Operations: [] Exploring Operation: 48-11=37, Resulting Numbers: [54, 1, 37] Generated Node #0,0: 18:[54, 1, 37] Operation: 48-11=37 Exploring Operation: 54-11=43, Resulting Numbers: [48, 1, 43] Generated Node #0,1: 18:[48, 1, 43] Operation: 54-11=43 Exploring Operation: 54-48=6, Resulting Numbers: [11, 1, 6] Generated Node #0,2: 18:[11, 1, 6] Operation: 54-48=6 Start Sub Search at level 1: Moving to Node #0,2 Current State: 18:[11, 1, 6], Operations: ['54-48=6'] Exploring Operation: 11/1=11, Resulting Numbers: [6, 11] Generated Node #0,2,0: 18:[6, 11] Operation: 11/1=11 Exploring Operation: 11-1=10, Resulting Numbers: [6, 10] Generated Node #0,2,1: 18:[6, 10] Operation: 11-1=10 Exploring Operation: 11*1=11, Resulting Numbers: [6, 11] Generated Node #0,2,2: 18:[6, 11] Operation: 11*1=11 Moving to Node #0,2,1 Current State: 18:[6, 10], Operations: ['54-48=6', '11-1=10'] Exploring Operation: 10-6=4, Resulting Numbers: [4] 4,18 unequal: No Solution Exploring Operation: 6+10=16, Resulting Numbers: [16] 16,18 unequal: No Solution Exploring Operation: 6*10=60, Resulting Numbers: [60] 60,18 unequal: No Solution Moving to Node #0,2,0 Current State: 18:[6, 11], Operations: ['54-48=6', '11/1=11'] Exploring Operation: 6+11=17, Resulting Numbers: [17] 17,18 unequal: No Solution Exploring Operation: 6*11=66, Resulting Numbers: [66] 66,18 unequal: No Solution Exploring Operation: 11-6=5, Resulting Numbers: [5] 5,18 unequal: No Solution Moving to Node #0,2,2 Current State: 18:[6, 11], Operations: ['54-48=6', '11*1=11'] Exploring Operation: 11-6=5, Resulting Numbers: [5] 5,18 unequal: No Solution Exploring Operation: 6+11=17, Resulting Numbers: [17] 17,18 unequal: No Solution Exploring Operation: 6*11=66, Resulting Numbers: [66] 66,18 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 18:[54, 1, 37], Operations: ['48-11=37'] Exploring Operation: 54-1=53, Resulting Numbers: [37, 53] Generated Node #0,0,0: 18:[37, 53] Operation: 54-1=53 Exploring Operation: 54-37=17, Resulting Numbers: [1, 17] Generated Node #0,0,1: 18:[1, 17] Operation: 54-37=17 Exploring Operation: 37-1=36, Resulting Numbers: [54, 36] Generated Node #0,0,2: 18:[54, 36] Operation: 37-1=36 Moving to Node #0,0,1 Current State: 18:[1, 17], Operations: ['48-11=37', '54-37=17'] Exploring Operation: 17/1=17, Resulting Numbers: [17] 17,18 unequal: No Solution Exploring Operation: 1*17=17, Resulting Numbers: [17] 17,18 unequal: No Solution Exploring Operation: 1+17=18, Resulting Numbers: [18] 18,18 equal: Goal Reached Moving to Node #0 Current State: 18:[48, 11, 54, 1], Operations: [] Exploring Operation: 48-11=37, Resulting Numbers: [54, 1, 37] Generated Node #0,0: 18:[54, 1, 37] Operation: 48-11=37 Moving to Node #0,0 Current State: 18:[54, 1, 37], Operations: ['48-11=37'] Exploring Operation: 54-37=17, Resulting Numbers: [1, 17] Generated Node #0,0,1: 18:[1, 17] Operation: 54-37=17 Moving to Node #0,0,1 Current State: 18:[1, 17], Operations: ['48-11=37', '54-37=17'] Exploring Operation: 1+17=18, Resulting Numbers: [18] 18,18 equal: Goal Reached Exit Sub Search at level 1
0.978299
hs_3
sum_heuristic
[ 24, 53, 11, 20 ]
13
[ "24+53=77", "77/11=7", "20-7=13" ]
Current State: 13:[24, 53, 11, 20], Operations: [] Exploring Operation: 24+53=77, Resulting Numbers: [11, 20, 77] Generated Node #2: [11, 20, 77] from Operation: 24+53=77 Current State: 13:[11, 20, 77], Operations: ['24+53=77'] Exploring Operation: 77/11=7, Resulting Numbers: [20, 7] Generated Node #3: [20, 7] from Operation: 77/11=7 Current State: 13:[20, 7], Operations: ['24+53=77', '77/11=7'] Exploring Operation: 20-7=13, Resulting Numbers: [13] 13,13 equal: Goal Reached
4
Current State: 13:[24, 53, 11, 20], Operations: [] Exploring Operation: 24-11=13, Resulting Numbers: [53, 20, 13] Generated Node #0,0: 13:[53, 20, 13] Operation: 24-11=13 Exploring Operation: 53-24=29, Resulting Numbers: [11, 20, 29] Generated Node #0,1: 13:[11, 20, 29] Operation: 53-24=29 Exploring Operation: 53-20=33, Resulting Numbers: [24, 11, 33] Generated Node #0,2: 13:[24, 11, 33] Operation: 53-20=33 Exploring Operation: 53-11=42, Resulting Numbers: [24, 20, 42] Generated Node #0,3: 13:[24, 20, 42] Operation: 53-11=42 Start Sub Search at level 1: Moving to Node #0,1 Current State: 13:[11, 20, 29], Operations: ['53-24=29'] Exploring Operation: 29-20=9, Resulting Numbers: [11, 9] Generated Node #0,1,0: 13:[11, 9] Operation: 29-20=9 Exploring Operation: 20-11=9, Resulting Numbers: [29, 9] Generated Node #0,1,1: 13:[29, 9] Operation: 20-11=9 Exploring Operation: 11+20=31, Resulting Numbers: [29, 31] Generated Node #0,1,2: 13:[29, 31] Operation: 11+20=31 Exploring Operation: 29-11=18, Resulting Numbers: [20, 18] Generated Node #0,1,3: 13:[20, 18] Operation: 29-11=18 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 13:[11, 9], Operations: ['53-24=29', '29-20=9'] Exploring Operation: 11-9=2, Resulting Numbers: [2] 2,13 unequal: No Solution Exploring Operation: 11*9=99, Resulting Numbers: [99] 99,13 unequal: No Solution Exploring Operation: 11+9=20, Resulting Numbers: [20] 20,13 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 13:[20, 18], Operations: ['53-24=29', '29-11=18'] Exploring Operation: 20-18=2, Resulting Numbers: [2] 2,13 unequal: No Solution Exploring Operation: 20+18=38, Resulting Numbers: [38] 38,13 unequal: No Solution Exploring Operation: 20*18=360, Resulting Numbers: [360] 360,13 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 13:[29, 9], Operations: ['53-24=29', '20-11=9'] Exploring Operation: 29*9=261, Resulting Numbers: [261] 261,13 unequal: No Solution Exploring Operation: 29-9=20, Resulting Numbers: [20] 20,13 unequal: No Solution Exploring Operation: 29+9=38, Resulting Numbers: [38] 38,13 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 13:[29, 31], Operations: ['53-24=29', '11+20=31'] Exploring Operation: 29*31=899, Resulting Numbers: [899] 899,13 unequal: No Solution Exploring Operation: 29+31=60, Resulting Numbers: [60] 60,13 unequal: No Solution Exploring Operation: 31-29=2, Resulting Numbers: [2] 2,13 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 13:[24, 11, 33], Operations: ['53-20=33'] Exploring Operation: 24-11=13, Resulting Numbers: [33, 13] Generated Node #0,2,0: 13:[33, 13] Operation: 24-11=13 Exploring Operation: 33-11=22, Resulting Numbers: [24, 22] Generated Node #0,2,1: 13:[24, 22] Operation: 33-11=22 Exploring Operation: 33/11=3, Resulting Numbers: [24, 3] Generated Node #0,2,2: 13:[24, 3] Operation: 33/11=3 Exploring Operation: 33-24=9, Resulting Numbers: [11, 9] Generated Node #0,2,3: 13:[11, 9] Operation: 33-24=9 Moving to Node #0,2,3 Current State: 13:[11, 9], Operations: ['53-20=33', '33-24=9'] Exploring Operation: 11+9=20, Resulting Numbers: [20] 20,13 unequal: No Solution Exploring Operation: 11-9=2, Resulting Numbers: [2] 2,13 unequal: No Solution Exploring Operation: 11*9=99, Resulting Numbers: [99] 99,13 unequal: No Solution Moving to Node #0,2,1 Current State: 13:[24, 22], Operations: ['53-20=33', '33-11=22'] Exploring Operation: 24*22=528, Resulting Numbers: [528] 528,13 unequal: No Solution Exploring Operation: 24-22=2, Resulting Numbers: [2] 2,13 unequal: No Solution Exploring Operation: 24+22=46, Resulting Numbers: [46] 46,13 unequal: No Solution Moving to Node #0,2,0 Current State: 13:[33, 13], Operations: ['53-20=33', '24-11=13'] Exploring Operation: 33*13=429, Resulting Numbers: [429] 429,13 unequal: No Solution Exploring Operation: 33-13=20, Resulting Numbers: [20] 20,13 unequal: No Solution Exploring Operation: 33+13=46, Resulting Numbers: [46] 46,13 unequal: No Solution Moving to Node #0,2,2 Current State: 13:[24, 3], Operations: ['53-20=33', '33/11=3'] Exploring Operation: 24/3=8, Resulting Numbers: [8] 8,13 unequal: No Solution Exploring Operation: 24*3=72, Resulting Numbers: [72] 72,13 unequal: No Solution Exploring Operation: 24-3=21, Resulting Numbers: [21] 21,13 unequal: No Solution Exploring Operation: 24+3=27, Resulting Numbers: [27] 27,13 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 13:[53, 20, 13], Operations: ['24-11=13'] Exploring Operation: 53-13=40, Resulting Numbers: [20, 40] Generated Node #0,0,0: 13:[20, 40] Operation: 53-13=40 Exploring Operation: 20-13=7, Resulting Numbers: [53, 7] Generated Node #0,0,1: 13:[53, 7] Operation: 20-13=7 Exploring Operation: 53-20=33, Resulting Numbers: [13, 33] Generated Node #0,0,2: 13:[13, 33] Operation: 53-20=33 Exploring Operation: 53+20=73, Resulting Numbers: [13, 73] Generated Node #0,0,3: 13:[13, 73] Operation: 53+20=73 Moving to Node #0,0,2 Current State: 13:[13, 33], Operations: ['24-11=13', '53-20=33'] Exploring Operation: 13+33=46, Resulting Numbers: [46] 46,13 unequal: No Solution Exploring Operation: 13*33=429, Resulting Numbers: [429] 429,13 unequal: No Solution Exploring Operation: 33-13=20, Resulting Numbers: [20] 20,13 unequal: No Solution Moving to Node #0,0,0 Current State: 13:[20, 40], Operations: ['24-11=13', '53-13=40'] Exploring Operation: 20*40=800, Resulting Numbers: [800] 800,13 unequal: No Solution Exploring Operation: 40-20=20, Resulting Numbers: [20] 20,13 unequal: No Solution Exploring Operation: 40/20=2, Resulting Numbers: [2] 2,13 unequal: No Solution Exploring Operation: 20+40=60, Resulting Numbers: [60] 60,13 unequal: No Solution Moving to Node #0,0,1 Current State: 13:[53, 7], Operations: ['24-11=13', '20-13=7'] Exploring Operation: 53*7=371, Resulting Numbers: [371] 371,13 unequal: No Solution Exploring Operation: 53+7=60, Resulting Numbers: [60] 60,13 unequal: No Solution Exploring Operation: 53-7=46, Resulting Numbers: [46] 46,13 unequal: No Solution Moving to Node #0,0,3 Current State: 13:[13, 73], Operations: ['24-11=13', '53+20=73'] Exploring Operation: 13+73=86, Resulting Numbers: [86] 86,13 unequal: No Solution Exploring Operation: 13*73=949, Resulting Numbers: [949] 949,13 unequal: No Solution Exploring Operation: 73-13=60, Resulting Numbers: [60] 60,13 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 13:[24, 20, 42], Operations: ['53-11=42'] Exploring Operation: 24-20=4, Resulting Numbers: [42, 4] Generated Node #0,3,0: 13:[42, 4] Operation: 24-20=4 Exploring Operation: 24+20=44, Resulting Numbers: [42, 44] Generated Node #0,3,1: 13:[42, 44] Operation: 24+20=44 Exploring Operation: 42-20=22, Resulting Numbers: [24, 22] Generated Node #0,3,2: 13:[24, 22] Operation: 42-20=22 Exploring Operation: 42-24=18, Resulting Numbers: [20, 18] Generated Node #0,3,3: 13:[20, 18] Operation: 42-24=18 Moving to Node #0,3,3 Current State: 13:[20, 18], Operations: ['53-11=42', '42-24=18'] Exploring Operation: 20*18=360, Resulting Numbers: [360] 360,13 unequal: No Solution Exploring Operation: 20-18=2, Resulting Numbers: [2] 2,13 unequal: No Solution Exploring Operation: 20+18=38, Resulting Numbers: [38] 38,13 unequal: No Solution Moving to Node #0,3,2 Current State: 13:[24, 22], Operations: ['53-11=42', '42-20=22'] Exploring Operation: 24+22=46, Resulting Numbers: [46] 46,13 unequal: No Solution Exploring Operation: 24-22=2, Resulting Numbers: [2] 2,13 unequal: No Solution Exploring Operation: 24*22=528, Resulting Numbers: [528] 528,13 unequal: No Solution Moving to Node #0,3,0 Current State: 13:[42, 4], Operations: ['53-11=42', '24-20=4'] Exploring Operation: 42+4=46, Resulting Numbers: [46] 46,13 unequal: No Solution Exploring Operation: 42*4=168, Resulting Numbers: [168] 168,13 unequal: No Solution Exploring Operation: 42-4=38, Resulting Numbers: [38] 38,13 unequal: No Solution Moving to Node #0,3,1 Current State: 13:[42, 44], Operations: ['53-11=42', '24+20=44'] Exploring Operation: 42*44=1848, Resulting Numbers: [1848] 1848,13 unequal: No Solution Exploring Operation: 44-42=2, Resulting Numbers: [2] 2,13 unequal: No Solution Exploring Operation: 42+44=86, Resulting Numbers: [86] 86,13 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_4
mult_heuristic
[ 36, 54, 11, 46 ]
33
[ "36+54=90", "11+46=57", "90-57=33" ]
Current State: 33:[36, 54, 11, 46], Operations: [] Exploring Operation: 36+54=90, Resulting Numbers: [11, 46, 90] Generated Node #2: [11, 46, 90] from Operation: 36+54=90 Current State: 33:[11, 46, 90], Operations: ['36+54=90'] Exploring Operation: 11+46=57, Resulting Numbers: [90, 57] Generated Node #3: [90, 57] from Operation: 11+46=57 Current State: 33:[90, 57], Operations: ['36+54=90', '11+46=57'] Exploring Operation: 90-57=33, Resulting Numbers: [33] 33,33 equal: Goal Reached
4
Current State: 33:[36, 54, 11, 46], Operations: [] Exploring Operation: 54-46=8, Resulting Numbers: [36, 11, 8] Generated Node #0,0: 33:[36, 11, 8] Operation: 54-46=8 Exploring Operation: 54-36=18, Resulting Numbers: [11, 46, 18] Generated Node #0,1: 33:[11, 46, 18] Operation: 54-36=18 Exploring Operation: 46-36=10, Resulting Numbers: [54, 11, 10] Generated Node #0,2: 33:[54, 11, 10] Operation: 46-36=10 Exploring Operation: 54-11=43, Resulting Numbers: [36, 46, 43] Generated Node #0,3: 33:[36, 46, 43] Operation: 54-11=43 Moving to Node #0,0 Current State: 33:[36, 11, 8], Operations: ['54-46=8'] Exploring Operation: 36+8=44, Resulting Numbers: [11, 44] Generated Node #0,0,0: 33:[11, 44] Operation: 36+8=44 Exploring Operation: 36-8=28, Resulting Numbers: [11, 28] Generated Node #0,0,1: 33:[11, 28] Operation: 36-8=28 Exploring Operation: 36-11=25, Resulting Numbers: [8, 25] Generated Node #0,0,2: 33:[8, 25] Operation: 36-11=25 Exploring Operation: 11-8=3, Resulting Numbers: [36, 3] Generated Node #0,0,3: 33:[36, 3] Operation: 11-8=3 Moving to Node #0,1 Current State: 33:[11, 46, 18], Operations: ['54-36=18'] Exploring Operation: 18-11=7, Resulting Numbers: [46, 7] Generated Node #0,1,0: 33:[46, 7] Operation: 18-11=7 Exploring Operation: 11+18=29, Resulting Numbers: [46, 29] Generated Node #0,1,1: 33:[46, 29] Operation: 11+18=29 Exploring Operation: 46-11=35, Resulting Numbers: [18, 35] Generated Node #0,1,2: 33:[18, 35] Operation: 46-11=35 Exploring Operation: 46-18=28, Resulting Numbers: [11, 28] Generated Node #0,1,3: 33:[11, 28] Operation: 46-18=28 Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 33:[11, 28], Operations: ['54-36=18', '46-18=28'] Exploring Operation: 11+28=39, Resulting Numbers: [39] 39,33 unequal: No Solution Exploring Operation: 28-11=17, Resulting Numbers: [17] 17,33 unequal: No Solution Exploring Operation: 11*28=308, Resulting Numbers: [308] 308,33 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 33:[18, 35], Operations: ['54-36=18', '46-11=35'] Exploring Operation: 18+35=53, Resulting Numbers: [53] 53,33 unequal: No Solution Exploring Operation: 35-18=17, Resulting Numbers: [17] 17,33 unequal: No Solution Exploring Operation: 18*35=630, Resulting Numbers: [630] 630,33 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 33:[46, 7], Operations: ['54-36=18', '18-11=7'] Exploring Operation: 46*7=322, Resulting Numbers: [322] 322,33 unequal: No Solution Exploring Operation: 46-7=39, Resulting Numbers: [39] 39,33 unequal: No Solution Exploring Operation: 46+7=53, Resulting Numbers: [53] 53,33 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 33:[46, 29], Operations: ['54-36=18', '11+18=29'] Exploring Operation: 46*29=1334, Resulting Numbers: [1334] 1334,33 unequal: No Solution Exploring Operation: 46-29=17, Resulting Numbers: [17] 17,33 unequal: No Solution Exploring Operation: 46+29=75, Resulting Numbers: [75] 75,33 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2 Current State: 33:[54, 11, 10], Operations: ['46-36=10'] Exploring Operation: 54-10=44, Resulting Numbers: [11, 44] Generated Node #0,2,0: 33:[11, 44] Operation: 54-10=44 Exploring Operation: 54+10=64, Resulting Numbers: [11, 64] Generated Node #0,2,1: 33:[11, 64] Operation: 54+10=64 Exploring Operation: 54-11=43, Resulting Numbers: [10, 43] Generated Node #0,2,2: 33:[10, 43] Operation: 54-11=43 Exploring Operation: 11-10=1, Resulting Numbers: [54, 1] Generated Node #0,2,3: 33:[54, 1] Operation: 11-10=1 Moving to Node #0,3 Current State: 33:[36, 46, 43], Operations: ['54-11=43'] Exploring Operation: 43-36=7, Resulting Numbers: [46, 7] Generated Node #0,3,0: 33:[46, 7] Operation: 43-36=7 Exploring Operation: 36+46=82, Resulting Numbers: [43, 82] Generated Node #0,3,1: 33:[43, 82] Operation: 36+46=82 Exploring Operation: 46-36=10, Resulting Numbers: [43, 10] Generated Node #0,3,2: 33:[43, 10] Operation: 46-36=10 Exploring Operation: 46-43=3, Resulting Numbers: [36, 3] Generated Node #0,3,3: 33:[36, 3] Operation: 46-43=3 Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 33:[36, 3], Operations: ['54-11=43', '46-43=3'] Exploring Operation: 36*3=108, Resulting Numbers: [108] 108,33 unequal: No Solution Exploring Operation: 36-3=33, Resulting Numbers: [33] 33,33 equal: Goal Reached Moving to Node #0 Current State: 33:[36, 54, 11, 46], Operations: [] Exploring Operation: 54-11=43, Resulting Numbers: [36, 46, 43] Generated Node #0,3: 33:[36, 46, 43] Operation: 54-11=43 Moving to Node #0,3 Current State: 33:[36, 46, 43], Operations: ['54-11=43'] Exploring Operation: 46-43=3, Resulting Numbers: [36, 3] Generated Node #0,3,3: 33:[36, 3] Operation: 46-43=3 Moving to Node #0,3,3 Current State: 33:[36, 3], Operations: ['54-11=43', '46-43=3'] Exploring Operation: 36-3=33, Resulting Numbers: [33] 33,33 equal: Goal Reached Exit Sub Search at level 1
0.967014
hs_4
sum_heuristic
[ 28, 44, 22, 12 ]
26
[ "44-28=16", "22-12=10", "16+10=26" ]
Current State: 26:[28, 44, 22, 12], Operations: [] Exploring Operation: 44-28=16, Resulting Numbers: [22, 12, 16] Generated Node #2: [22, 12, 16] from Operation: 44-28=16 Current State: 26:[22, 12, 16], Operations: ['44-28=16'] Exploring Operation: 22-12=10, Resulting Numbers: [16, 10] Generated Node #3: [16, 10] from Operation: 22-12=10 Current State: 26:[16, 10], Operations: ['44-28=16', '22-12=10'] Exploring Operation: 16+10=26, Resulting Numbers: [26] 26,26 equal: Goal Reached
4
Current State: 26:[28, 44, 22, 12], Operations: [] Exploring Operation: 44-22=22, Resulting Numbers: [28, 12, 22] Generated Node #0,0: 26:[28, 12, 22] Operation: 44-22=22 Exploring Operation: 44/22=2, Resulting Numbers: [28, 12, 2] Generated Node #0,1: 26:[28, 12, 2] Operation: 44/22=2 Exploring Operation: 44-28=16, Resulting Numbers: [22, 12, 16] Generated Node #0,2: 26:[22, 12, 16] Operation: 44-28=16 Exploring Operation: 44-12=32, Resulting Numbers: [28, 22, 32] Generated Node #0,3: 26:[28, 22, 32] Operation: 44-12=32 Moving to Node #0,1 Current State: 26:[28, 12, 2], Operations: ['44/22=2'] Exploring Operation: 28-2=26, Resulting Numbers: [12, 26] Generated Node #0,1,0: 26:[12, 26] Operation: 28-2=26 Exploring Operation: 12+2=14, Resulting Numbers: [28, 14] Generated Node #0,1,1: 26:[28, 14] Operation: 12+2=14 Exploring Operation: 28-12=16, Resulting Numbers: [2, 16] Generated Node #0,1,2: 26:[2, 16] Operation: 28-12=16 Exploring Operation: 28/2=14, Resulting Numbers: [12, 14] Generated Node #0,1,3: 26:[12, 14] Operation: 28/2=14 Moving to Node #0,0 Current State: 26:[28, 12, 22], Operations: ['44-22=22'] Exploring Operation: 28-22=6, Resulting Numbers: [12, 6] Generated Node #0,0,0: 26:[12, 6] Operation: 28-22=6 Exploring Operation: 22-12=10, Resulting Numbers: [28, 10] Generated Node #0,0,1: 26:[28, 10] Operation: 22-12=10 Exploring Operation: 28-12=16, Resulting Numbers: [22, 16] Generated Node #0,0,2: 26:[22, 16] Operation: 28-12=16 Exploring Operation: 12+22=34, Resulting Numbers: [28, 34] Generated Node #0,0,3: 26:[28, 34] Operation: 12+22=34 Moving to Node #0,2 Current State: 26:[22, 12, 16], Operations: ['44-28=16'] Exploring Operation: 12+16=28, Resulting Numbers: [22, 28] Generated Node #0,2,0: 26:[22, 28] Operation: 12+16=28 Exploring Operation: 22-12=10, Resulting Numbers: [16, 10] Generated Node #0,2,1: 26:[16, 10] Operation: 22-12=10 Exploring Operation: 22-16=6, Resulting Numbers: [12, 6] Generated Node #0,2,2: 26:[12, 6] Operation: 22-16=6 Exploring Operation: 16-12=4, Resulting Numbers: [22, 4] Generated Node #0,2,3: 26:[22, 4] Operation: 16-12=4 Moving to Node #0,3 Current State: 26:[28, 22, 32], Operations: ['44-12=32'] Exploring Operation: 32-28=4, Resulting Numbers: [22, 4] Generated Node #0,3,0: 26:[22, 4] Operation: 32-28=4 Exploring Operation: 32-22=10, Resulting Numbers: [28, 10] Generated Node #0,3,1: 26:[28, 10] Operation: 32-22=10 Exploring Operation: 28+22=50, Resulting Numbers: [32, 50] Generated Node #0,3,2: 26:[32, 50] Operation: 28+22=50 Exploring Operation: 28-22=6, Resulting Numbers: [32, 6] Generated Node #0,3,3: 26:[32, 6] Operation: 28-22=6 Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 26:[28, 10], Operations: ['44-12=32', '32-22=10'] Exploring Operation: 28-10=18, Resulting Numbers: [18] 18,26 unequal: No Solution Exploring Operation: 28+10=38, Resulting Numbers: [38] 38,26 unequal: No Solution Exploring Operation: 28*10=280, Resulting Numbers: [280] 280,26 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 26:[22, 4], Operations: ['44-12=32', '32-28=4'] Exploring Operation: 22-4=18, Resulting Numbers: [18] 18,26 unequal: No Solution Exploring Operation: 22*4=88, Resulting Numbers: [88] 88,26 unequal: No Solution Exploring Operation: 22+4=26, Resulting Numbers: [26] 26,26 equal: Goal Reached Moving to Node #0 Current State: 26:[28, 44, 22, 12], Operations: [] Exploring Operation: 44-12=32, Resulting Numbers: [28, 22, 32] Generated Node #0,3: 26:[28, 22, 32] Operation: 44-12=32 Moving to Node #0,3 Current State: 26:[28, 22, 32], Operations: ['44-12=32'] Exploring Operation: 32-28=4, Resulting Numbers: [22, 4] Generated Node #0,3,0: 26:[22, 4] Operation: 32-28=4 Moving to Node #0,3,0 Current State: 26:[22, 4], Operations: ['44-12=32', '32-28=4'] Exploring Operation: 22+4=26, Resulting Numbers: [26] 26,26 equal: Goal Reached Exit Sub Search at level 1
0.973958
hs_4
sum_heuristic
[ 51, 63, 88, 80 ]
91
[ "80-63=17", "51/17=3", "88+3=91" ]
Current State: 91:[51, 63, 88, 80], Operations: [] Exploring Operation: 80-63=17, Resulting Numbers: [51, 88, 17] Generated Node #2: [51, 88, 17] from Operation: 80-63=17 Current State: 91:[51, 88, 17], Operations: ['80-63=17'] Exploring Operation: 51/17=3, Resulting Numbers: [88, 3] Generated Node #3: [88, 3] from Operation: 51/17=3 Current State: 91:[88, 3], Operations: ['80-63=17', '51/17=3'] Exploring Operation: 88+3=91, Resulting Numbers: [91] 91,91 equal: Goal Reached
4
Current State: 91:[51, 63, 88, 80], Operations: [] Exploring Operation: 51+63=114, Resulting Numbers: [88, 80, 114] Generated Node #0,0: 91:[88, 80, 114] Operation: 51+63=114 Exploring Operation: 80-63=17, Resulting Numbers: [51, 88, 17] Generated Node #0,1: 91:[51, 88, 17] Operation: 80-63=17 Exploring Operation: 80-51=29, Resulting Numbers: [63, 88, 29] Generated Node #0,2: 91:[63, 88, 29] Operation: 80-51=29 Exploring Operation: 63-51=12, Resulting Numbers: [88, 80, 12] Generated Node #0,3: 91:[88, 80, 12] Operation: 63-51=12 Exploring Operation: 88-63=25, Resulting Numbers: [51, 80, 25] Generated Node #0,4: 91:[51, 80, 25] Operation: 88-63=25 Start Sub Search at level 1: Moving to Node #0,3 Current State: 91:[88, 80, 12], Operations: ['63-51=12'] Exploring Operation: 80-12=68, Resulting Numbers: [88, 68] Generated Node #0,3,0: 91:[88, 68] Operation: 80-12=68 Exploring Operation: 88-12=76, Resulting Numbers: [80, 76] Generated Node #0,3,1: 91:[80, 76] Operation: 88-12=76 Exploring Operation: 88-80=8, Resulting Numbers: [12, 8] Generated Node #0,3,2: 91:[12, 8] Operation: 88-80=8 Exploring Operation: 80+12=92, Resulting Numbers: [88, 92] Generated Node #0,3,3: 91:[88, 92] Operation: 80+12=92 Exploring Operation: 88+12=100, Resulting Numbers: [80, 100] Generated Node #0,3,4: 91:[80, 100] Operation: 88+12=100 Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 91:[12, 8], Operations: ['63-51=12', '88-80=8'] Exploring Operation: 12-8=4, Resulting Numbers: [4] 4,91 unequal: No Solution Exploring Operation: 12+8=20, Resulting Numbers: [20] 20,91 unequal: No Solution Exploring Operation: 12*8=96, Resulting Numbers: [96] 96,91 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 91:[88, 92], Operations: ['63-51=12', '80+12=92'] Exploring Operation: 88*92=8096, Resulting Numbers: [8096] 8096,91 unequal: No Solution Exploring Operation: 88+92=180, Resulting Numbers: [180] 180,91 unequal: No Solution Exploring Operation: 92-88=4, Resulting Numbers: [4] 4,91 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,4 Current State: 91:[80, 100], Operations: ['63-51=12', '88+12=100'] Exploring Operation: 80+100=180, Resulting Numbers: [180] 180,91 unequal: No Solution Exploring Operation: 100-80=20, Resulting Numbers: [20] 20,91 unequal: No Solution Exploring Operation: 80*100=8000, Resulting Numbers: [8000] 8000,91 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 91:[88, 68], Operations: ['63-51=12', '80-12=68'] Exploring Operation: 88*68=5984, Resulting Numbers: [5984] 5984,91 unequal: No Solution Exploring Operation: 88+68=156, Resulting Numbers: [156] 156,91 unequal: No Solution Exploring Operation: 88-68=20, Resulting Numbers: [20] 20,91 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 91:[80, 76], Operations: ['63-51=12', '88-12=76'] Exploring Operation: 80-76=4, Resulting Numbers: [4] 4,91 unequal: No Solution Exploring Operation: 80*76=6080, Resulting Numbers: [6080] 6080,91 unequal: No Solution Exploring Operation: 80+76=156, Resulting Numbers: [156] 156,91 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 91:[88, 80, 114], Operations: ['51+63=114'] Exploring Operation: 114-88=26, Resulting Numbers: [80, 26] Generated Node #0,0,0: 91:[80, 26] Operation: 114-88=26 Exploring Operation: 114-80=34, Resulting Numbers: [88, 34] Generated Node #0,0,1: 91:[88, 34] Operation: 114-80=34 Exploring Operation: 88+80=168, Resulting Numbers: [114, 168] Generated Node #0,0,2: 91:[114, 168] Operation: 88+80=168 Exploring Operation: 80+114=194, Resulting Numbers: [88, 194] Generated Node #0,0,3: 91:[88, 194] Operation: 80+114=194 Exploring Operation: 88-80=8, Resulting Numbers: [114, 8] Generated Node #0,0,4: 91:[114, 8] Operation: 88-80=8 Moving to Node #0,0,0 Current State: 91:[80, 26], Operations: ['51+63=114', '114-88=26'] Exploring Operation: 80-26=54, Resulting Numbers: [54] 54,91 unequal: No Solution Exploring Operation: 80*26=2080, Resulting Numbers: [2080] 2080,91 unequal: No Solution Exploring Operation: 80+26=106, Resulting Numbers: [106] 106,91 unequal: No Solution Moving to Node #0,0,4 Current State: 91:[114, 8], Operations: ['51+63=114', '88-80=8'] Exploring Operation: 114-8=106, Resulting Numbers: [106] 106,91 unequal: No Solution Exploring Operation: 114*8=912, Resulting Numbers: [912] 912,91 unequal: No Solution Exploring Operation: 114+8=122, Resulting Numbers: [122] 122,91 unequal: No Solution Moving to Node #0,0,1 Current State: 91:[88, 34], Operations: ['51+63=114', '114-80=34'] Exploring Operation: 88-34=54, Resulting Numbers: [54] 54,91 unequal: No Solution Exploring Operation: 88+34=122, Resulting Numbers: [122] 122,91 unequal: No Solution Exploring Operation: 88*34=2992, Resulting Numbers: [2992] 2992,91 unequal: No Solution Moving to Node #0,0,2 Current State: 91:[114, 168], Operations: ['51+63=114', '88+80=168'] Exploring Operation: 114+168=282, Resulting Numbers: [282] 282,91 unequal: No Solution Exploring Operation: 168-114=54, Resulting Numbers: [54] 54,91 unequal: No Solution Exploring Operation: 114*168=19152, Resulting Numbers: [19152] 19152,91 unequal: No Solution Moving to Node #0,0,3 Current State: 91:[88, 194], Operations: ['51+63=114', '80+114=194'] Exploring Operation: 88*194=17072, Resulting Numbers: [17072] 17072,91 unequal: No Solution Exploring Operation: 88+194=282, Resulting Numbers: [282] 282,91 unequal: No Solution Exploring Operation: 194-88=106, Resulting Numbers: [106] 106,91 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 91:[51, 88, 17], Operations: ['80-63=17'] Exploring Operation: 51/17=3, Resulting Numbers: [88, 3] Generated Node #0,1,0: 91:[88, 3] Operation: 51/17=3 Exploring Operation: 51-17=34, Resulting Numbers: [88, 34] Generated Node #0,1,1: 91:[88, 34] Operation: 51-17=34 Exploring Operation: 88-51=37, Resulting Numbers: [17, 37] Generated Node #0,1,2: 91:[17, 37] Operation: 88-51=37 Exploring Operation: 51+88=139, Resulting Numbers: [17, 139] Generated Node #0,1,3: 91:[17, 139] Operation: 51+88=139 Exploring Operation: 51+17=68, Resulting Numbers: [88, 68] Generated Node #0,1,4: 91:[88, 68] Operation: 51+17=68 Moving to Node #0,1,0 Current State: 91:[88, 3], Operations: ['80-63=17', '51/17=3'] Exploring Operation: 88*3=264, Resulting Numbers: [264] 264,91 unequal: No Solution Exploring Operation: 88+3=91, Resulting Numbers: [91] 91,91 equal: Goal Reached Moving to Node #0 Current State: 91:[51, 63, 88, 80], Operations: [] Exploring Operation: 80-63=17, Resulting Numbers: [51, 88, 17] Generated Node #0,1: 91:[51, 88, 17] Operation: 80-63=17 Moving to Node #0,1 Current State: 91:[51, 88, 17], Operations: ['80-63=17'] Exploring Operation: 51/17=3, Resulting Numbers: [88, 3] Generated Node #0,1,0: 91:[88, 3] Operation: 51/17=3 Moving to Node #0,1,0 Current State: 91:[88, 3], Operations: ['80-63=17', '51/17=3'] Exploring Operation: 88+3=91, Resulting Numbers: [91] 91,91 equal: Goal Reached Exit Sub Search at level 1
0.951389
hs_5
mult_heuristic
[ 32, 64, 28, 59 ]
89
[ "64/32=2", "28+59=87", "2+87=89" ]
Current State: 89:[32, 64, 28, 59], Operations: [] Exploring Operation: 64/32=2, Resulting Numbers: [28, 59, 2] Generated Node #2: [28, 59, 2] from Operation: 64/32=2 Current State: 89:[28, 59, 2], Operations: ['64/32=2'] Exploring Operation: 28+59=87, Resulting Numbers: [2, 87] Generated Node #3: [2, 87] from Operation: 28+59=87 Current State: 89:[2, 87], Operations: ['64/32=2', '28+59=87'] Exploring Operation: 2+87=89, Resulting Numbers: [89] 89,89 equal: Goal Reached
4
Current State: 89:[32, 64, 28, 59], Operations: [] Exploring Operation: 28+59=87, Resulting Numbers: [32, 64, 87] Generated Node #0,0: 89:[32, 64, 87] Operation: 28+59=87 Exploring Operation: 32+28=60, Resulting Numbers: [64, 59, 60] Generated Node #0,1: 89:[64, 59, 60] Operation: 32+28=60 Moving to Node #0,0 Current State: 89:[32, 64, 87], Operations: ['28+59=87'] Exploring Operation: 32+64=96, Resulting Numbers: [87, 96] Generated Node #0,0,0: 89:[87, 96] Operation: 32+64=96 Exploring Operation: 32+87=119, Resulting Numbers: [64, 119] Generated Node #0,0,1: 89:[64, 119] Operation: 32+87=119 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 89:[87, 96], Operations: ['28+59=87', '32+64=96'] Exploring Operation: 87+96=183, Resulting Numbers: [183] 183,89 unequal: No Solution Exploring Operation: 96-87=9, Resulting Numbers: [9] 9,89 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 89:[64, 119], Operations: ['28+59=87', '32+87=119'] Exploring Operation: 64+119=183, Resulting Numbers: [183] 183,89 unequal: No Solution Exploring Operation: 119-64=55, Resulting Numbers: [55] 55,89 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 89:[64, 59, 60], Operations: ['32+28=60'] Exploring Operation: 59+60=119, Resulting Numbers: [64, 119] Generated Node #0,1,0: 89:[64, 119] Operation: 59+60=119 Exploring Operation: 64+59=123, Resulting Numbers: [60, 123] Generated Node #0,1,1: 89:[60, 123] Operation: 64+59=123 Moving to Node #0,1,0 Current State: 89:[64, 119], Operations: ['32+28=60', '59+60=119'] Exploring Operation: 64+119=183, Resulting Numbers: [183] 183,89 unequal: No Solution Exploring Operation: 119-64=55, Resulting Numbers: [55] 55,89 unequal: No Solution Moving to Node #0,1,1 Current State: 89:[60, 123], Operations: ['32+28=60', '64+59=123'] Exploring Operation: 123-60=63, Resulting Numbers: [63] 63,89 unequal: No Solution Exploring Operation: 60+123=183, Resulting Numbers: [183] 183,89 unequal: No Solution No solution found.
0
hs_2
mult_heuristic
[ 30, 68, 75, 12 ]
35
[ "30+68=98", "75-12=63", "98-63=35" ]
Current State: 35:[30, 68, 75, 12], Operations: [] Exploring Operation: 30+68=98, Resulting Numbers: [75, 12, 98] Generated Node #2: [75, 12, 98] from Operation: 30+68=98 Current State: 35:[75, 12, 98], Operations: ['30+68=98'] Exploring Operation: 75-12=63, Resulting Numbers: [98, 63] Generated Node #3: [98, 63] from Operation: 75-12=63 Current State: 35:[98, 63], Operations: ['30+68=98', '75-12=63'] Exploring Operation: 98-63=35, Resulting Numbers: [35] 35,35 equal: Goal Reached
4
Current State: 35:[30, 68, 75, 12], Operations: [] Exploring Operation: 75-12=63, Resulting Numbers: [30, 68, 63] Generated Node #0,0: 35:[30, 68, 63] Operation: 75-12=63 Exploring Operation: 68-30=38, Resulting Numbers: [75, 12, 38] Generated Node #0,1: 35:[75, 12, 38] Operation: 68-30=38 Exploring Operation: 75-30=45, Resulting Numbers: [68, 12, 45] Generated Node #0,2: 35:[68, 12, 45] Operation: 75-30=45 Exploring Operation: 75-68=7, Resulting Numbers: [30, 12, 7] Generated Node #0,3: 35:[30, 12, 7] Operation: 75-68=7 Exploring Operation: 68-12=56, Resulting Numbers: [30, 75, 56] Generated Node #0,4: 35:[30, 75, 56] Operation: 68-12=56 Start Sub Search at level 1: Moving to Node #0,3 Current State: 35:[30, 12, 7], Operations: ['75-68=7'] Exploring Operation: 12-7=5, Resulting Numbers: [30, 5] Generated Node #0,3,0: 35:[30, 5] Operation: 12-7=5 Exploring Operation: 30-12=18, Resulting Numbers: [7, 18] Generated Node #0,3,1: 35:[7, 18] Operation: 30-12=18 Exploring Operation: 30+7=37, Resulting Numbers: [12, 37] Generated Node #0,3,2: 35:[12, 37] Operation: 30+7=37 Exploring Operation: 30-7=23, Resulting Numbers: [12, 23] Generated Node #0,3,3: 35:[12, 23] Operation: 30-7=23 Exploring Operation: 30+12=42, Resulting Numbers: [7, 42] Generated Node #0,3,4: 35:[7, 42] Operation: 30+12=42 Moving to Node #0,3,0 Current State: 35:[30, 5], Operations: ['75-68=7', '12-7=5'] Exploring Operation: 30/5=6, Resulting Numbers: [6] 6,35 unequal: No Solution Exploring Operation: 30-5=25, Resulting Numbers: [25] 25,35 unequal: No Solution Exploring Operation: 30*5=150, Resulting Numbers: [150] 150,35 unequal: No Solution Exploring Operation: 30+5=35, Resulting Numbers: [35] 35,35 equal: Goal Reached Moving to Node #0 Current State: 35:[30, 68, 75, 12], Operations: [] Exploring Operation: 75-68=7, Resulting Numbers: [30, 12, 7] Generated Node #0,3: 35:[30, 12, 7] Operation: 75-68=7 Moving to Node #0,3 Current State: 35:[30, 12, 7], Operations: ['75-68=7'] Exploring Operation: 12-7=5, Resulting Numbers: [30, 5] Generated Node #0,3,0: 35:[30, 5] Operation: 12-7=5 Moving to Node #0,3,0 Current State: 35:[30, 5], Operations: ['75-68=7', '12-7=5'] Exploring Operation: 30+5=35, Resulting Numbers: [35] 35,35 equal: Goal Reached Exit Sub Search at level 1
0.984375
hs_5
sum_heuristic
[ 71, 7, 20, 4 ]
94
[ "71+7=78", "20-4=16", "78+16=94" ]
Current State: 94:[71, 7, 20, 4], Operations: [] Exploring Operation: 71+7=78, Resulting Numbers: [20, 4, 78] Generated Node #2: [20, 4, 78] from Operation: 71+7=78 Current State: 94:[20, 4, 78], Operations: ['71+7=78'] Exploring Operation: 20-4=16, Resulting Numbers: [78, 16] Generated Node #3: [78, 16] from Operation: 20-4=16 Current State: 94:[78, 16], Operations: ['71+7=78', '20-4=16'] Exploring Operation: 78+16=94, Resulting Numbers: [94] 94,94 equal: Goal Reached
4
Current State: 94:[71, 7, 20, 4], Operations: [] Exploring Operation: 71+7=78, Resulting Numbers: [20, 4, 78] Generated Node #0,0: 94:[20, 4, 78] Operation: 71+7=78 Exploring Operation: 71-20=51, Resulting Numbers: [7, 4, 51] Generated Node #0,1: 94:[7, 4, 51] Operation: 71-20=51 Exploring Operation: 71+20=91, Resulting Numbers: [7, 4, 91] Generated Node #0,2: 94:[7, 4, 91] Operation: 71+20=91 Exploring Operation: 20/4=5, Resulting Numbers: [71, 7, 5] Generated Node #0,3: 94:[71, 7, 5] Operation: 20/4=5 Start Sub Search at level 1: Moving to Node #0,2 Current State: 94:[7, 4, 91], Operations: ['71+20=91'] Exploring Operation: 7-4=3, Resulting Numbers: [91, 3] Generated Node #0,2,0: 94:[91, 3] Operation: 7-4=3 Exploring Operation: 7+4=11, Resulting Numbers: [91, 11] Generated Node #0,2,1: 94:[91, 11] Operation: 7+4=11 Exploring Operation: 7+91=98, Resulting Numbers: [4, 98] Generated Node #0,2,2: 94:[4, 98] Operation: 7+91=98 Exploring Operation: 4+91=95, Resulting Numbers: [7, 95] Generated Node #0,2,3: 94:[7, 95] Operation: 4+91=95 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 94:[91, 3], Operations: ['71+20=91', '7-4=3'] Exploring Operation: 91-3=88, Resulting Numbers: [88] 88,94 unequal: No Solution Exploring Operation: 91+3=94, Resulting Numbers: [94] 94,94 equal: Goal Reached Moving to Node #0 Current State: 94:[71, 7, 20, 4], Operations: [] Exploring Operation: 71+20=91, Resulting Numbers: [7, 4, 91] Generated Node #0,2: 94:[7, 4, 91] Operation: 71+20=91 Moving to Node #0,2 Current State: 94:[7, 4, 91], Operations: ['71+20=91'] Exploring Operation: 7-4=3, Resulting Numbers: [91, 3] Generated Node #0,2,0: 94:[91, 3] Operation: 7-4=3 Moving to Node #0,2,0 Current State: 94:[91, 3], Operations: ['71+20=91', '7-4=3'] Exploring Operation: 91+3=94, Resulting Numbers: [94] 94,94 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.987847
hs_4
sum_heuristic
[ 48, 61, 52, 87 ]
83
[ "61-48=13", "52/13=4", "87-4=83" ]
Current State: 83:[48, 61, 52, 87], Operations: [] Exploring Operation: 61-48=13, Resulting Numbers: [52, 87, 13] Generated Node #2: [52, 87, 13] from Operation: 61-48=13 Current State: 83:[52, 87, 13], Operations: ['61-48=13'] Exploring Operation: 52/13=4, Resulting Numbers: [87, 4] Generated Node #3: [87, 4] from Operation: 52/13=4 Current State: 83:[87, 4], Operations: ['61-48=13', '52/13=4'] Exploring Operation: 87-4=83, Resulting Numbers: [83] 83,83 equal: Goal Reached
4
Current State: 83:[48, 61, 52, 87], Operations: [] Exploring Operation: 48+61=109, Resulting Numbers: [52, 87, 109] Generated Node #0,0: 83:[52, 87, 109] Operation: 48+61=109 Exploring Operation: 61+52=113, Resulting Numbers: [48, 87, 113] Generated Node #0,1: 83:[48, 87, 113] Operation: 61+52=113 Exploring Operation: 48+52=100, Resulting Numbers: [61, 87, 100] Generated Node #0,2: 83:[61, 87, 100] Operation: 48+52=100 Moving to Node #0,2 Current State: 83:[61, 87, 100], Operations: ['48+52=100'] Exploring Operation: 61+87=148, Resulting Numbers: [100, 148] Generated Node #0,2,0: 83:[100, 148] Operation: 61+87=148 Exploring Operation: 100-61=39, Resulting Numbers: [87, 39] Generated Node #0,2,1: 83:[87, 39] Operation: 100-61=39 Exploring Operation: 87-61=26, Resulting Numbers: [100, 26] Generated Node #0,2,2: 83:[100, 26] Operation: 87-61=26 Moving to Node #0,0 Current State: 83:[52, 87, 109], Operations: ['48+61=109'] Exploring Operation: 52+87=139, Resulting Numbers: [109, 139] Generated Node #0,0,0: 83:[109, 139] Operation: 52+87=139 Exploring Operation: 109-52=57, Resulting Numbers: [87, 57] Generated Node #0,0,1: 83:[87, 57] Operation: 109-52=57 Exploring Operation: 87-52=35, Resulting Numbers: [109, 35] Generated Node #0,0,2: 83:[109, 35] Operation: 87-52=35 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 83:[87, 57], Operations: ['48+61=109', '109-52=57'] Exploring Operation: 87*57=4959, Resulting Numbers: [4959] 4959,83 unequal: No Solution Exploring Operation: 87-57=30, Resulting Numbers: [30] 30,83 unequal: No Solution Exploring Operation: 87+57=144, Resulting Numbers: [144] 144,83 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 83:[109, 35], Operations: ['48+61=109', '87-52=35'] Exploring Operation: 109+35=144, Resulting Numbers: [144] 144,83 unequal: No Solution Exploring Operation: 109-35=74, Resulting Numbers: [74] 74,83 unequal: No Solution Exploring Operation: 109*35=3815, Resulting Numbers: [3815] 3815,83 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 83:[109, 139], Operations: ['48+61=109', '52+87=139'] Exploring Operation: 139-109=30, Resulting Numbers: [30] 30,83 unequal: No Solution Exploring Operation: 109+139=248, Resulting Numbers: [248] 248,83 unequal: No Solution Exploring Operation: 109*139=15151, Resulting Numbers: [15151] 15151,83 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 83:[48, 87, 113], Operations: ['61+52=113'] Exploring Operation: 87-48=39, Resulting Numbers: [113, 39] Generated Node #0,1,0: 83:[113, 39] Operation: 87-48=39 Exploring Operation: 48+87=135, Resulting Numbers: [113, 135] Generated Node #0,1,1: 83:[113, 135] Operation: 48+87=135 Exploring Operation: 113-48=65, Resulting Numbers: [87, 65] Generated Node #0,1,2: 83:[87, 65] Operation: 113-48=65 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 83:[87, 65], Operations: ['61+52=113', '113-48=65'] Exploring Operation: 87*65=5655, Resulting Numbers: [5655] 5655,83 unequal: No Solution Exploring Operation: 87-65=22, Resulting Numbers: [22] 22,83 unequal: No Solution Exploring Operation: 87+65=152, Resulting Numbers: [152] 152,83 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 83:[113, 39], Operations: ['61+52=113', '87-48=39'] Exploring Operation: 113-39=74, Resulting Numbers: [74] 74,83 unequal: No Solution Exploring Operation: 113*39=4407, Resulting Numbers: [4407] 4407,83 unequal: No Solution Exploring Operation: 113+39=152, Resulting Numbers: [152] 152,83 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 83:[113, 135], Operations: ['61+52=113', '48+87=135'] Exploring Operation: 113*135=15255, Resulting Numbers: [15255] 15255,83 unequal: No Solution Exploring Operation: 113+135=248, Resulting Numbers: [248] 248,83 unequal: No Solution Exploring Operation: 135-113=22, Resulting Numbers: [22] 22,83 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2,1 Current State: 83:[87, 39], Operations: ['48+52=100', '100-61=39'] Exploring Operation: 87*39=3393, Resulting Numbers: [3393] 3393,83 unequal: No Solution Exploring Operation: 87-39=48, Resulting Numbers: [48] 48,83 unequal: No Solution Exploring Operation: 87+39=126, Resulting Numbers: [126] 126,83 unequal: No Solution Moving to Node #0,2,2 Current State: 83:[100, 26], Operations: ['48+52=100', '87-61=26'] Exploring Operation: 100+26=126, Resulting Numbers: [126] 126,83 unequal: No Solution Exploring Operation: 100-26=74, Resulting Numbers: [74] 74,83 unequal: No Solution Exploring Operation: 100*26=2600, Resulting Numbers: [2600] 2600,83 unequal: No Solution Moving to Node #0,2,0 Current State: 83:[100, 148], Operations: ['48+52=100', '61+87=148'] Exploring Operation: 148-100=48, Resulting Numbers: [48] 48,83 unequal: No Solution Exploring Operation: 100*148=14800, Resulting Numbers: [14800] 14800,83 unequal: No Solution Exploring Operation: 100+148=248, Resulting Numbers: [248] 248,83 unequal: No Solution No solution found.
0
hs_3
mult_heuristic
[ 54, 78, 87, 36 ]
35
[ "78*36=2808", "2808/54=52", "87-52=35" ]
Current State: 35:[54, 78, 87, 36], Operations: [] Exploring Operation: 78*36=2808, Resulting Numbers: [54, 87, 2808] Generated Node #2: [54, 87, 2808] from Operation: 78*36=2808 Current State: 35:[54, 87, 2808], Operations: ['78*36=2808'] Exploring Operation: 2808/54=52, Resulting Numbers: [87, 52] Generated Node #3: [87, 52] from Operation: 2808/54=52 Current State: 35:[87, 52], Operations: ['78*36=2808', '2808/54=52'] Exploring Operation: 87-52=35, Resulting Numbers: [35] 35,35 equal: Goal Reached
4
Current State: 35:[54, 78, 87, 36], Operations: [] Exploring Operation: 78-54=24, Resulting Numbers: [87, 36, 24] Generated Node #0,0: 35:[87, 36, 24] Operation: 78-54=24 Exploring Operation: 87-78=9, Resulting Numbers: [54, 36, 9] Generated Node #0,1: 35:[54, 36, 9] Operation: 87-78=9 Exploring Operation: 87-54=33, Resulting Numbers: [78, 36, 33] Generated Node #0,2: 35:[78, 36, 33] Operation: 87-54=33 Moving to Node #0,1 Current State: 35:[54, 36, 9], Operations: ['87-78=9'] Exploring Operation: 54-9=45, Resulting Numbers: [36, 45] Generated Node #0,1,0: 35:[36, 45] Operation: 54-9=45 Exploring Operation: 54-36=18, Resulting Numbers: [9, 18] Generated Node #0,1,1: 35:[9, 18] Operation: 54-36=18 Exploring Operation: 54/9=6, Resulting Numbers: [36, 6] Generated Node #0,1,2: 35:[36, 6] Operation: 54/9=6 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 35:[36, 6], Operations: ['87-78=9', '54/9=6'] Exploring Operation: 36+6=42, Resulting Numbers: [42] 42,35 unequal: No Solution Exploring Operation: 36-6=30, Resulting Numbers: [30] 30,35 unequal: No Solution Exploring Operation: 36/6=6, Resulting Numbers: [6] 6,35 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 35:[36, 45], Operations: ['87-78=9', '54-9=45'] Exploring Operation: 45-36=9, Resulting Numbers: [9] 9,35 unequal: No Solution Exploring Operation: 36+45=81, Resulting Numbers: [81] 81,35 unequal: No Solution Exploring Operation: 36*45=1620, Resulting Numbers: [1620] 1620,35 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 35:[9, 18], Operations: ['87-78=9', '54-36=18'] Exploring Operation: 18/9=2, Resulting Numbers: [2] 2,35 unequal: No Solution Exploring Operation: 9+18=27, Resulting Numbers: [27] 27,35 unequal: No Solution Exploring Operation: 18-9=9, Resulting Numbers: [9] 9,35 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2 Current State: 35:[78, 36, 33], Operations: ['87-54=33'] Exploring Operation: 78-33=45, Resulting Numbers: [36, 45] Generated Node #0,2,0: 35:[36, 45] Operation: 78-33=45 Exploring Operation: 36-33=3, Resulting Numbers: [78, 3] Generated Node #0,2,1: 35:[78, 3] Operation: 36-33=3 Exploring Operation: 78-36=42, Resulting Numbers: [33, 42] Generated Node #0,2,2: 35:[33, 42] Operation: 78-36=42 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 35:[33, 42], Operations: ['87-54=33', '78-36=42'] Exploring Operation: 42-33=9, Resulting Numbers: [9] 9,35 unequal: No Solution Exploring Operation: 33+42=75, Resulting Numbers: [75] 75,35 unequal: No Solution Exploring Operation: 33*42=1386, Resulting Numbers: [1386] 1386,35 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 35:[36, 45], Operations: ['87-54=33', '78-33=45'] Exploring Operation: 45-36=9, Resulting Numbers: [9] 9,35 unequal: No Solution Exploring Operation: 36+45=81, Resulting Numbers: [81] 81,35 unequal: No Solution Exploring Operation: 36*45=1620, Resulting Numbers: [1620] 1620,35 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 35:[78, 3], Operations: ['87-54=33', '36-33=3'] Exploring Operation: 78+3=81, Resulting Numbers: [81] 81,35 unequal: No Solution Exploring Operation: 78/3=26, Resulting Numbers: [26] 26,35 unequal: No Solution Exploring Operation: 78-3=75, Resulting Numbers: [75] 75,35 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0 Current State: 35:[87, 36, 24], Operations: ['78-54=24'] Exploring Operation: 36-24=12, Resulting Numbers: [87, 12] Generated Node #0,0,0: 35:[87, 12] Operation: 36-24=12 Exploring Operation: 87-36=51, Resulting Numbers: [24, 51] Generated Node #0,0,1: 35:[24, 51] Operation: 87-36=51 Exploring Operation: 87-24=63, Resulting Numbers: [36, 63] Generated Node #0,0,2: 35:[36, 63] Operation: 87-24=63 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 35:[24, 51], Operations: ['78-54=24', '87-36=51'] Exploring Operation: 24*51=1224, Resulting Numbers: [1224] 1224,35 unequal: No Solution Exploring Operation: 24+51=75, Resulting Numbers: [75] 75,35 unequal: No Solution Exploring Operation: 51-24=27, Resulting Numbers: [27] 27,35 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 35:[36, 63], Operations: ['78-54=24', '87-24=63'] Exploring Operation: 36*63=2268, Resulting Numbers: [2268] 2268,35 unequal: No Solution Exploring Operation: 63-36=27, Resulting Numbers: [27] 27,35 unequal: No Solution Exploring Operation: 36+63=99, Resulting Numbers: [99] 99,35 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 35:[87, 12], Operations: ['78-54=24', '36-24=12'] Exploring Operation: 87+12=99, Resulting Numbers: [99] 99,35 unequal: No Solution Exploring Operation: 87*12=1044, Resulting Numbers: [1044] 1044,35 unequal: No Solution Exploring Operation: 87-12=75, Resulting Numbers: [75] 75,35 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_3
mult_heuristic
[ 93, 23, 16, 56 ]
20
[ "93-23=70", "16*70=1120", "1120/56=20" ]
Current State: 20:[93, 23, 16, 56], Operations: [] Exploring Operation: 93-23=70, Resulting Numbers: [16, 56, 70] Generated Node #2: [16, 56, 70] from Operation: 93-23=70 Current State: 20:[16, 56, 70], Operations: ['93-23=70'] Exploring Operation: 16*70=1120, Resulting Numbers: [56, 1120] Generated Node #3: [56, 1120] from Operation: 16*70=1120 Current State: 20:[56, 1120], Operations: ['93-23=70', '16*70=1120'] Exploring Operation: 1120/56=20, Resulting Numbers: [20] 20,20 equal: Goal Reached
4
Current State: 20:[93, 23, 16, 56], Operations: [] Exploring Operation: 93-23=70, Resulting Numbers: [16, 56, 70] Generated Node #0,0: 20:[16, 56, 70] Operation: 93-23=70 Exploring Operation: 93-56=37, Resulting Numbers: [23, 16, 37] Generated Node #0,1: 20:[23, 16, 37] Operation: 93-56=37 Moving to Node #0,1 Current State: 20:[23, 16, 37], Operations: ['93-56=37'] Exploring Operation: 37-16=21, Resulting Numbers: [23, 21] Generated Node #0,1,0: 20:[23, 21] Operation: 37-16=21 Exploring Operation: 37-23=14, Resulting Numbers: [16, 14] Generated Node #0,1,1: 20:[16, 14] Operation: 37-23=14 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 20:[23, 21], Operations: ['93-56=37', '37-16=21'] Exploring Operation: 23+21=44, Resulting Numbers: [44] 44,20 unequal: No Solution Exploring Operation: 23-21=2, Resulting Numbers: [2] 2,20 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 20:[16, 14], Operations: ['93-56=37', '37-23=14'] Exploring Operation: 16+14=30, Resulting Numbers: [30] 30,20 unequal: No Solution Exploring Operation: 16-14=2, Resulting Numbers: [2] 2,20 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0 Current State: 20:[16, 56, 70], Operations: ['93-23=70'] Exploring Operation: 70-56=14, Resulting Numbers: [16, 14] Generated Node #0,0,0: 20:[16, 14] Operation: 70-56=14 Exploring Operation: 56-16=40, Resulting Numbers: [70, 40] Generated Node #0,0,1: 20:[70, 40] Operation: 56-16=40 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 20:[16, 14], Operations: ['93-23=70', '70-56=14'] Exploring Operation: 16+14=30, Resulting Numbers: [30] 30,20 unequal: No Solution Exploring Operation: 16-14=2, Resulting Numbers: [2] 2,20 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 20:[70, 40], Operations: ['93-23=70', '56-16=40'] Exploring Operation: 70+40=110, Resulting Numbers: [110] 110,20 unequal: No Solution Exploring Operation: 70-40=30, Resulting Numbers: [30] 30,20 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
sum_heuristic
[ 77, 71, 97, 10 ]
93
[ "77-71=6", "97-10=87", "6+87=93" ]
Current State: 93:[77, 71, 97, 10], Operations: [] Exploring Operation: 77-71=6, Resulting Numbers: [97, 10, 6] Generated Node #2: [97, 10, 6] from Operation: 77-71=6 Current State: 93:[97, 10, 6], Operations: ['77-71=6'] Exploring Operation: 97-10=87, Resulting Numbers: [6, 87] Generated Node #3: [6, 87] from Operation: 97-10=87 Current State: 93:[6, 87], Operations: ['77-71=6', '97-10=87'] Exploring Operation: 6+87=93, Resulting Numbers: [93] 93,93 equal: Goal Reached
4
Current State: 93:[77, 71, 97, 10], Operations: [] Exploring Operation: 77-71=6, Resulting Numbers: [97, 10, 6] Generated Node #0,0: 93:[97, 10, 6] Operation: 77-71=6 Exploring Operation: 97-71=26, Resulting Numbers: [77, 10, 26] Generated Node #0,1: 93:[77, 10, 26] Operation: 97-71=26 Moving to Node #0,0 Current State: 93:[97, 10, 6], Operations: ['77-71=6'] Exploring Operation: 10-6=4, Resulting Numbers: [97, 4] Generated Node #0,0,0: 93:[97, 4] Operation: 10-6=4 Exploring Operation: 97-10=87, Resulting Numbers: [6, 87] Generated Node #0,0,1: 93:[6, 87] Operation: 97-10=87 Moving to Node #0,1 Current State: 93:[77, 10, 26], Operations: ['97-71=26'] Exploring Operation: 77+26=103, Resulting Numbers: [10, 103] Generated Node #0,1,0: 93:[10, 103] Operation: 77+26=103 Exploring Operation: 77+10=87, Resulting Numbers: [26, 87] Generated Node #0,1,1: 93:[26, 87] Operation: 77+10=87 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 93:[26, 87], Operations: ['97-71=26', '77+10=87'] Exploring Operation: 26+87=113, Resulting Numbers: [113] 113,93 unequal: No Solution Exploring Operation: 87-26=61, Resulting Numbers: [61] 61,93 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 93:[10, 103], Operations: ['97-71=26', '77+26=103'] Exploring Operation: 103-10=93, Resulting Numbers: [93] 93,93 equal: Goal Reached Moving to Node #0 Current State: 93:[77, 71, 97, 10], Operations: [] Exploring Operation: 97-71=26, Resulting Numbers: [77, 10, 26] Generated Node #0,1: 93:[77, 10, 26] Operation: 97-71=26 Moving to Node #0,1 Current State: 93:[77, 10, 26], Operations: ['97-71=26'] Exploring Operation: 77+26=103, Resulting Numbers: [10, 103] Generated Node #0,1,0: 93:[10, 103] Operation: 77+26=103 Moving to Node #0,1,0 Current State: 93:[10, 103], Operations: ['97-71=26', '77+26=103'] Exploring Operation: 103-10=93, Resulting Numbers: [93] 93,93 equal: Goal Reached Exit Sub Search at level 1
0.988715
hs_2
sum_heuristic
[ 28, 2, 42, 11 ]
78
[ "42+11=53", "2*53=106", "106-28=78" ]
Current State: 78:[28, 2, 42, 11], Operations: [] Exploring Operation: 42+11=53, Resulting Numbers: [28, 2, 53] Generated Node #2: [28, 2, 53] from Operation: 42+11=53 Current State: 78:[28, 2, 53], Operations: ['42+11=53'] Exploring Operation: 2*53=106, Resulting Numbers: [28, 106] Generated Node #3: [28, 106] from Operation: 2*53=106 Current State: 78:[28, 106], Operations: ['42+11=53', '2*53=106'] Exploring Operation: 106-28=78, Resulting Numbers: [78] 78,78 equal: Goal Reached
4
Current State: 78:[28, 2, 42, 11], Operations: [] Exploring Operation: 42-2=40, Resulting Numbers: [28, 11, 40] Generated Node #0,0: 78:[28, 11, 40] Operation: 42-2=40 Exploring Operation: 28-2=26, Resulting Numbers: [42, 11, 26] Generated Node #0,1: 78:[42, 11, 26] Operation: 28-2=26 Exploring Operation: 42-28=14, Resulting Numbers: [2, 11, 14] Generated Node #0,2: 78:[2, 11, 14] Operation: 42-28=14 Exploring Operation: 28+11=39, Resulting Numbers: [2, 42, 39] Generated Node #0,3: 78:[2, 42, 39] Operation: 28+11=39 Start Sub Search at level 1: Moving to Node #0,2 Current State: 78:[2, 11, 14], Operations: ['42-28=14'] Exploring Operation: 14-11=3, Resulting Numbers: [2, 3] Generated Node #0,2,0: 78:[2, 3] Operation: 14-11=3 Exploring Operation: 2+11=13, Resulting Numbers: [14, 13] Generated Node #0,2,1: 78:[14, 13] Operation: 2+11=13 Exploring Operation: 11+14=25, Resulting Numbers: [2, 25] Generated Node #0,2,2: 78:[2, 25] Operation: 11+14=25 Exploring Operation: 14-2=12, Resulting Numbers: [11, 12] Generated Node #0,2,3: 78:[11, 12] Operation: 14-2=12 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 78:[2, 3], Operations: ['42-28=14', '14-11=3'] Exploring Operation: 3-2=1, Resulting Numbers: [1] 1,78 unequal: No Solution Exploring Operation: 2+3=5, Resulting Numbers: [5] 5,78 unequal: No Solution Exploring Operation: 2*3=6, Resulting Numbers: [6] 6,78 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 78:[14, 13], Operations: ['42-28=14', '2+11=13'] Exploring Operation: 14*13=182, Resulting Numbers: [182] 182,78 unequal: No Solution Exploring Operation: 14-13=1, Resulting Numbers: [1] 1,78 unequal: No Solution Exploring Operation: 14+13=27, Resulting Numbers: [27] 27,78 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 78:[2, 25], Operations: ['42-28=14', '11+14=25'] Exploring Operation: 2*25=50, Resulting Numbers: [50] 50,78 unequal: No Solution Exploring Operation: 25-2=23, Resulting Numbers: [23] 23,78 unequal: No Solution Exploring Operation: 2+25=27, Resulting Numbers: [27] 27,78 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 78:[11, 12], Operations: ['42-28=14', '14-2=12'] Exploring Operation: 11*12=132, Resulting Numbers: [132] 132,78 unequal: No Solution Exploring Operation: 11+12=23, Resulting Numbers: [23] 23,78 unequal: No Solution Exploring Operation: 12-11=1, Resulting Numbers: [1] 1,78 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 78:[2, 42, 39], Operations: ['28+11=39'] Exploring Operation: 42-39=3, Resulting Numbers: [2, 3] Generated Node #0,3,0: 78:[2, 3] Operation: 42-39=3 Exploring Operation: 42+39=81, Resulting Numbers: [2, 81] Generated Node #0,3,1: 78:[2, 81] Operation: 42+39=81 Exploring Operation: 42-2=40, Resulting Numbers: [39, 40] Generated Node #0,3,2: 78:[39, 40] Operation: 42-2=40 Exploring Operation: 2*39=78, Resulting Numbers: [42, 78] Generated Node #0,3,3: 78:[42, 78] Operation: 2*39=78 Moving to Node #0,3,0 Current State: 78:[2, 3], Operations: ['28+11=39', '42-39=3'] Exploring Operation: 3-2=1, Resulting Numbers: [1] 1,78 unequal: No Solution Exploring Operation: 2*3=6, Resulting Numbers: [6] 6,78 unequal: No Solution Exploring Operation: 2+3=5, Resulting Numbers: [5] 5,78 unequal: No Solution Moving to Node #0,3,2 Current State: 78:[39, 40], Operations: ['28+11=39', '42-2=40'] Exploring Operation: 40-39=1, Resulting Numbers: [1] 1,78 unequal: No Solution Exploring Operation: 39+40=79, Resulting Numbers: [79] 79,78 unequal: No Solution Exploring Operation: 39*40=1560, Resulting Numbers: [1560] 1560,78 unequal: No Solution Moving to Node #0,3,3 Current State: 78:[42, 78], Operations: ['28+11=39', '2*39=78'] Exploring Operation: 42*78=3276, Resulting Numbers: [3276] 3276,78 unequal: No Solution Exploring Operation: 78-42=36, Resulting Numbers: [36] 36,78 unequal: No Solution Exploring Operation: 42+78=120, Resulting Numbers: [120] 120,78 unequal: No Solution Moving to Node #0,3,1 Current State: 78:[2, 81], Operations: ['28+11=39', '42+39=81'] Exploring Operation: 2+81=83, Resulting Numbers: [83] 83,78 unequal: No Solution Exploring Operation: 2*81=162, Resulting Numbers: [162] 162,78 unequal: No Solution Exploring Operation: 81-2=79, Resulting Numbers: [79] 79,78 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 78:[28, 11, 40], Operations: ['42-2=40'] Exploring Operation: 28+11=39, Resulting Numbers: [40, 39] Generated Node #0,0,0: 78:[40, 39] Operation: 28+11=39 Exploring Operation: 40-11=29, Resulting Numbers: [28, 29] Generated Node #0,0,1: 78:[28, 29] Operation: 40-11=29 Exploring Operation: 40-28=12, Resulting Numbers: [11, 12] Generated Node #0,0,2: 78:[11, 12] Operation: 40-28=12 Exploring Operation: 28-11=17, Resulting Numbers: [40, 17] Generated Node #0,0,3: 78:[40, 17] Operation: 28-11=17 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 78:[40, 39], Operations: ['42-2=40', '28+11=39'] Exploring Operation: 40*39=1560, Resulting Numbers: [1560] 1560,78 unequal: No Solution Exploring Operation: 40+39=79, Resulting Numbers: [79] 79,78 unequal: No Solution Exploring Operation: 40-39=1, Resulting Numbers: [1] 1,78 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 78:[11, 12], Operations: ['42-2=40', '40-28=12'] Exploring Operation: 11+12=23, Resulting Numbers: [23] 23,78 unequal: No Solution Exploring Operation: 12-11=1, Resulting Numbers: [1] 1,78 unequal: No Solution Exploring Operation: 11*12=132, Resulting Numbers: [132] 132,78 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 78:[28, 29], Operations: ['42-2=40', '40-11=29'] Exploring Operation: 28+29=57, Resulting Numbers: [57] 57,78 unequal: No Solution Exploring Operation: 28*29=812, Resulting Numbers: [812] 812,78 unequal: No Solution Exploring Operation: 29-28=1, Resulting Numbers: [1] 1,78 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 78:[40, 17], Operations: ['42-2=40', '28-11=17'] Exploring Operation: 40*17=680, Resulting Numbers: [680] 680,78 unequal: No Solution Exploring Operation: 40-17=23, Resulting Numbers: [23] 23,78 unequal: No Solution Exploring Operation: 40+17=57, Resulting Numbers: [57] 57,78 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 78:[42, 11, 26], Operations: ['28-2=26'] Exploring Operation: 42-26=16, Resulting Numbers: [11, 16] Generated Node #0,1,0: 78:[11, 16] Operation: 42-26=16 Exploring Operation: 42-11=31, Resulting Numbers: [26, 31] Generated Node #0,1,1: 78:[26, 31] Operation: 42-11=31 Exploring Operation: 26-11=15, Resulting Numbers: [42, 15] Generated Node #0,1,2: 78:[42, 15] Operation: 26-11=15 Exploring Operation: 11+26=37, Resulting Numbers: [42, 37] Generated Node #0,1,3: 78:[42, 37] Operation: 11+26=37 Moving to Node #0,1,0 Current State: 78:[11, 16], Operations: ['28-2=26', '42-26=16'] Exploring Operation: 16-11=5, Resulting Numbers: [5] 5,78 unequal: No Solution Exploring Operation: 11+16=27, Resulting Numbers: [27] 27,78 unequal: No Solution Exploring Operation: 11*16=176, Resulting Numbers: [176] 176,78 unequal: No Solution Moving to Node #0,1,2 Current State: 78:[42, 15], Operations: ['28-2=26', '26-11=15'] Exploring Operation: 42*15=630, Resulting Numbers: [630] 630,78 unequal: No Solution Exploring Operation: 42+15=57, Resulting Numbers: [57] 57,78 unequal: No Solution Exploring Operation: 42-15=27, Resulting Numbers: [27] 27,78 unequal: No Solution Moving to Node #0,1,1 Current State: 78:[26, 31], Operations: ['28-2=26', '42-11=31'] Exploring Operation: 26+31=57, Resulting Numbers: [57] 57,78 unequal: No Solution Exploring Operation: 26*31=806, Resulting Numbers: [806] 806,78 unequal: No Solution Exploring Operation: 31-26=5, Resulting Numbers: [5] 5,78 unequal: No Solution Moving to Node #0,1,3 Current State: 78:[42, 37], Operations: ['28-2=26', '11+26=37'] Exploring Operation: 42+37=79, Resulting Numbers: [79] 79,78 unequal: No Solution Exploring Operation: 42-37=5, Resulting Numbers: [5] 5,78 unequal: No Solution Exploring Operation: 42*37=1554, Resulting Numbers: [1554] 1554,78 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_4
mult_heuristic
[ 18, 77, 80, 99 ]
27
[ "99-18=81", "80-77=3", "81/3=27" ]
Current State: 27:[18, 77, 80, 99], Operations: [] Exploring Operation: 99-18=81, Resulting Numbers: [77, 80, 81] Generated Node #2: [77, 80, 81] from Operation: 99-18=81 Current State: 27:[77, 80, 81], Operations: ['99-18=81'] Exploring Operation: 80-77=3, Resulting Numbers: [81, 3] Generated Node #3: [81, 3] from Operation: 80-77=3 Current State: 27:[81, 3], Operations: ['99-18=81', '80-77=3'] Exploring Operation: 81/3=27, Resulting Numbers: [27] 27,27 equal: Goal Reached
4
Current State: 27:[18, 77, 80, 99], Operations: [] Exploring Operation: 99-80=19, Resulting Numbers: [18, 77, 19] Generated Node #0,0: 27:[18, 77, 19] Operation: 99-80=19 Exploring Operation: 80-77=3, Resulting Numbers: [18, 99, 3] Generated Node #0,1: 27:[18, 99, 3] Operation: 80-77=3 Exploring Operation: 77-18=59, Resulting Numbers: [80, 99, 59] Generated Node #0,2: 27:[80, 99, 59] Operation: 77-18=59 Exploring Operation: 99-77=22, Resulting Numbers: [18, 80, 22] Generated Node #0,3: 27:[18, 80, 22] Operation: 99-77=22 Start Sub Search at level 1: Moving to Node #0,0 Current State: 27:[18, 77, 19], Operations: ['99-80=19'] Exploring Operation: 77-18=59, Resulting Numbers: [19, 59] Generated Node #0,0,0: 27:[19, 59] Operation: 77-18=59 Exploring Operation: 18+19=37, Resulting Numbers: [77, 37] Generated Node #0,0,1: 27:[77, 37] Operation: 18+19=37 Exploring Operation: 77-19=58, Resulting Numbers: [18, 58] Generated Node #0,0,2: 27:[18, 58] Operation: 77-19=58 Exploring Operation: 19-18=1, Resulting Numbers: [77, 1] Generated Node #0,0,3: 27:[77, 1] Operation: 19-18=1 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 27:[19, 59], Operations: ['99-80=19', '77-18=59'] Exploring Operation: 59-19=40, Resulting Numbers: [40] 40,27 unequal: No Solution Exploring Operation: 19*59=1121, Resulting Numbers: [1121] 1121,27 unequal: No Solution Exploring Operation: 19+59=78, Resulting Numbers: [78] 78,27 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 27:[18, 58], Operations: ['99-80=19', '77-19=58'] Exploring Operation: 18*58=1044, Resulting Numbers: [1044] 1044,27 unequal: No Solution Exploring Operation: 18+58=76, Resulting Numbers: [76] 76,27 unequal: No Solution Exploring Operation: 58-18=40, Resulting Numbers: [40] 40,27 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 27:[77, 1], Operations: ['99-80=19', '19-18=1'] Exploring Operation: 77-1=76, Resulting Numbers: [76] 76,27 unequal: No Solution Exploring Operation: 77+1=78, Resulting Numbers: [78] 78,27 unequal: No Solution Exploring Operation: 77*1=77, Resulting Numbers: [77] 77,27 unequal: No Solution Exploring Operation: 77/1=77, Resulting Numbers: [77] 77,27 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 27:[77, 37], Operations: ['99-80=19', '18+19=37'] Exploring Operation: 77+37=114, Resulting Numbers: [114] 114,27 unequal: No Solution Exploring Operation: 77-37=40, Resulting Numbers: [40] 40,27 unequal: No Solution Exploring Operation: 77*37=2849, Resulting Numbers: [2849] 2849,27 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 27:[18, 80, 22], Operations: ['99-77=22'] Exploring Operation: 22-18=4, Resulting Numbers: [80, 4] Generated Node #0,3,0: 27:[80, 4] Operation: 22-18=4 Exploring Operation: 80-18=62, Resulting Numbers: [22, 62] Generated Node #0,3,1: 27:[22, 62] Operation: 80-18=62 Exploring Operation: 18+22=40, Resulting Numbers: [80, 40] Generated Node #0,3,2: 27:[80, 40] Operation: 18+22=40 Exploring Operation: 80-22=58, Resulting Numbers: [18, 58] Generated Node #0,3,3: 27:[18, 58] Operation: 80-22=58 Moving to Node #0,3,1 Current State: 27:[22, 62], Operations: ['99-77=22', '80-18=62'] Exploring Operation: 22+62=84, Resulting Numbers: [84] 84,27 unequal: No Solution Exploring Operation: 62-22=40, Resulting Numbers: [40] 40,27 unequal: No Solution Exploring Operation: 22*62=1364, Resulting Numbers: [1364] 1364,27 unequal: No Solution Moving to Node #0,3,3 Current State: 27:[18, 58], Operations: ['99-77=22', '80-22=58'] Exploring Operation: 18*58=1044, Resulting Numbers: [1044] 1044,27 unequal: No Solution Exploring Operation: 18+58=76, Resulting Numbers: [76] 76,27 unequal: No Solution Exploring Operation: 58-18=40, Resulting Numbers: [40] 40,27 unequal: No Solution Moving to Node #0,3,0 Current State: 27:[80, 4], Operations: ['99-77=22', '22-18=4'] Exploring Operation: 80-4=76, Resulting Numbers: [76] 76,27 unequal: No Solution Exploring Operation: 80/4=20, Resulting Numbers: [20] 20,27 unequal: No Solution Exploring Operation: 80+4=84, Resulting Numbers: [84] 84,27 unequal: No Solution Exploring Operation: 80*4=320, Resulting Numbers: [320] 320,27 unequal: No Solution Moving to Node #0,3,2 Current State: 27:[80, 40], Operations: ['99-77=22', '18+22=40'] Exploring Operation: 80*40=3200, Resulting Numbers: [3200] 3200,27 unequal: No Solution Exploring Operation: 80/40=2, Resulting Numbers: [2] 2,27 unequal: No Solution Exploring Operation: 80+40=120, Resulting Numbers: [120] 120,27 unequal: No Solution Exploring Operation: 80-40=40, Resulting Numbers: [40] 40,27 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 27:[18, 99, 3], Operations: ['80-77=3'] Exploring Operation: 99-18=81, Resulting Numbers: [3, 81] Generated Node #0,1,0: 27:[3, 81] Operation: 99-18=81 Exploring Operation: 18/3=6, Resulting Numbers: [99, 6] Generated Node #0,1,1: 27:[99, 6] Operation: 18/3=6 Exploring Operation: 18+3=21, Resulting Numbers: [99, 21] Generated Node #0,1,2: 27:[99, 21] Operation: 18+3=21 Exploring Operation: 99/3=33, Resulting Numbers: [18, 33] Generated Node #0,1,3: 27:[18, 33] Operation: 99/3=33 Moving to Node #0,1,3 Current State: 27:[18, 33], Operations: ['80-77=3', '99/3=33'] Exploring Operation: 33-18=15, Resulting Numbers: [15] 15,27 unequal: No Solution Exploring Operation: 18+33=51, Resulting Numbers: [51] 51,27 unequal: No Solution Exploring Operation: 18*33=594, Resulting Numbers: [594] 594,27 unequal: No Solution Moving to Node #0,1,0 Current State: 27:[3, 81], Operations: ['80-77=3', '99-18=81'] Exploring Operation: 3*81=243, Resulting Numbers: [243] 243,27 unequal: No Solution Exploring Operation: 81/3=27, Resulting Numbers: [27] 27,27 equal: Goal Reached Moving to Node #0 Current State: 27:[18, 77, 80, 99], Operations: [] Exploring Operation: 80-77=3, Resulting Numbers: [18, 99, 3] Generated Node #0,1: 27:[18, 99, 3] Operation: 80-77=3 Moving to Node #0,1 Current State: 27:[18, 99, 3], Operations: ['80-77=3'] Exploring Operation: 99-18=81, Resulting Numbers: [3, 81] Generated Node #0,1,0: 27:[3, 81] Operation: 99-18=81 Moving to Node #0,1,0 Current State: 27:[3, 81], Operations: ['80-77=3', '99-18=81'] Exploring Operation: 81/3=27, Resulting Numbers: [27] 27,27 equal: Goal Reached Exit Sub Search at level 1
0.954861
hs_4
sum_heuristic
[ 2, 62, 81, 46 ]
49
[ "62-46=16", "2*16=32", "81-32=49" ]
Current State: 49:[2, 62, 81, 46], Operations: [] Exploring Operation: 62-46=16, Resulting Numbers: [2, 81, 16] Generated Node #2: [2, 81, 16] from Operation: 62-46=16 Current State: 49:[2, 81, 16], Operations: ['62-46=16'] Exploring Operation: 2*16=32, Resulting Numbers: [81, 32] Generated Node #3: [81, 32] from Operation: 2*16=32 Current State: 49:[81, 32], Operations: ['62-46=16', '2*16=32'] Exploring Operation: 81-32=49, Resulting Numbers: [49] 49,49 equal: Goal Reached
4
Current State: 49:[2, 62, 81, 46], Operations: [] Exploring Operation: 81-2=79, Resulting Numbers: [62, 46, 79] Generated Node #0,0: 49:[62, 46, 79] Operation: 81-2=79 Exploring Operation: 62-2=60, Resulting Numbers: [81, 46, 60] Generated Node #0,1: 49:[81, 46, 60] Operation: 62-2=60 Exploring Operation: 81-62=19, Resulting Numbers: [2, 46, 19] Generated Node #0,2: 49:[2, 46, 19] Operation: 81-62=19 Exploring Operation: 81-46=35, Resulting Numbers: [2, 62, 35] Generated Node #0,3: 49:[2, 62, 35] Operation: 81-46=35 Start Sub Search at level 1: Moving to Node #0,2 Current State: 49:[2, 46, 19], Operations: ['81-62=19'] Exploring Operation: 2*19=38, Resulting Numbers: [46, 38] Generated Node #0,2,0: 49:[46, 38] Operation: 2*19=38 Exploring Operation: 2+46=48, Resulting Numbers: [19, 48] Generated Node #0,2,1: 49:[19, 48] Operation: 2+46=48 Exploring Operation: 46-2=44, Resulting Numbers: [19, 44] Generated Node #0,2,2: 49:[19, 44] Operation: 46-2=44 Exploring Operation: 19-2=17, Resulting Numbers: [46, 17] Generated Node #0,2,3: 49:[46, 17] Operation: 19-2=17 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 49:[19, 48], Operations: ['81-62=19', '2+46=48'] Exploring Operation: 19*48=912, Resulting Numbers: [912] 912,49 unequal: No Solution Exploring Operation: 19+48=67, Resulting Numbers: [67] 67,49 unequal: No Solution Exploring Operation: 48-19=29, Resulting Numbers: [29] 29,49 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 49:[46, 17], Operations: ['81-62=19', '19-2=17'] Exploring Operation: 46-17=29, Resulting Numbers: [29] 29,49 unequal: No Solution Exploring Operation: 46+17=63, Resulting Numbers: [63] 63,49 unequal: No Solution Exploring Operation: 46*17=782, Resulting Numbers: [782] 782,49 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 49:[46, 38], Operations: ['81-62=19', '2*19=38'] Exploring Operation: 46+38=84, Resulting Numbers: [84] 84,49 unequal: No Solution Exploring Operation: 46*38=1748, Resulting Numbers: [1748] 1748,49 unequal: No Solution Exploring Operation: 46-38=8, Resulting Numbers: [8] 8,49 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 49:[19, 44], Operations: ['81-62=19', '46-2=44'] Exploring Operation: 19+44=63, Resulting Numbers: [63] 63,49 unequal: No Solution Exploring Operation: 19*44=836, Resulting Numbers: [836] 836,49 unequal: No Solution Exploring Operation: 44-19=25, Resulting Numbers: [25] 25,49 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 49:[2, 62, 35], Operations: ['81-46=35'] Exploring Operation: 62-35=27, Resulting Numbers: [2, 27] Generated Node #0,3,0: 49:[2, 27] Operation: 62-35=27 Exploring Operation: 62-2=60, Resulting Numbers: [35, 60] Generated Node #0,3,1: 49:[35, 60] Operation: 62-2=60 Exploring Operation: 2+35=37, Resulting Numbers: [62, 37] Generated Node #0,3,2: 49:[62, 37] Operation: 2+35=37 Exploring Operation: 2+62=64, Resulting Numbers: [35, 64] Generated Node #0,3,3: 49:[35, 64] Operation: 2+62=64 Moving to Node #0,3,0 Current State: 49:[2, 27], Operations: ['81-46=35', '62-35=27'] Exploring Operation: 2*27=54, Resulting Numbers: [54] 54,49 unequal: No Solution Exploring Operation: 27-2=25, Resulting Numbers: [25] 25,49 unequal: No Solution Exploring Operation: 2+27=29, Resulting Numbers: [29] 29,49 unequal: No Solution Moving to Node #0,3,2 Current State: 49:[62, 37], Operations: ['81-46=35', '2+35=37'] Exploring Operation: 62*37=2294, Resulting Numbers: [2294] 2294,49 unequal: No Solution Exploring Operation: 62+37=99, Resulting Numbers: [99] 99,49 unequal: No Solution Exploring Operation: 62-37=25, Resulting Numbers: [25] 25,49 unequal: No Solution Moving to Node #0,3,1 Current State: 49:[35, 60], Operations: ['81-46=35', '62-2=60'] Exploring Operation: 35+60=95, Resulting Numbers: [95] 95,49 unequal: No Solution Exploring Operation: 60-35=25, Resulting Numbers: [25] 25,49 unequal: No Solution Exploring Operation: 35*60=2100, Resulting Numbers: [2100] 2100,49 unequal: No Solution Moving to Node #0,3,3 Current State: 49:[35, 64], Operations: ['81-46=35', '2+62=64'] Exploring Operation: 35*64=2240, Resulting Numbers: [2240] 2240,49 unequal: No Solution Exploring Operation: 64-35=29, Resulting Numbers: [29] 29,49 unequal: No Solution Exploring Operation: 35+64=99, Resulting Numbers: [99] 99,49 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 49:[62, 46, 79], Operations: ['81-2=79'] Exploring Operation: 79-46=33, Resulting Numbers: [62, 33] Generated Node #0,0,0: 49:[62, 33] Operation: 79-46=33 Exploring Operation: 79-62=17, Resulting Numbers: [46, 17] Generated Node #0,0,1: 49:[46, 17] Operation: 79-62=17 Exploring Operation: 62+46=108, Resulting Numbers: [79, 108] Generated Node #0,0,2: 49:[79, 108] Operation: 62+46=108 Exploring Operation: 62-46=16, Resulting Numbers: [79, 16] Generated Node #0,0,3: 49:[79, 16] Operation: 62-46=16 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 49:[46, 17], Operations: ['81-2=79', '79-62=17'] Exploring Operation: 46+17=63, Resulting Numbers: [63] 63,49 unequal: No Solution Exploring Operation: 46-17=29, Resulting Numbers: [29] 29,49 unequal: No Solution Exploring Operation: 46*17=782, Resulting Numbers: [782] 782,49 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 49:[62, 33], Operations: ['81-2=79', '79-46=33'] Exploring Operation: 62-33=29, Resulting Numbers: [29] 29,49 unequal: No Solution Exploring Operation: 62*33=2046, Resulting Numbers: [2046] 2046,49 unequal: No Solution Exploring Operation: 62+33=95, Resulting Numbers: [95] 95,49 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 49:[79, 16], Operations: ['81-2=79', '62-46=16'] Exploring Operation: 79+16=95, Resulting Numbers: [95] 95,49 unequal: No Solution Exploring Operation: 79-16=63, Resulting Numbers: [63] 63,49 unequal: No Solution Exploring Operation: 79*16=1264, Resulting Numbers: [1264] 1264,49 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 49:[79, 108], Operations: ['81-2=79', '62+46=108'] Exploring Operation: 108-79=29, Resulting Numbers: [29] 29,49 unequal: No Solution Exploring Operation: 79+108=187, Resulting Numbers: [187] 187,49 unequal: No Solution Exploring Operation: 79*108=8532, Resulting Numbers: [8532] 8532,49 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 49:[81, 46, 60], Operations: ['62-2=60'] Exploring Operation: 60-46=14, Resulting Numbers: [81, 14] Generated Node #0,1,0: 49:[81, 14] Operation: 60-46=14 Exploring Operation: 81-60=21, Resulting Numbers: [46, 21] Generated Node #0,1,1: 49:[46, 21] Operation: 81-60=21 Exploring Operation: 81-46=35, Resulting Numbers: [60, 35] Generated Node #0,1,2: 49:[60, 35] Operation: 81-46=35 Exploring Operation: 81+46=127, Resulting Numbers: [60, 127] Generated Node #0,1,3: 49:[60, 127] Operation: 81+46=127 Moving to Node #0,1,1 Current State: 49:[46, 21], Operations: ['62-2=60', '81-60=21'] Exploring Operation: 46*21=966, Resulting Numbers: [966] 966,49 unequal: No Solution Exploring Operation: 46+21=67, Resulting Numbers: [67] 67,49 unequal: No Solution Exploring Operation: 46-21=25, Resulting Numbers: [25] 25,49 unequal: No Solution Moving to Node #0,1,2 Current State: 49:[60, 35], Operations: ['62-2=60', '81-46=35'] Exploring Operation: 60-35=25, Resulting Numbers: [25] 25,49 unequal: No Solution Exploring Operation: 60+35=95, Resulting Numbers: [95] 95,49 unequal: No Solution Exploring Operation: 60*35=2100, Resulting Numbers: [2100] 2100,49 unequal: No Solution Moving to Node #0,1,0 Current State: 49:[81, 14], Operations: ['62-2=60', '60-46=14'] Exploring Operation: 81+14=95, Resulting Numbers: [95] 95,49 unequal: No Solution Exploring Operation: 81-14=67, Resulting Numbers: [67] 67,49 unequal: No Solution Exploring Operation: 81*14=1134, Resulting Numbers: [1134] 1134,49 unequal: No Solution Moving to Node #0,1,3 Current State: 49:[60, 127], Operations: ['62-2=60', '81+46=127'] Exploring Operation: 60*127=7620, Resulting Numbers: [7620] 7620,49 unequal: No Solution Exploring Operation: 127-60=67, Resulting Numbers: [67] 67,49 unequal: No Solution Exploring Operation: 60+127=187, Resulting Numbers: [187] 187,49 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_4
sum_heuristic
[ 68, 32, 34, 96 ]
62
[ "68/34=2", "96-32=64", "64-2=62" ]
Current State: 62:[68, 32, 34, 96], Operations: [] Exploring Operation: 68/34=2, Resulting Numbers: [32, 96, 2] Generated Node #2: [32, 96, 2] from Operation: 68/34=2 Current State: 62:[32, 96, 2], Operations: ['68/34=2'] Exploring Operation: 96-32=64, Resulting Numbers: [2, 64] Generated Node #3: [2, 64] from Operation: 96-32=64 Current State: 62:[2, 64], Operations: ['68/34=2', '96-32=64'] Exploring Operation: 64-2=62, Resulting Numbers: [62] 62,62 equal: Goal Reached
4
Current State: 62:[68, 32, 34, 96], Operations: [] Exploring Operation: 96-68=28, Resulting Numbers: [32, 34, 28] Generated Node #0,0: 62:[32, 34, 28] Operation: 96-68=28 Exploring Operation: 96-34=62, Resulting Numbers: [68, 32, 62] Generated Node #0,1: 62:[68, 32, 62] Operation: 96-34=62 Exploring Operation: 96/32=3, Resulting Numbers: [68, 34, 3] Generated Node #0,2: 62:[68, 34, 3] Operation: 96/32=3 Start Sub Search at level 1: Moving to Node #0,0 Current State: 62:[32, 34, 28], Operations: ['96-68=28'] Exploring Operation: 34+28=62, Resulting Numbers: [32, 62] Generated Node #0,0,0: 62:[32, 62] Operation: 34+28=62 Exploring Operation: 32+28=60, Resulting Numbers: [34, 60] Generated Node #0,0,1: 62:[34, 60] Operation: 32+28=60 Exploring Operation: 34-32=2, Resulting Numbers: [28, 2] Generated Node #0,0,2: 62:[28, 2] Operation: 34-32=2 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 62:[32, 62], Operations: ['96-68=28', '34+28=62'] Exploring Operation: 62-32=30, Resulting Numbers: [30] 30,62 unequal: No Solution Exploring Operation: 32+62=94, Resulting Numbers: [94] 94,62 unequal: No Solution Exploring Operation: 32*62=1984, Resulting Numbers: [1984] 1984,62 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 62:[28, 2], Operations: ['96-68=28', '34-32=2'] Exploring Operation: 28*2=56, Resulting Numbers: [56] 56,62 unequal: No Solution Exploring Operation: 28+2=30, Resulting Numbers: [30] 30,62 unequal: No Solution Exploring Operation: 28-2=26, Resulting Numbers: [26] 26,62 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 62:[34, 60], Operations: ['96-68=28', '32+28=60'] Exploring Operation: 60-34=26, Resulting Numbers: [26] 26,62 unequal: No Solution Exploring Operation: 34*60=2040, Resulting Numbers: [2040] 2040,62 unequal: No Solution Exploring Operation: 34+60=94, Resulting Numbers: [94] 94,62 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 62:[68, 32, 62], Operations: ['96-34=62'] Exploring Operation: 62-32=30, Resulting Numbers: [68, 30] Generated Node #0,1,0: 62:[68, 30] Operation: 62-32=30 Exploring Operation: 68-62=6, Resulting Numbers: [32, 6] Generated Node #0,1,1: 62:[32, 6] Operation: 68-62=6 Exploring Operation: 68-32=36, Resulting Numbers: [62, 36] Generated Node #0,1,2: 62:[62, 36] Operation: 68-32=36 Moving to Node #0,1,1 Current State: 62:[32, 6], Operations: ['96-34=62', '68-62=6'] Exploring Operation: 32+6=38, Resulting Numbers: [38] 38,62 unequal: No Solution Exploring Operation: 32-6=26, Resulting Numbers: [26] 26,62 unequal: No Solution Exploring Operation: 32*6=192, Resulting Numbers: [192] 192,62 unequal: No Solution Moving to Node #0,1,2 Current State: 62:[62, 36], Operations: ['96-34=62', '68-32=36'] Exploring Operation: 62*36=2232, Resulting Numbers: [2232] 2232,62 unequal: No Solution Exploring Operation: 62-36=26, Resulting Numbers: [26] 26,62 unequal: No Solution Exploring Operation: 62+36=98, Resulting Numbers: [98] 98,62 unequal: No Solution Moving to Node #0,1,0 Current State: 62:[68, 30], Operations: ['96-34=62', '62-32=30'] Exploring Operation: 68*30=2040, Resulting Numbers: [2040] 2040,62 unequal: No Solution Exploring Operation: 68-30=38, Resulting Numbers: [38] 38,62 unequal: No Solution Exploring Operation: 68+30=98, Resulting Numbers: [98] 98,62 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 62:[68, 34, 3], Operations: ['96/32=3'] Exploring Operation: 68-34=34, Resulting Numbers: [3, 34] Generated Node #0,2,0: 62:[3, 34] Operation: 68-34=34 Exploring Operation: 68/34=2, Resulting Numbers: [3, 2] Generated Node #0,2,1: 62:[3, 2] Operation: 68/34=2 Exploring Operation: 68-3=65, Resulting Numbers: [34, 65] Generated Node #0,2,2: 62:[34, 65] Operation: 68-3=65 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 62:[3, 2], Operations: ['96/32=3', '68/34=2'] Exploring Operation: 3+2=5, Resulting Numbers: [5] 5,62 unequal: No Solution Exploring Operation: 3-2=1, Resulting Numbers: [1] 1,62 unequal: No Solution Exploring Operation: 3*2=6, Resulting Numbers: [6] 6,62 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 62:[3, 34], Operations: ['96/32=3', '68-34=34'] Exploring Operation: 3*34=102, Resulting Numbers: [102] 102,62 unequal: No Solution Exploring Operation: 34-3=31, Resulting Numbers: [31] 31,62 unequal: No Solution Exploring Operation: 3+34=37, Resulting Numbers: [37] 37,62 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 62:[34, 65], Operations: ['96/32=3', '68-3=65'] Exploring Operation: 34+65=99, Resulting Numbers: [99] 99,62 unequal: No Solution Exploring Operation: 65-34=31, Resulting Numbers: [31] 31,62 unequal: No Solution Exploring Operation: 34*65=2210, Resulting Numbers: [2210] 2210,62 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_3
mult_heuristic
[ 53, 21, 73, 19 ]
63
[ "53+73=126", "21-19=2", "126/2=63" ]
Current State: 63:[53, 21, 73, 19], Operations: [] Exploring Operation: 53+73=126, Resulting Numbers: [21, 19, 126] Generated Node #2: [21, 19, 126] from Operation: 53+73=126 Current State: 63:[21, 19, 126], Operations: ['53+73=126'] Exploring Operation: 21-19=2, Resulting Numbers: [126, 2] Generated Node #3: [126, 2] from Operation: 21-19=2 Current State: 63:[126, 2], Operations: ['53+73=126', '21-19=2'] Exploring Operation: 126/2=63, Resulting Numbers: [63] 63,63 equal: Goal Reached
4
Current State: 63:[53, 21, 73, 19], Operations: [] Exploring Operation: 73-53=20, Resulting Numbers: [21, 19, 20] Generated Node #0,0: 63:[21, 19, 20] Operation: 73-53=20 Exploring Operation: 21-19=2, Resulting Numbers: [53, 73, 2] Generated Node #0,1: 63:[53, 73, 2] Operation: 21-19=2 Exploring Operation: 53+19=72, Resulting Numbers: [21, 73, 72] Generated Node #0,2: 63:[21, 73, 72] Operation: 53+19=72 Exploring Operation: 73-19=54, Resulting Numbers: [53, 21, 54] Generated Node #0,3: 63:[53, 21, 54] Operation: 73-19=54 Start Sub Search at level 1: Moving to Node #0,0 Current State: 63:[21, 19, 20], Operations: ['73-53=20'] Exploring Operation: 21-19=2, Resulting Numbers: [20, 2] Generated Node #0,0,0: 63:[20, 2] Operation: 21-19=2 Exploring Operation: 19+20=39, Resulting Numbers: [21, 39] Generated Node #0,0,1: 63:[21, 39] Operation: 19+20=39 Exploring Operation: 21-20=1, Resulting Numbers: [19, 1] Generated Node #0,0,2: 63:[19, 1] Operation: 21-20=1 Exploring Operation: 20-19=1, Resulting Numbers: [21, 1] Generated Node #0,0,3: 63:[21, 1] Operation: 20-19=1 Moving to Node #0,0,0 Current State: 63:[20, 2], Operations: ['73-53=20', '21-19=2'] Exploring Operation: 20+2=22, Resulting Numbers: [22] 22,63 unequal: No Solution Exploring Operation: 20/2=10, Resulting Numbers: [10] 10,63 unequal: No Solution Exploring Operation: 20*2=40, Resulting Numbers: [40] 40,63 unequal: No Solution Exploring Operation: 20-2=18, Resulting Numbers: [18] 18,63 unequal: No Solution Moving to Node #0,0,3 Current State: 63:[21, 1], Operations: ['73-53=20', '20-19=1'] Exploring Operation: 21+1=22, Resulting Numbers: [22] 22,63 unequal: No Solution Exploring Operation: 21/1=21, Resulting Numbers: [21] 21,63 unequal: No Solution Exploring Operation: 21-1=20, Resulting Numbers: [20] 20,63 unequal: No Solution Exploring Operation: 21*1=21, Resulting Numbers: [21] 21,63 unequal: No Solution Moving to Node #0,0,2 Current State: 63:[19, 1], Operations: ['73-53=20', '21-20=1'] Exploring Operation: 19-1=18, Resulting Numbers: [18] 18,63 unequal: No Solution Exploring Operation: 19/1=19, Resulting Numbers: [19] 19,63 unequal: No Solution Exploring Operation: 19*1=19, Resulting Numbers: [19] 19,63 unequal: No Solution Exploring Operation: 19+1=20, Resulting Numbers: [20] 20,63 unequal: No Solution Moving to Node #0,0,1 Current State: 63:[21, 39], Operations: ['73-53=20', '19+20=39'] Exploring Operation: 21+39=60, Resulting Numbers: [60] 60,63 unequal: No Solution Exploring Operation: 39-21=18, Resulting Numbers: [18] 18,63 unequal: No Solution Exploring Operation: 21*39=819, Resulting Numbers: [819] 819,63 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 63:[21, 73, 72], Operations: ['53+19=72'] Exploring Operation: 73-21=52, Resulting Numbers: [72, 52] Generated Node #0,2,0: 63:[72, 52] Operation: 73-21=52 Exploring Operation: 73-72=1, Resulting Numbers: [21, 1] Generated Node #0,2,1: 63:[21, 1] Operation: 73-72=1 Exploring Operation: 21+73=94, Resulting Numbers: [72, 94] Generated Node #0,2,2: 63:[72, 94] Operation: 21+73=94 Exploring Operation: 72-21=51, Resulting Numbers: [73, 51] Generated Node #0,2,3: 63:[73, 51] Operation: 72-21=51 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 63:[21, 1], Operations: ['53+19=72', '73-72=1'] Exploring Operation: 21+1=22, Resulting Numbers: [22] 22,63 unequal: No Solution Exploring Operation: 21*1=21, Resulting Numbers: [21] 21,63 unequal: No Solution Exploring Operation: 21-1=20, Resulting Numbers: [20] 20,63 unequal: No Solution Exploring Operation: 21/1=21, Resulting Numbers: [21] 21,63 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 63:[72, 52], Operations: ['53+19=72', '73-21=52'] Exploring Operation: 72-52=20, Resulting Numbers: [20] 20,63 unequal: No Solution Exploring Operation: 72+52=124, Resulting Numbers: [124] 124,63 unequal: No Solution Exploring Operation: 72*52=3744, Resulting Numbers: [3744] 3744,63 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 63:[73, 51], Operations: ['53+19=72', '72-21=51'] Exploring Operation: 73*51=3723, Resulting Numbers: [3723] 3723,63 unequal: No Solution Exploring Operation: 73-51=22, Resulting Numbers: [22] 22,63 unequal: No Solution Exploring Operation: 73+51=124, Resulting Numbers: [124] 124,63 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 63:[72, 94], Operations: ['53+19=72', '21+73=94'] Exploring Operation: 72+94=166, Resulting Numbers: [166] 166,63 unequal: No Solution Exploring Operation: 94-72=22, Resulting Numbers: [22] 22,63 unequal: No Solution Exploring Operation: 72*94=6768, Resulting Numbers: [6768] 6768,63 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 63:[53, 21, 54], Operations: ['73-19=54'] Exploring Operation: 21+54=75, Resulting Numbers: [53, 75] Generated Node #0,3,0: 63:[53, 75] Operation: 21+54=75 Exploring Operation: 53-21=32, Resulting Numbers: [54, 32] Generated Node #0,3,1: 63:[54, 32] Operation: 53-21=32 Exploring Operation: 54-53=1, Resulting Numbers: [21, 1] Generated Node #0,3,2: 63:[21, 1] Operation: 54-53=1 Exploring Operation: 53+21=74, Resulting Numbers: [54, 74] Generated Node #0,3,3: 63:[54, 74] Operation: 53+21=74 Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 63:[21, 1], Operations: ['73-19=54', '54-53=1'] Exploring Operation: 21/1=21, Resulting Numbers: [21] 21,63 unequal: No Solution Exploring Operation: 21-1=20, Resulting Numbers: [20] 20,63 unequal: No Solution Exploring Operation: 21*1=21, Resulting Numbers: [21] 21,63 unequal: No Solution Exploring Operation: 21+1=22, Resulting Numbers: [22] 22,63 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 63:[54, 32], Operations: ['73-19=54', '53-21=32'] Exploring Operation: 54-32=22, Resulting Numbers: [22] 22,63 unequal: No Solution Exploring Operation: 54+32=86, Resulting Numbers: [86] 86,63 unequal: No Solution Exploring Operation: 54*32=1728, Resulting Numbers: [1728] 1728,63 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 63:[54, 74], Operations: ['73-19=54', '53+21=74'] Exploring Operation: 54*74=3996, Resulting Numbers: [3996] 3996,63 unequal: No Solution Exploring Operation: 74-54=20, Resulting Numbers: [20] 20,63 unequal: No Solution Exploring Operation: 54+74=128, Resulting Numbers: [128] 128,63 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 63:[53, 75], Operations: ['73-19=54', '21+54=75'] Exploring Operation: 75-53=22, Resulting Numbers: [22] 22,63 unequal: No Solution Exploring Operation: 53+75=128, Resulting Numbers: [128] 128,63 unequal: No Solution Exploring Operation: 53*75=3975, Resulting Numbers: [3975] 3975,63 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 63:[53, 73, 2], Operations: ['21-19=2'] Exploring Operation: 73-53=20, Resulting Numbers: [2, 20] Generated Node #0,1,0: 63:[2, 20] Operation: 73-53=20 Exploring Operation: 53-2=51, Resulting Numbers: [73, 51] Generated Node #0,1,1: 63:[73, 51] Operation: 53-2=51 Exploring Operation: 73-2=71, Resulting Numbers: [53, 71] Generated Node #0,1,2: 63:[53, 71] Operation: 73-2=71 Exploring Operation: 53+2=55, Resulting Numbers: [73, 55] Generated Node #0,1,3: 63:[73, 55] Operation: 53+2=55 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 63:[2, 20], Operations: ['21-19=2', '73-53=20'] Exploring Operation: 2*20=40, Resulting Numbers: [40] 40,63 unequal: No Solution Exploring Operation: 2+20=22, Resulting Numbers: [22] 22,63 unequal: No Solution Exploring Operation: 20/2=10, Resulting Numbers: [10] 10,63 unequal: No Solution Exploring Operation: 20-2=18, Resulting Numbers: [18] 18,63 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 63:[53, 71], Operations: ['21-19=2', '73-2=71'] Exploring Operation: 53+71=124, Resulting Numbers: [124] 124,63 unequal: No Solution Exploring Operation: 71-53=18, Resulting Numbers: [18] 18,63 unequal: No Solution Exploring Operation: 53*71=3763, Resulting Numbers: [3763] 3763,63 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 63:[73, 55], Operations: ['21-19=2', '53+2=55'] Exploring Operation: 73-55=18, Resulting Numbers: [18] 18,63 unequal: No Solution Exploring Operation: 73+55=128, Resulting Numbers: [128] 128,63 unequal: No Solution Exploring Operation: 73*55=4015, Resulting Numbers: [4015] 4015,63 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 63:[73, 51], Operations: ['21-19=2', '53-2=51'] Exploring Operation: 73*51=3723, Resulting Numbers: [3723] 3723,63 unequal: No Solution Exploring Operation: 73+51=124, Resulting Numbers: [124] 124,63 unequal: No Solution Exploring Operation: 73-51=22, Resulting Numbers: [22] 22,63 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_4
mult_heuristic
[ 52, 8, 71, 96 ]
56
[ "71-52=19", "8*19=152", "152-96=56" ]
Current State: 56:[52, 8, 71, 96], Operations: [] Exploring Operation: 71-52=19, Resulting Numbers: [8, 96, 19] Generated Node #2: [8, 96, 19] from Operation: 71-52=19 Current State: 56:[8, 96, 19], Operations: ['71-52=19'] Exploring Operation: 8*19=152, Resulting Numbers: [96, 152] Generated Node #3: [96, 152] from Operation: 8*19=152 Current State: 56:[96, 152], Operations: ['71-52=19', '8*19=152'] Exploring Operation: 152-96=56, Resulting Numbers: [56] 56,56 equal: Goal Reached
4
Current State: 56:[52, 8, 71, 96], Operations: [] Exploring Operation: 96-52=44, Resulting Numbers: [8, 71, 44] Generated Node #0,0: 56:[8, 71, 44] Operation: 96-52=44 Exploring Operation: 96/8=12, Resulting Numbers: [52, 71, 12] Generated Node #0,1: 56:[52, 71, 12] Operation: 96/8=12 Exploring Operation: 96-71=25, Resulting Numbers: [52, 8, 25] Generated Node #0,2: 56:[52, 8, 25] Operation: 96-71=25 Exploring Operation: 71-52=19, Resulting Numbers: [8, 96, 19] Generated Node #0,3: 56:[8, 96, 19] Operation: 71-52=19 Moving to Node #0,2 Current State: 56:[52, 8, 25], Operations: ['96-71=25'] Exploring Operation: 25-8=17, Resulting Numbers: [52, 17] Generated Node #0,2,0: 56:[52, 17] Operation: 25-8=17 Exploring Operation: 8+25=33, Resulting Numbers: [52, 33] Generated Node #0,2,1: 56:[52, 33] Operation: 8+25=33 Exploring Operation: 52+8=60, Resulting Numbers: [25, 60] Generated Node #0,2,2: 56:[25, 60] Operation: 52+8=60 Exploring Operation: 52-25=27, Resulting Numbers: [8, 27] Generated Node #0,2,3: 56:[8, 27] Operation: 52-25=27 Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 56:[8, 27], Operations: ['96-71=25', '52-25=27'] Exploring Operation: 27-8=19, Resulting Numbers: [19] 19,56 unequal: No Solution Exploring Operation: 8+27=35, Resulting Numbers: [35] 35,56 unequal: No Solution Exploring Operation: 8*27=216, Resulting Numbers: [216] 216,56 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 56:[52, 17], Operations: ['96-71=25', '25-8=17'] Exploring Operation: 52-17=35, Resulting Numbers: [35] 35,56 unequal: No Solution Exploring Operation: 52+17=69, Resulting Numbers: [69] 69,56 unequal: No Solution Exploring Operation: 52*17=884, Resulting Numbers: [884] 884,56 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 56:[25, 60], Operations: ['96-71=25', '52+8=60'] Exploring Operation: 60-25=35, Resulting Numbers: [35] 35,56 unequal: No Solution Exploring Operation: 25*60=1500, Resulting Numbers: [1500] 1500,56 unequal: No Solution Exploring Operation: 25+60=85, Resulting Numbers: [85] 85,56 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 56:[52, 33], Operations: ['96-71=25', '8+25=33'] Exploring Operation: 52-33=19, Resulting Numbers: [19] 19,56 unequal: No Solution Exploring Operation: 52*33=1716, Resulting Numbers: [1716] 1716,56 unequal: No Solution Exploring Operation: 52+33=85, Resulting Numbers: [85] 85,56 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 56:[52, 71, 12], Operations: ['96/8=12'] Exploring Operation: 71-52=19, Resulting Numbers: [12, 19] Generated Node #0,1,0: 56:[12, 19] Operation: 71-52=19 Exploring Operation: 52+12=64, Resulting Numbers: [71, 64] Generated Node #0,1,1: 56:[71, 64] Operation: 52+12=64 Exploring Operation: 71-12=59, Resulting Numbers: [52, 59] Generated Node #0,1,2: 56:[52, 59] Operation: 71-12=59 Exploring Operation: 52-12=40, Resulting Numbers: [71, 40] Generated Node #0,1,3: 56:[71, 40] Operation: 52-12=40 Moving to Node #0,0 Current State: 56:[8, 71, 44], Operations: ['96-52=44'] Exploring Operation: 71-8=63, Resulting Numbers: [44, 63] Generated Node #0,0,0: 56:[44, 63] Operation: 71-8=63 Exploring Operation: 44-8=36, Resulting Numbers: [71, 36] Generated Node #0,0,1: 56:[71, 36] Operation: 44-8=36 Exploring Operation: 8+44=52, Resulting Numbers: [71, 52] Generated Node #0,0,2: 56:[71, 52] Operation: 8+44=52 Exploring Operation: 71-44=27, Resulting Numbers: [8, 27] Generated Node #0,0,3: 56:[8, 27] Operation: 71-44=27 Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 56:[8, 27], Operations: ['96-52=44', '71-44=27'] Exploring Operation: 8*27=216, Resulting Numbers: [216] 216,56 unequal: No Solution Exploring Operation: 27-8=19, Resulting Numbers: [19] 19,56 unequal: No Solution Exploring Operation: 8+27=35, Resulting Numbers: [35] 35,56 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 56:[44, 63], Operations: ['96-52=44', '71-8=63'] Exploring Operation: 63-44=19, Resulting Numbers: [19] 19,56 unequal: No Solution Exploring Operation: 44+63=107, Resulting Numbers: [107] 107,56 unequal: No Solution Exploring Operation: 44*63=2772, Resulting Numbers: [2772] 2772,56 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 56:[71, 52], Operations: ['96-52=44', '8+44=52'] Exploring Operation: 71*52=3692, Resulting Numbers: [3692] 3692,56 unequal: No Solution Exploring Operation: 71-52=19, Resulting Numbers: [19] 19,56 unequal: No Solution Exploring Operation: 71+52=123, Resulting Numbers: [123] 123,56 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 56:[71, 36], Operations: ['96-52=44', '44-8=36'] Exploring Operation: 71-36=35, Resulting Numbers: [35] 35,56 unequal: No Solution Exploring Operation: 71+36=107, Resulting Numbers: [107] 107,56 unequal: No Solution Exploring Operation: 71*36=2556, Resulting Numbers: [2556] 2556,56 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,3 Current State: 56:[8, 96, 19], Operations: ['71-52=19'] Exploring Operation: 96-8=88, Resulting Numbers: [19, 88] Generated Node #0,3,0: 56:[19, 88] Operation: 96-8=88 Exploring Operation: 96-19=77, Resulting Numbers: [8, 77] Generated Node #0,3,1: 56:[8, 77] Operation: 96-19=77 Exploring Operation: 96/8=12, Resulting Numbers: [19, 12] Generated Node #0,3,2: 56:[19, 12] Operation: 96/8=12 Exploring Operation: 8+19=27, Resulting Numbers: [96, 27] Generated Node #0,3,3: 56:[96, 27] Operation: 8+19=27 Moving to Node #0,1,0 Current State: 56:[12, 19], Operations: ['96/8=12', '71-52=19'] Exploring Operation: 12+19=31, Resulting Numbers: [31] 31,56 unequal: No Solution Exploring Operation: 19-12=7, Resulting Numbers: [7] 7,56 unequal: No Solution Exploring Operation: 12*19=228, Resulting Numbers: [228] 228,56 unequal: No Solution Moving to Node #0,1,2 Current State: 56:[52, 59], Operations: ['96/8=12', '71-12=59'] Exploring Operation: 52*59=3068, Resulting Numbers: [3068] 3068,56 unequal: No Solution Exploring Operation: 52+59=111, Resulting Numbers: [111] 111,56 unequal: No Solution Exploring Operation: 59-52=7, Resulting Numbers: [7] 7,56 unequal: No Solution Moving to Node #0,3,2 Current State: 56:[19, 12], Operations: ['71-52=19', '96/8=12'] Exploring Operation: 19-12=7, Resulting Numbers: [7] 7,56 unequal: No Solution Exploring Operation: 19+12=31, Resulting Numbers: [31] 31,56 unequal: No Solution Exploring Operation: 19*12=228, Resulting Numbers: [228] 228,56 unequal: No Solution Moving to Node #0,3,1 Current State: 56:[8, 77], Operations: ['71-52=19', '96-19=77'] Exploring Operation: 8*77=616, Resulting Numbers: [616] 616,56 unequal: No Solution Exploring Operation: 77-8=69, Resulting Numbers: [69] 69,56 unequal: No Solution Exploring Operation: 8+77=85, Resulting Numbers: [85] 85,56 unequal: No Solution Moving to Node #0,1,1 Current State: 56:[71, 64], Operations: ['96/8=12', '52+12=64'] Exploring Operation: 71+64=135, Resulting Numbers: [135] 135,56 unequal: No Solution Exploring Operation: 71*64=4544, Resulting Numbers: [4544] 4544,56 unequal: No Solution Exploring Operation: 71-64=7, Resulting Numbers: [7] 7,56 unequal: No Solution Moving to Node #0,1,3 Current State: 56:[71, 40], Operations: ['96/8=12', '52-12=40'] Exploring Operation: 71+40=111, Resulting Numbers: [111] 111,56 unequal: No Solution Exploring Operation: 71*40=2840, Resulting Numbers: [2840] 2840,56 unequal: No Solution Exploring Operation: 71-40=31, Resulting Numbers: [31] 31,56 unequal: No Solution Moving to Node #0,3,0 Current State: 56:[19, 88], Operations: ['71-52=19', '96-8=88'] Exploring Operation: 88-19=69, Resulting Numbers: [69] 69,56 unequal: No Solution Exploring Operation: 19+88=107, Resulting Numbers: [107] 107,56 unequal: No Solution Exploring Operation: 19*88=1672, Resulting Numbers: [1672] 1672,56 unequal: No Solution Moving to Node #0,3,3 Current State: 56:[96, 27], Operations: ['71-52=19', '8+19=27'] Exploring Operation: 96-27=69, Resulting Numbers: [69] 69,56 unequal: No Solution Exploring Operation: 96*27=2592, Resulting Numbers: [2592] 2592,56 unequal: No Solution Exploring Operation: 96+27=123, Resulting Numbers: [123] 123,56 unequal: No Solution No solution found.
0
hs_4
sum_heuristic
[ 71, 7, 4, 17 ]
99
[ "71+7=78", "4+17=21", "78+21=99" ]
Current State: 99:[71, 7, 4, 17], Operations: [] Exploring Operation: 71+7=78, Resulting Numbers: [4, 17, 78] Generated Node #2: [4, 17, 78] from Operation: 71+7=78 Current State: 99:[4, 17, 78], Operations: ['71+7=78'] Exploring Operation: 4+17=21, Resulting Numbers: [78, 21] Generated Node #3: [78, 21] from Operation: 4+17=21 Current State: 99:[78, 21], Operations: ['71+7=78', '4+17=21'] Exploring Operation: 78+21=99, Resulting Numbers: [99] 99,99 equal: Goal Reached
4
Current State: 99:[71, 7, 4, 17], Operations: [] Exploring Operation: 71+17=88, Resulting Numbers: [7, 4, 88] Generated Node #0,0: 99:[7, 4, 88] Operation: 71+17=88 Exploring Operation: 71-17=54, Resulting Numbers: [7, 4, 54] Generated Node #0,1: 99:[7, 4, 54] Operation: 71-17=54 Exploring Operation: 71+7=78, Resulting Numbers: [4, 17, 78] Generated Node #0,2: 99:[4, 17, 78] Operation: 71+7=78 Exploring Operation: 71+4=75, Resulting Numbers: [7, 17, 75] Generated Node #0,3: 99:[7, 17, 75] Operation: 71+4=75 Exploring Operation: 17-7=10, Resulting Numbers: [71, 4, 10] Generated Node #0,4: 99:[71, 4, 10] Operation: 17-7=10 Start Sub Search at level 1: Moving to Node #0,0 Current State: 99:[7, 4, 88], Operations: ['71+17=88'] Exploring Operation: 88/4=22, Resulting Numbers: [7, 22] Generated Node #0,0,0: 99:[7, 22] Operation: 88/4=22 Exploring Operation: 4+88=92, Resulting Numbers: [7, 92] Generated Node #0,0,1: 99:[7, 92] Operation: 4+88=92 Exploring Operation: 7+88=95, Resulting Numbers: [4, 95] Generated Node #0,0,2: 99:[4, 95] Operation: 7+88=95 Exploring Operation: 7+4=11, Resulting Numbers: [88, 11] Generated Node #0,0,3: 99:[88, 11] Operation: 7+4=11 Exploring Operation: 7-4=3, Resulting Numbers: [88, 3] Generated Node #0,0,4: 99:[88, 3] Operation: 7-4=3 Moving to Node #0,0,2 Current State: 99:[4, 95], Operations: ['71+17=88', '7+88=95'] Exploring Operation: 4+95=99, Resulting Numbers: [99] 99,99 equal: Goal Reached Moving to Node #0 Current State: 99:[71, 7, 4, 17], Operations: [] Exploring Operation: 71+17=88, Resulting Numbers: [7, 4, 88] Generated Node #0,0: 99:[7, 4, 88] Operation: 71+17=88 Moving to Node #0,0 Current State: 99:[7, 4, 88], Operations: ['71+17=88'] Exploring Operation: 7+88=95, Resulting Numbers: [4, 95] Generated Node #0,0,2: 99:[4, 95] Operation: 7+88=95 Moving to Node #0,0,2 Current State: 99:[4, 95], Operations: ['71+17=88', '7+88=95'] Exploring Operation: 4+95=99, Resulting Numbers: [99] 99,99 equal: Goal Reached Exit Sub Search at level 1
0.986979
hs_5
mult_heuristic
[ 67, 34, 3, 14 ]
84
[ "67+34=101", "3+14=17", "101-17=84" ]
Current State: 84:[67, 34, 3, 14], Operations: [] Exploring Operation: 67+34=101, Resulting Numbers: [3, 14, 101] Generated Node #2: [3, 14, 101] from Operation: 67+34=101 Current State: 84:[3, 14, 101], Operations: ['67+34=101'] Exploring Operation: 3+14=17, Resulting Numbers: [101, 17] Generated Node #3: [101, 17] from Operation: 3+14=17 Current State: 84:[101, 17], Operations: ['67+34=101', '3+14=17'] Exploring Operation: 101-17=84, Resulting Numbers: [84] 84,84 equal: Goal Reached
4
Current State: 84:[67, 34, 3, 14], Operations: [] Exploring Operation: 67+14=81, Resulting Numbers: [34, 3, 81] Generated Node #0,0: 84:[34, 3, 81] Operation: 67+14=81 Exploring Operation: 67-34=33, Resulting Numbers: [3, 14, 33] Generated Node #0,1: 84:[3, 14, 33] Operation: 67-34=33 Moving to Node #0,1 Current State: 84:[3, 14, 33], Operations: ['67-34=33'] Exploring Operation: 33-3=30, Resulting Numbers: [14, 30] Generated Node #0,1,0: 84:[14, 30] Operation: 33-3=30 Exploring Operation: 33/3=11, Resulting Numbers: [14, 11] Generated Node #0,1,1: 84:[14, 11] Operation: 33/3=11 Moving to Node #0,0 Current State: 84:[34, 3, 81], Operations: ['67+14=81'] Exploring Operation: 81-34=47, Resulting Numbers: [3, 47] Generated Node #0,0,0: 84:[3, 47] Operation: 81-34=47 Exploring Operation: 34-3=31, Resulting Numbers: [81, 31] Generated Node #0,0,1: 84:[81, 31] Operation: 34-3=31 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 84:[3, 47], Operations: ['67+14=81', '81-34=47'] Exploring Operation: 3+47=50, Resulting Numbers: [50] 50,84 unequal: No Solution Exploring Operation: 47-3=44, Resulting Numbers: [44] 44,84 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 84:[81, 31], Operations: ['67+14=81', '34-3=31'] Exploring Operation: 81-31=50, Resulting Numbers: [50] 50,84 unequal: No Solution Exploring Operation: 81+31=112, Resulting Numbers: [112] 112,84 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1,1 Current State: 84:[14, 11], Operations: ['67-34=33', '33/3=11'] Exploring Operation: 14-11=3, Resulting Numbers: [3] 3,84 unequal: No Solution Exploring Operation: 14+11=25, Resulting Numbers: [25] 25,84 unequal: No Solution Moving to Node #0,1,0 Current State: 84:[14, 30], Operations: ['67-34=33', '33-3=30'] Exploring Operation: 30-14=16, Resulting Numbers: [16] 16,84 unequal: No Solution Exploring Operation: 14+30=44, Resulting Numbers: [44] 44,84 unequal: No Solution No solution found.
0
hs_2
sum_heuristic
[ 26, 38, 82, 72 ]
54
[ "26+38=64", "82-72=10", "64-10=54" ]
Current State: 54:[26, 38, 82, 72], Operations: [] Exploring Operation: 26+38=64, Resulting Numbers: [82, 72, 64] Generated Node #2: [82, 72, 64] from Operation: 26+38=64 Current State: 54:[82, 72, 64], Operations: ['26+38=64'] Exploring Operation: 82-72=10, Resulting Numbers: [64, 10] Generated Node #3: [64, 10] from Operation: 82-72=10 Current State: 54:[64, 10], Operations: ['26+38=64', '82-72=10'] Exploring Operation: 64-10=54, Resulting Numbers: [54] 54,54 equal: Goal Reached
4
Current State: 54:[26, 38, 82, 72], Operations: [] Exploring Operation: 82-72=10, Resulting Numbers: [26, 38, 10] Generated Node #0,0: 54:[26, 38, 10] Operation: 82-72=10 Moving to Node #0,0 Current State: 54:[26, 38, 10], Operations: ['82-72=10'] Exploring Operation: 38-10=28, Resulting Numbers: [26, 28] Generated Node #0,0,0: 54:[26, 28] Operation: 38-10=28 Moving to Node #0,0,0 Current State: 54:[26, 28], Operations: ['82-72=10', '38-10=28'] Exploring Operation: 26+28=54, Resulting Numbers: [54] 54,54 equal: Goal Reached Moving to Node #0 Current State: 54:[26, 38, 82, 72], Operations: [] Exploring Operation: 82-72=10, Resulting Numbers: [26, 38, 10] Generated Node #0,0: 54:[26, 38, 10] Operation: 82-72=10 Moving to Node #0,0 Current State: 54:[26, 38, 10], Operations: ['82-72=10'] Exploring Operation: 38-10=28, Resulting Numbers: [26, 28] Generated Node #0,0,0: 54:[26, 28] Operation: 38-10=28 Moving to Node #0,0,0 Current State: 54:[26, 28], Operations: ['82-72=10', '38-10=28'] Exploring Operation: 26+28=54, Resulting Numbers: [54] 54,54 equal: Goal Reached
0.993924
hs_1
sum_heuristic
[ 72, 35, 73, 19 ]
74
[ "73-35=38", "38/19=2", "72+2=74" ]
Current State: 74:[72, 35, 73, 19], Operations: [] Exploring Operation: 73-35=38, Resulting Numbers: [72, 19, 38] Generated Node #2: [72, 19, 38] from Operation: 73-35=38 Current State: 74:[72, 19, 38], Operations: ['73-35=38'] Exploring Operation: 38/19=2, Resulting Numbers: [72, 2] Generated Node #3: [72, 2] from Operation: 38/19=2 Current State: 74:[72, 2], Operations: ['73-35=38', '38/19=2'] Exploring Operation: 72+2=74, Resulting Numbers: [74] 74,74 equal: Goal Reached
4
Current State: 74:[72, 35, 73, 19], Operations: [] Exploring Operation: 35-19=16, Resulting Numbers: [72, 73, 16] Generated Node #0,0: 74:[72, 73, 16] Operation: 35-19=16 Exploring Operation: 72-35=37, Resulting Numbers: [73, 19, 37] Generated Node #0,1: 74:[73, 19, 37] Operation: 72-35=37 Start Sub Search at level 1: Moving to Node #0,0 Current State: 74:[72, 73, 16], Operations: ['35-19=16'] Exploring Operation: 73-72=1, Resulting Numbers: [16, 1] Generated Node #0,0,0: 74:[16, 1] Operation: 73-72=1 Exploring Operation: 72+16=88, Resulting Numbers: [73, 88] Generated Node #0,0,1: 74:[73, 88] Operation: 72+16=88 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 74:[16, 1], Operations: ['35-19=16', '73-72=1'] Exploring Operation: 16*1=16, Resulting Numbers: [16] 16,74 unequal: No Solution Exploring Operation: 16-1=15, Resulting Numbers: [15] 15,74 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 74:[73, 88], Operations: ['35-19=16', '72+16=88'] Exploring Operation: 73+88=161, Resulting Numbers: [161] 161,74 unequal: No Solution Exploring Operation: 88-73=15, Resulting Numbers: [15] 15,74 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 74:[73, 19, 37], Operations: ['72-35=37'] Exploring Operation: 37-19=18, Resulting Numbers: [73, 18] Generated Node #0,1,0: 74:[73, 18] Operation: 37-19=18 Exploring Operation: 73-19=54, Resulting Numbers: [37, 54] Generated Node #0,1,1: 74:[37, 54] Operation: 73-19=54 Moving to Node #0,1,0 Current State: 74:[73, 18], Operations: ['72-35=37', '37-19=18'] Exploring Operation: 73-18=55, Resulting Numbers: [55] 55,74 unequal: No Solution Exploring Operation: 73+18=91, Resulting Numbers: [91] 91,74 unequal: No Solution Moving to Node #0,1,1 Current State: 74:[37, 54], Operations: ['72-35=37', '73-19=54'] Exploring Operation: 54-37=17, Resulting Numbers: [17] 17,74 unequal: No Solution Exploring Operation: 37+54=91, Resulting Numbers: [91] 91,74 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
mult_heuristic
[ 17, 56, 24, 21 ]
29
[ "24-17=7", "56/7=8", "21+8=29" ]
Current State: 29:[17, 56, 24, 21], Operations: [] Exploring Operation: 24-17=7, Resulting Numbers: [56, 21, 7] Generated Node #2: [56, 21, 7] from Operation: 24-17=7 Current State: 29:[56, 21, 7], Operations: ['24-17=7'] Exploring Operation: 56/7=8, Resulting Numbers: [21, 8] Generated Node #3: [21, 8] from Operation: 56/7=8 Current State: 29:[21, 8], Operations: ['24-17=7', '56/7=8'] Exploring Operation: 21+8=29, Resulting Numbers: [29] 29,29 equal: Goal Reached
4
Current State: 29:[17, 56, 24, 21], Operations: [] Exploring Operation: 17+24=41, Resulting Numbers: [56, 21, 41] Generated Node #0,0: 29:[56, 21, 41] Operation: 17+24=41 Exploring Operation: 17+21=38, Resulting Numbers: [56, 24, 38] Generated Node #0,1: 29:[56, 24, 38] Operation: 17+21=38 Exploring Operation: 56-21=35, Resulting Numbers: [17, 24, 35] Generated Node #0,2: 29:[17, 24, 35] Operation: 56-21=35 Exploring Operation: 56-24=32, Resulting Numbers: [17, 21, 32] Generated Node #0,3: 29:[17, 21, 32] Operation: 56-24=32 Exploring Operation: 56-17=39, Resulting Numbers: [24, 21, 39] Generated Node #0,4: 29:[24, 21, 39] Operation: 56-17=39 Moving to Node #0,2 Current State: 29:[17, 24, 35], Operations: ['56-21=35'] Exploring Operation: 35-24=11, Resulting Numbers: [17, 11] Generated Node #0,2,0: 29:[17, 11] Operation: 35-24=11 Exploring Operation: 35-17=18, Resulting Numbers: [24, 18] Generated Node #0,2,1: 29:[24, 18] Operation: 35-17=18 Exploring Operation: 17+24=41, Resulting Numbers: [35, 41] Generated Node #0,2,2: 29:[35, 41] Operation: 17+24=41 Exploring Operation: 24-17=7, Resulting Numbers: [35, 7] Generated Node #0,2,3: 29:[35, 7] Operation: 24-17=7 Exploring Operation: 17+35=52, Resulting Numbers: [24, 52] Generated Node #0,2,4: 29:[24, 52] Operation: 17+35=52 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 29:[24, 18], Operations: ['56-21=35', '35-17=18'] Exploring Operation: 24*18=432, Resulting Numbers: [432] 432,29 unequal: No Solution Exploring Operation: 24+18=42, Resulting Numbers: [42] 42,29 unequal: No Solution Exploring Operation: 24-18=6, Resulting Numbers: [6] 6,29 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 29:[35, 41], Operations: ['56-21=35', '17+24=41'] Exploring Operation: 35+41=76, Resulting Numbers: [76] 76,29 unequal: No Solution Exploring Operation: 35*41=1435, Resulting Numbers: [1435] 1435,29 unequal: No Solution Exploring Operation: 41-35=6, Resulting Numbers: [6] 6,29 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 29:[35, 7], Operations: ['56-21=35', '24-17=7'] Exploring Operation: 35+7=42, Resulting Numbers: [42] 42,29 unequal: No Solution Exploring Operation: 35*7=245, Resulting Numbers: [245] 245,29 unequal: No Solution Exploring Operation: 35/7=5, Resulting Numbers: [5] 5,29 unequal: No Solution Exploring Operation: 35-7=28, Resulting Numbers: [28] 28,29 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,4 Current State: 29:[24, 52], Operations: ['56-21=35', '17+35=52'] Exploring Operation: 24*52=1248, Resulting Numbers: [1248] 1248,29 unequal: No Solution Exploring Operation: 24+52=76, Resulting Numbers: [76] 76,29 unequal: No Solution Exploring Operation: 52-24=28, Resulting Numbers: [28] 28,29 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 29:[17, 11], Operations: ['56-21=35', '35-24=11'] Exploring Operation: 17*11=187, Resulting Numbers: [187] 187,29 unequal: No Solution Exploring Operation: 17-11=6, Resulting Numbers: [6] 6,29 unequal: No Solution Exploring Operation: 17+11=28, Resulting Numbers: [28] 28,29 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,4 Current State: 29:[24, 21, 39], Operations: ['56-17=39'] Exploring Operation: 39-21=18, Resulting Numbers: [24, 18] Generated Node #0,4,0: 29:[24, 18] Operation: 39-21=18 Exploring Operation: 24+21=45, Resulting Numbers: [39, 45] Generated Node #0,4,1: 29:[39, 45] Operation: 24+21=45 Exploring Operation: 24-21=3, Resulting Numbers: [39, 3] Generated Node #0,4,2: 29:[39, 3] Operation: 24-21=3 Exploring Operation: 39-24=15, Resulting Numbers: [21, 15] Generated Node #0,4,3: 29:[21, 15] Operation: 39-24=15 Exploring Operation: 21+39=60, Resulting Numbers: [24, 60] Generated Node #0,4,4: 29:[24, 60] Operation: 21+39=60 Start Sub Search at level 1: Moving to Node #0,4,0 Current State: 29:[24, 18], Operations: ['56-17=39', '39-21=18'] Exploring Operation: 24+18=42, Resulting Numbers: [42] 42,29 unequal: No Solution Exploring Operation: 24-18=6, Resulting Numbers: [6] 6,29 unequal: No Solution Exploring Operation: 24*18=432, Resulting Numbers: [432] 432,29 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,3 Current State: 29:[21, 15], Operations: ['56-17=39', '39-24=15'] Exploring Operation: 21+15=36, Resulting Numbers: [36] 36,29 unequal: No Solution Exploring Operation: 21*15=315, Resulting Numbers: [315] 315,29 unequal: No Solution Exploring Operation: 21-15=6, Resulting Numbers: [6] 6,29 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,1 Current State: 29:[39, 45], Operations: ['56-17=39', '24+21=45'] Exploring Operation: 39*45=1755, Resulting Numbers: [1755] 1755,29 unequal: No Solution Exploring Operation: 45-39=6, Resulting Numbers: [6] 6,29 unequal: No Solution Exploring Operation: 39+45=84, Resulting Numbers: [84] 84,29 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,2 Current State: 29:[39, 3], Operations: ['56-17=39', '24-21=3'] Exploring Operation: 39*3=117, Resulting Numbers: [117] 117,29 unequal: No Solution Exploring Operation: 39/3=13, Resulting Numbers: [13] 13,29 unequal: No Solution Exploring Operation: 39-3=36, Resulting Numbers: [36] 36,29 unequal: No Solution Exploring Operation: 39+3=42, Resulting Numbers: [42] 42,29 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,4 Current State: 29:[24, 60], Operations: ['56-17=39', '21+39=60'] Exploring Operation: 24*60=1440, Resulting Numbers: [1440] 1440,29 unequal: No Solution Exploring Operation: 60-24=36, Resulting Numbers: [36] 36,29 unequal: No Solution Exploring Operation: 24+60=84, Resulting Numbers: [84] 84,29 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,3 Current State: 29:[17, 21, 32], Operations: ['56-24=32'] Exploring Operation: 17+32=49, Resulting Numbers: [21, 49] Generated Node #0,3,0: 29:[21, 49] Operation: 17+32=49 Exploring Operation: 21-17=4, Resulting Numbers: [32, 4] Generated Node #0,3,1: 29:[32, 4] Operation: 21-17=4 Exploring Operation: 17+21=38, Resulting Numbers: [32, 38] Generated Node #0,3,2: 29:[32, 38] Operation: 17+21=38 Exploring Operation: 32-17=15, Resulting Numbers: [21, 15] Generated Node #0,3,3: 29:[21, 15] Operation: 32-17=15 Exploring Operation: 32-21=11, Resulting Numbers: [17, 11] Generated Node #0,3,4: 29:[17, 11] Operation: 32-21=11 Moving to Node #0,1 Current State: 29:[56, 24, 38], Operations: ['17+21=38'] Exploring Operation: 56+24=80, Resulting Numbers: [38, 80] Generated Node #0,1,0: 29:[38, 80] Operation: 56+24=80 Exploring Operation: 38-24=14, Resulting Numbers: [56, 14] Generated Node #0,1,1: 29:[56, 14] Operation: 38-24=14 Exploring Operation: 56-24=32, Resulting Numbers: [38, 32] Generated Node #0,1,2: 29:[38, 32] Operation: 56-24=32 Exploring Operation: 24+38=62, Resulting Numbers: [56, 62] Generated Node #0,1,3: 29:[56, 62] Operation: 24+38=62 Exploring Operation: 56-38=18, Resulting Numbers: [24, 18] Generated Node #0,1,4: 29:[24, 18] Operation: 56-38=18 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 29:[38, 32], Operations: ['17+21=38', '56-24=32'] Exploring Operation: 38-32=6, Resulting Numbers: [6] 6,29 unequal: No Solution Exploring Operation: 38*32=1216, Resulting Numbers: [1216] 1216,29 unequal: No Solution Exploring Operation: 38+32=70, Resulting Numbers: [70] 70,29 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,4 Current State: 29:[24, 18], Operations: ['17+21=38', '56-38=18'] Exploring Operation: 24*18=432, Resulting Numbers: [432] 432,29 unequal: No Solution Exploring Operation: 24-18=6, Resulting Numbers: [6] 6,29 unequal: No Solution Exploring Operation: 24+18=42, Resulting Numbers: [42] 42,29 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 29:[56, 14], Operations: ['17+21=38', '38-24=14'] Exploring Operation: 56*14=784, Resulting Numbers: [784] 784,29 unequal: No Solution Exploring Operation: 56/14=4, Resulting Numbers: [4] 4,29 unequal: No Solution Exploring Operation: 56-14=42, Resulting Numbers: [42] 42,29 unequal: No Solution Exploring Operation: 56+14=70, Resulting Numbers: [70] 70,29 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 29:[38, 80], Operations: ['17+21=38', '56+24=80'] Exploring Operation: 38+80=118, Resulting Numbers: [118] 118,29 unequal: No Solution Exploring Operation: 38*80=3040, Resulting Numbers: [3040] 3040,29 unequal: No Solution Exploring Operation: 80-38=42, Resulting Numbers: [42] 42,29 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 29:[56, 62], Operations: ['17+21=38', '24+38=62'] Exploring Operation: 56+62=118, Resulting Numbers: [118] 118,29 unequal: No Solution Exploring Operation: 62-56=6, Resulting Numbers: [6] 6,29 unequal: No Solution Exploring Operation: 56*62=3472, Resulting Numbers: [3472] 3472,29 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0 Current State: 29:[56, 21, 41], Operations: ['17+24=41'] Exploring Operation: 41-21=20, Resulting Numbers: [56, 20] Generated Node #0,0,0: 29:[56, 20] Operation: 41-21=20 Exploring Operation: 56-41=15, Resulting Numbers: [21, 15] Generated Node #0,0,1: 29:[21, 15] Operation: 56-41=15 Exploring Operation: 21+41=62, Resulting Numbers: [56, 62] Generated Node #0,0,2: 29:[56, 62] Operation: 21+41=62 Exploring Operation: 56-21=35, Resulting Numbers: [41, 35] Generated Node #0,0,3: 29:[41, 35] Operation: 56-21=35 Exploring Operation: 56+21=77, Resulting Numbers: [41, 77] Generated Node #0,0,4: 29:[41, 77] Operation: 56+21=77 Moving to Node #0,3,2 Current State: 29:[32, 38], Operations: ['56-24=32', '17+21=38'] Exploring Operation: 38-32=6, Resulting Numbers: [6] 6,29 unequal: No Solution Exploring Operation: 32*38=1216, Resulting Numbers: [1216] 1216,29 unequal: No Solution Exploring Operation: 32+38=70, Resulting Numbers: [70] 70,29 unequal: No Solution Moving to Node #0,0,3 Current State: 29:[41, 35], Operations: ['17+24=41', '56-21=35'] Exploring Operation: 41*35=1435, Resulting Numbers: [1435] 1435,29 unequal: No Solution Exploring Operation: 41-35=6, Resulting Numbers: [6] 6,29 unequal: No Solution Exploring Operation: 41+35=76, Resulting Numbers: [76] 76,29 unequal: No Solution Moving to Node #0,0,1 Current State: 29:[21, 15], Operations: ['17+24=41', '56-41=15'] Exploring Operation: 21-15=6, Resulting Numbers: [6] 6,29 unequal: No Solution Exploring Operation: 21+15=36, Resulting Numbers: [36] 36,29 unequal: No Solution Exploring Operation: 21*15=315, Resulting Numbers: [315] 315,29 unequal: No Solution Moving to Node #0,3,3 Current State: 29:[21, 15], Operations: ['56-24=32', '32-17=15'] Exploring Operation: 21*15=315, Resulting Numbers: [315] 315,29 unequal: No Solution Exploring Operation: 21+15=36, Resulting Numbers: [36] 36,29 unequal: No Solution Exploring Operation: 21-15=6, Resulting Numbers: [6] 6,29 unequal: No Solution Moving to Node #0,3,0 Current State: 29:[21, 49], Operations: ['56-24=32', '17+32=49'] Exploring Operation: 21+49=70, Resulting Numbers: [70] 70,29 unequal: No Solution Exploring Operation: 49-21=28, Resulting Numbers: [28] 28,29 unequal: No Solution Exploring Operation: 21*49=1029, Resulting Numbers: [1029] 1029,29 unequal: No Solution Moving to Node #0,3,1 Current State: 29:[32, 4], Operations: ['56-24=32', '21-17=4'] Exploring Operation: 32*4=128, Resulting Numbers: [128] 128,29 unequal: No Solution Exploring Operation: 32-4=28, Resulting Numbers: [28] 28,29 unequal: No Solution Exploring Operation: 32+4=36, Resulting Numbers: [36] 36,29 unequal: No Solution Exploring Operation: 32/4=8, Resulting Numbers: [8] 8,29 unequal: No Solution Moving to Node #0,3,4 Current State: 29:[17, 11], Operations: ['56-24=32', '32-21=11'] Exploring Operation: 17+11=28, Resulting Numbers: [28] 28,29 unequal: No Solution Exploring Operation: 17-11=6, Resulting Numbers: [6] 6,29 unequal: No Solution Exploring Operation: 17*11=187, Resulting Numbers: [187] 187,29 unequal: No Solution Moving to Node #0,0,0 Current State: 29:[56, 20], Operations: ['17+24=41', '41-21=20'] Exploring Operation: 56*20=1120, Resulting Numbers: [1120] 1120,29 unequal: No Solution Exploring Operation: 56-20=36, Resulting Numbers: [36] 36,29 unequal: No Solution Exploring Operation: 56+20=76, Resulting Numbers: [76] 76,29 unequal: No Solution Moving to Node #0,0,4 Current State: 29:[41, 77], Operations: ['17+24=41', '56+21=77'] Exploring Operation: 41*77=3157, Resulting Numbers: [3157] 3157,29 unequal: No Solution Exploring Operation: 41+77=118, Resulting Numbers: [118] 118,29 unequal: No Solution Exploring Operation: 77-41=36, Resulting Numbers: [36] 36,29 unequal: No Solution Moving to Node #0,0,2 Current State: 29:[56, 62], Operations: ['17+24=41', '21+41=62'] Exploring Operation: 56*62=3472, Resulting Numbers: [3472] 3472,29 unequal: No Solution Exploring Operation: 62-56=6, Resulting Numbers: [6] 6,29 unequal: No Solution Exploring Operation: 56+62=118, Resulting Numbers: [118] 118,29 unequal: No Solution No solution found.
0
hs_5
sum_heuristic
[ 24, 70, 3, 3 ]
88
[ "24+70=94", "3+3=6", "94-6=88" ]
Current State: 88:[24, 70, 3, 3], Operations: [] Exploring Operation: 24+70=94, Resulting Numbers: [3, 3, 94] Generated Node #2: [3, 3, 94] from Operation: 24+70=94 Current State: 88:[3, 3, 94], Operations: ['24+70=94'] Exploring Operation: 3+3=6, Resulting Numbers: [94, 6] Generated Node #3: [94, 6] from Operation: 3+3=6 Current State: 88:[94, 6], Operations: ['24+70=94', '3+3=6'] Exploring Operation: 94-6=88, Resulting Numbers: [88] 88,88 equal: Goal Reached
4
Current State: 88:[24, 70, 3, 3], Operations: [] Exploring Operation: 70-24=46, Resulting Numbers: [3, 3, 46] Generated Node #0,0: 88:[3, 3, 46] Operation: 70-24=46 Exploring Operation: 70+3=73, Resulting Numbers: [24, 3, 73] Generated Node #0,1: 88:[24, 3, 73] Operation: 70+3=73 Exploring Operation: 24+70=94, Resulting Numbers: [3, 3, 94] Generated Node #0,2: 88:[3, 3, 94] Operation: 24+70=94 Exploring Operation: 24/3=8, Resulting Numbers: [70, 3, 8] Generated Node #0,3: 88:[70, 3, 8] Operation: 24/3=8 Exploring Operation: 70+3=73, Resulting Numbers: [24, 3, 73] Generated Node #0,4: 88:[24, 3, 73] Operation: 70+3=73 Start Sub Search at level 1: Moving to Node #0,0 Current State: 88:[3, 3, 46], Operations: ['70-24=46'] Exploring Operation: 46-3=43, Resulting Numbers: [3, 43] Generated Node #0,0,0: 88:[3, 43] Operation: 46-3=43 Exploring Operation: 3*3=9, Resulting Numbers: [46, 9] Generated Node #0,0,1: 88:[46, 9] Operation: 3*3=9 Exploring Operation: 46-3=43, Resulting Numbers: [3, 43] Generated Node #0,0,2: 88:[3, 43] Operation: 46-3=43 Exploring Operation: 3+3=6, Resulting Numbers: [46, 6] Generated Node #0,0,3: 88:[46, 6] Operation: 3+3=6 Exploring Operation: 3/3=1, Resulting Numbers: [46, 1] Generated Node #0,0,4: 88:[46, 1] Operation: 3/3=1 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 88:[3, 43], Operations: ['70-24=46', '46-3=43'] Exploring Operation: 3*43=129, Resulting Numbers: [129] 129,88 unequal: No Solution Exploring Operation: 43-3=40, Resulting Numbers: [40] 40,88 unequal: No Solution Exploring Operation: 3+43=46, Resulting Numbers: [46] 46,88 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 88:[3, 43], Operations: ['70-24=46', '46-3=43'] Exploring Operation: 43-3=40, Resulting Numbers: [40] 40,88 unequal: No Solution Exploring Operation: 3+43=46, Resulting Numbers: [46] 46,88 unequal: No Solution Exploring Operation: 3*43=129, Resulting Numbers: [129] 129,88 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 88:[46, 9], Operations: ['70-24=46', '3*3=9'] Exploring Operation: 46-9=37, Resulting Numbers: [37] 37,88 unequal: No Solution Exploring Operation: 46+9=55, Resulting Numbers: [55] 55,88 unequal: No Solution Exploring Operation: 46*9=414, Resulting Numbers: [414] 414,88 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,4 Current State: 88:[46, 1], Operations: ['70-24=46', '3/3=1'] Exploring Operation: 46/1=46, Resulting Numbers: [46] 46,88 unequal: No Solution Exploring Operation: 46*1=46, Resulting Numbers: [46] 46,88 unequal: No Solution Exploring Operation: 46+1=47, Resulting Numbers: [47] 47,88 unequal: No Solution Exploring Operation: 46-1=45, Resulting Numbers: [45] 45,88 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 88:[46, 6], Operations: ['70-24=46', '3+3=6'] Exploring Operation: 46-6=40, Resulting Numbers: [40] 40,88 unequal: No Solution Exploring Operation: 46*6=276, Resulting Numbers: [276] 276,88 unequal: No Solution Exploring Operation: 46+6=52, Resulting Numbers: [52] 52,88 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 88:[3, 3, 94], Operations: ['24+70=94'] Exploring Operation: 3+3=6, Resulting Numbers: [94, 6] Generated Node #0,2,0: 88:[94, 6] Operation: 3+3=6 Exploring Operation: 94-3=91, Resulting Numbers: [3, 91] Generated Node #0,2,1: 88:[3, 91] Operation: 94-3=91 Exploring Operation: 3/3=1, Resulting Numbers: [94, 1] Generated Node #0,2,2: 88:[94, 1] Operation: 3/3=1 Exploring Operation: 3*3=9, Resulting Numbers: [94, 9] Generated Node #0,2,3: 88:[94, 9] Operation: 3*3=9 Exploring Operation: 94-3=91, Resulting Numbers: [3, 91] Generated Node #0,2,4: 88:[3, 91] Operation: 94-3=91 Moving to Node #0,2,1 Current State: 88:[3, 91], Operations: ['24+70=94', '94-3=91'] Exploring Operation: 91-3=88, Resulting Numbers: [88] 88,88 equal: Goal Reached Moving to Node #0 Current State: 88:[24, 70, 3, 3], Operations: [] Exploring Operation: 24+70=94, Resulting Numbers: [3, 3, 94] Generated Node #0,2: 88:[3, 3, 94] Operation: 24+70=94 Moving to Node #0,2 Current State: 88:[3, 3, 94], Operations: ['24+70=94'] Exploring Operation: 94-3=91, Resulting Numbers: [3, 91] Generated Node #0,2,1: 88:[3, 91] Operation: 94-3=91 Moving to Node #0,2,1 Current State: 88:[3, 91], Operations: ['24+70=94', '94-3=91'] Exploring Operation: 91-3=88, Resulting Numbers: [88] 88,88 equal: Goal Reached Exit Sub Search at level 1
0.96875
hs_5
mult_heuristic
[ 34, 5, 31, 15 ]
16
[ "34+31=65", "15+65=80", "80/5=16" ]
Current State: 16:[34, 5, 31, 15], Operations: [] Exploring Operation: 34+31=65, Resulting Numbers: [5, 15, 65] Generated Node #2: [5, 15, 65] from Operation: 34+31=65 Current State: 16:[5, 15, 65], Operations: ['34+31=65'] Exploring Operation: 15+65=80, Resulting Numbers: [5, 80] Generated Node #3: [5, 80] from Operation: 15+65=80 Current State: 16:[5, 80], Operations: ['34+31=65', '15+65=80'] Exploring Operation: 80/5=16, Resulting Numbers: [16] 16,16 equal: Goal Reached
4
Current State: 16:[34, 5, 31, 15], Operations: [] Exploring Operation: 31-15=16, Resulting Numbers: [34, 5, 16] Generated Node #0,0: 16:[34, 5, 16] Operation: 31-15=16 Exploring Operation: 34-5=29, Resulting Numbers: [31, 15, 29] Generated Node #0,1: 16:[31, 15, 29] Operation: 34-5=29 Exploring Operation: 34-31=3, Resulting Numbers: [5, 15, 3] Generated Node #0,2: 16:[5, 15, 3] Operation: 34-31=3 Exploring Operation: 34-15=19, Resulting Numbers: [5, 31, 19] Generated Node #0,3: 16:[5, 31, 19] Operation: 34-15=19 Moving to Node #0,2 Current State: 16:[5, 15, 3], Operations: ['34-31=3'] Exploring Operation: 5*3=15, Resulting Numbers: [15, 15] Generated Node #0,2,0: 16:[15, 15] Operation: 5*3=15 Exploring Operation: 15/5=3, Resulting Numbers: [3, 3] Generated Node #0,2,1: 16:[3, 3] Operation: 15/5=3 Exploring Operation: 5-3=2, Resulting Numbers: [15, 2] Generated Node #0,2,2: 16:[15, 2] Operation: 5-3=2 Exploring Operation: 5+3=8, Resulting Numbers: [15, 8] Generated Node #0,2,3: 16:[15, 8] Operation: 5+3=8 Moving to Node #0,3 Current State: 16:[5, 31, 19], Operations: ['34-15=19'] Exploring Operation: 31-5=26, Resulting Numbers: [19, 26] Generated Node #0,3,0: 16:[19, 26] Operation: 31-5=26 Exploring Operation: 19-5=14, Resulting Numbers: [31, 14] Generated Node #0,3,1: 16:[31, 14] Operation: 19-5=14 Exploring Operation: 5+31=36, Resulting Numbers: [19, 36] Generated Node #0,3,2: 16:[19, 36] Operation: 5+31=36 Exploring Operation: 31-19=12, Resulting Numbers: [5, 12] Generated Node #0,3,3: 16:[5, 12] Operation: 31-19=12 Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 16:[5, 12], Operations: ['34-15=19', '31-19=12'] Exploring Operation: 12-5=7, Resulting Numbers: [7] 7,16 unequal: No Solution Exploring Operation: 5*12=60, Resulting Numbers: [60] 60,16 unequal: No Solution Exploring Operation: 5+12=17, Resulting Numbers: [17] 17,16 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 16:[19, 26], Operations: ['34-15=19', '31-5=26'] Exploring Operation: 19+26=45, Resulting Numbers: [45] 45,16 unequal: No Solution Exploring Operation: 26-19=7, Resulting Numbers: [7] 7,16 unequal: No Solution Exploring Operation: 19*26=494, Resulting Numbers: [494] 494,16 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 16:[31, 14], Operations: ['34-15=19', '19-5=14'] Exploring Operation: 31+14=45, Resulting Numbers: [45] 45,16 unequal: No Solution Exploring Operation: 31-14=17, Resulting Numbers: [17] 17,16 unequal: No Solution Exploring Operation: 31*14=434, Resulting Numbers: [434] 434,16 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 16:[19, 36], Operations: ['34-15=19', '5+31=36'] Exploring Operation: 19*36=684, Resulting Numbers: [684] 684,16 unequal: No Solution Exploring Operation: 19+36=55, Resulting Numbers: [55] 55,16 unequal: No Solution Exploring Operation: 36-19=17, Resulting Numbers: [17] 17,16 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0 Current State: 16:[34, 5, 16], Operations: ['31-15=16'] Exploring Operation: 16-5=11, Resulting Numbers: [34, 11] Generated Node #0,0,0: 16:[34, 11] Operation: 16-5=11 Exploring Operation: 34-5=29, Resulting Numbers: [16, 29] Generated Node #0,0,1: 16:[16, 29] Operation: 34-5=29 Exploring Operation: 34+5=39, Resulting Numbers: [16, 39] Generated Node #0,0,2: 16:[16, 39] Operation: 34+5=39 Exploring Operation: 34-16=18, Resulting Numbers: [5, 18] Generated Node #0,0,3: 16:[5, 18] Operation: 34-16=18 Moving to Node #0,1 Current State: 16:[31, 15, 29], Operations: ['34-5=29'] Exploring Operation: 31-15=16, Resulting Numbers: [29, 16] Generated Node #0,1,0: 16:[29, 16] Operation: 31-15=16 Exploring Operation: 29-15=14, Resulting Numbers: [31, 14] Generated Node #0,1,1: 16:[31, 14] Operation: 29-15=14 Exploring Operation: 31-29=2, Resulting Numbers: [15, 2] Generated Node #0,1,2: 16:[15, 2] Operation: 31-29=2 Exploring Operation: 31+15=46, Resulting Numbers: [29, 46] Generated Node #0,1,3: 16:[29, 46] Operation: 31+15=46 Moving to Node #0,2,2 Current State: 16:[15, 2], Operations: ['34-31=3', '5-3=2'] Exploring Operation: 15*2=30, Resulting Numbers: [30] 30,16 unequal: No Solution Exploring Operation: 15-2=13, Resulting Numbers: [13] 13,16 unequal: No Solution Exploring Operation: 15+2=17, Resulting Numbers: [17] 17,16 unequal: No Solution Moving to Node #0,2,3 Current State: 16:[15, 8], Operations: ['34-31=3', '5+3=8'] Exploring Operation: 15-8=7, Resulting Numbers: [7] 7,16 unequal: No Solution Exploring Operation: 15*8=120, Resulting Numbers: [120] 120,16 unequal: No Solution Exploring Operation: 15+8=23, Resulting Numbers: [23] 23,16 unequal: No Solution Moving to Node #0,1,2 Current State: 16:[15, 2], Operations: ['34-5=29', '31-29=2'] Exploring Operation: 15-2=13, Resulting Numbers: [13] 13,16 unequal: No Solution Exploring Operation: 15+2=17, Resulting Numbers: [17] 17,16 unequal: No Solution Exploring Operation: 15*2=30, Resulting Numbers: [30] 30,16 unequal: No Solution Moving to Node #0,2,0 Current State: 16:[15, 15], Operations: ['34-31=3', '5*3=15'] Exploring Operation: 15+15=30, Resulting Numbers: [30] 30,16 unequal: No Solution Exploring Operation: 15-15=0, Resulting Numbers: [0] 0,16 unequal: No Solution Exploring Operation: 15*15=225, Resulting Numbers: [225] 225,16 unequal: No Solution Exploring Operation: 15/15=1, Resulting Numbers: [1] 1,16 unequal: No Solution Moving to Node #0,2,1 Current State: 16:[3, 3], Operations: ['34-31=3', '15/5=3'] Exploring Operation: 3*3=9, Resulting Numbers: [9] 9,16 unequal: No Solution Exploring Operation: 3+3=6, Resulting Numbers: [6] 6,16 unequal: No Solution Exploring Operation: 3/3=1, Resulting Numbers: [1] 1,16 unequal: No Solution Exploring Operation: 3-3=0, Resulting Numbers: [0] 0,16 unequal: No Solution Moving to Node #0,0,3 Current State: 16:[5, 18], Operations: ['31-15=16', '34-16=18'] Exploring Operation: 5*18=90, Resulting Numbers: [90] 90,16 unequal: No Solution Exploring Operation: 18-5=13, Resulting Numbers: [13] 13,16 unequal: No Solution Exploring Operation: 5+18=23, Resulting Numbers: [23] 23,16 unequal: No Solution Moving to Node #0,0,1 Current State: 16:[16, 29], Operations: ['31-15=16', '34-5=29'] Exploring Operation: 16*29=464, Resulting Numbers: [464] 464,16 unequal: No Solution Exploring Operation: 29-16=13, Resulting Numbers: [13] 13,16 unequal: No Solution Exploring Operation: 16+29=45, Resulting Numbers: [45] 45,16 unequal: No Solution Moving to Node #0,1,0 Current State: 16:[29, 16], Operations: ['34-5=29', '31-15=16'] Exploring Operation: 29*16=464, Resulting Numbers: [464] 464,16 unequal: No Solution Exploring Operation: 29-16=13, Resulting Numbers: [13] 13,16 unequal: No Solution Exploring Operation: 29+16=45, Resulting Numbers: [45] 45,16 unequal: No Solution Moving to Node #0,1,1 Current State: 16:[31, 14], Operations: ['34-5=29', '29-15=14'] Exploring Operation: 31+14=45, Resulting Numbers: [45] 45,16 unequal: No Solution Exploring Operation: 31-14=17, Resulting Numbers: [17] 17,16 unequal: No Solution Exploring Operation: 31*14=434, Resulting Numbers: [434] 434,16 unequal: No Solution Moving to Node #0,0,0 Current State: 16:[34, 11], Operations: ['31-15=16', '16-5=11'] Exploring Operation: 34*11=374, Resulting Numbers: [374] 374,16 unequal: No Solution Exploring Operation: 34-11=23, Resulting Numbers: [23] 23,16 unequal: No Solution Exploring Operation: 34+11=45, Resulting Numbers: [45] 45,16 unequal: No Solution Moving to Node #0,0,2 Current State: 16:[16, 39], Operations: ['31-15=16', '34+5=39'] Exploring Operation: 39-16=23, Resulting Numbers: [23] 23,16 unequal: No Solution Exploring Operation: 16+39=55, Resulting Numbers: [55] 55,16 unequal: No Solution Exploring Operation: 16*39=624, Resulting Numbers: [624] 624,16 unequal: No Solution Moving to Node #0,1,3 Current State: 16:[29, 46], Operations: ['34-5=29', '31+15=46'] Exploring Operation: 29+46=75, Resulting Numbers: [75] 75,16 unequal: No Solution Exploring Operation: 29*46=1334, Resulting Numbers: [1334] 1334,16 unequal: No Solution Exploring Operation: 46-29=17, Resulting Numbers: [17] 17,16 unequal: No Solution No solution found.
0
hs_4
sum_heuristic
[ 91, 24, 9, 75 ]
50
[ "91+75=166", "24*9=216", "216-166=50" ]
Current State: 50:[91, 24, 9, 75], Operations: [] Exploring Operation: 91+75=166, Resulting Numbers: [24, 9, 166] Generated Node #2: [24, 9, 166] from Operation: 91+75=166 Current State: 50:[24, 9, 166], Operations: ['91+75=166'] Exploring Operation: 24*9=216, Resulting Numbers: [166, 216] Generated Node #3: [166, 216] from Operation: 24*9=216 Current State: 50:[166, 216], Operations: ['91+75=166', '24*9=216'] Exploring Operation: 216-166=50, Resulting Numbers: [50] 50,50 equal: Goal Reached
4
Current State: 50:[91, 24, 9, 75], Operations: [] Exploring Operation: 91-75=16, Resulting Numbers: [24, 9, 16] Generated Node #0,0: 50:[24, 9, 16] Operation: 91-75=16 Exploring Operation: 91-24=67, Resulting Numbers: [9, 75, 67] Generated Node #0,1: 50:[9, 75, 67] Operation: 91-24=67 Moving to Node #0,0 Current State: 50:[24, 9, 16], Operations: ['91-75=16'] Exploring Operation: 9+16=25, Resulting Numbers: [24, 25] Generated Node #0,0,0: 50:[24, 25] Operation: 9+16=25 Exploring Operation: 24-16=8, Resulting Numbers: [9, 8] Generated Node #0,0,1: 50:[9, 8] Operation: 24-16=8 Moving to Node #0,1 Current State: 50:[9, 75, 67], Operations: ['91-24=67'] Exploring Operation: 75-9=66, Resulting Numbers: [67, 66] Generated Node #0,1,0: 50:[67, 66] Operation: 75-9=66 Exploring Operation: 75-67=8, Resulting Numbers: [9, 8] Generated Node #0,1,1: 50:[9, 8] Operation: 75-67=8 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 50:[9, 8], Operations: ['91-24=67', '75-67=8'] Exploring Operation: 9-8=1, Resulting Numbers: [1] 1,50 unequal: No Solution Exploring Operation: 9+8=17, Resulting Numbers: [17] 17,50 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 50:[67, 66], Operations: ['91-24=67', '75-9=66'] Exploring Operation: 67+66=133, Resulting Numbers: [133] 133,50 unequal: No Solution Exploring Operation: 67-66=1, Resulting Numbers: [1] 1,50 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0,0 Current State: 50:[24, 25], Operations: ['91-75=16', '9+16=25'] Exploring Operation: 24+25=49, Resulting Numbers: [49] 49,50 unequal: No Solution Exploring Operation: 25-24=1, Resulting Numbers: [1] 1,50 unequal: No Solution Moving to Node #0,0,1 Current State: 50:[9, 8], Operations: ['91-75=16', '24-16=8'] Exploring Operation: 9-8=1, Resulting Numbers: [1] 1,50 unequal: No Solution Exploring Operation: 9+8=17, Resulting Numbers: [17] 17,50 unequal: No Solution No solution found.
0
hs_2
sum_heuristic
[ 44, 39, 60, 29 ]
50
[ "39-29=10", "60/10=6", "44+6=50" ]
Current State: 50:[44, 39, 60, 29], Operations: [] Exploring Operation: 39-29=10, Resulting Numbers: [44, 60, 10] Generated Node #2: [44, 60, 10] from Operation: 39-29=10 Current State: 50:[44, 60, 10], Operations: ['39-29=10'] Exploring Operation: 60/10=6, Resulting Numbers: [44, 6] Generated Node #3: [44, 6] from Operation: 60/10=6 Current State: 50:[44, 6], Operations: ['39-29=10', '60/10=6'] Exploring Operation: 44+6=50, Resulting Numbers: [50] 50,50 equal: Goal Reached
4
Current State: 50:[44, 39, 60, 29], Operations: [] Exploring Operation: 60-39=21, Resulting Numbers: [44, 29, 21] Generated Node #0,0: 50:[44, 29, 21] Operation: 60-39=21 Exploring Operation: 39-29=10, Resulting Numbers: [44, 60, 10] Generated Node #0,1: 50:[44, 60, 10] Operation: 39-29=10 Exploring Operation: 44-39=5, Resulting Numbers: [60, 29, 5] Generated Node #0,2: 50:[60, 29, 5] Operation: 44-39=5 Start Sub Search at level 1: Moving to Node #0,0 Current State: 50:[44, 29, 21], Operations: ['60-39=21'] Exploring Operation: 29+21=50, Resulting Numbers: [44, 50] Generated Node #0,0,0: 50:[44, 50] Operation: 29+21=50 Exploring Operation: 29-21=8, Resulting Numbers: [44, 8] Generated Node #0,0,1: 50:[44, 8] Operation: 29-21=8 Exploring Operation: 44-21=23, Resulting Numbers: [29, 23] Generated Node #0,0,2: 50:[29, 23] Operation: 44-21=23 Moving to Node #0,0,0 Current State: 50:[44, 50], Operations: ['60-39=21', '29+21=50'] Exploring Operation: 44*50=2200, Resulting Numbers: [2200] 2200,50 unequal: No Solution Exploring Operation: 44+50=94, Resulting Numbers: [94] 94,50 unequal: No Solution Exploring Operation: 50-44=6, Resulting Numbers: [6] 6,50 unequal: No Solution Moving to Node #0,0,2 Current State: 50:[29, 23], Operations: ['60-39=21', '44-21=23'] Exploring Operation: 29+23=52, Resulting Numbers: [52] 52,50 unequal: No Solution Exploring Operation: 29-23=6, Resulting Numbers: [6] 6,50 unequal: No Solution Exploring Operation: 29*23=667, Resulting Numbers: [667] 667,50 unequal: No Solution Moving to Node #0,0,1 Current State: 50:[44, 8], Operations: ['60-39=21', '29-21=8'] Exploring Operation: 44*8=352, Resulting Numbers: [352] 352,50 unequal: No Solution Exploring Operation: 44+8=52, Resulting Numbers: [52] 52,50 unequal: No Solution Exploring Operation: 44-8=36, Resulting Numbers: [36] 36,50 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 50:[60, 29, 5], Operations: ['44-39=5'] Exploring Operation: 60/5=12, Resulting Numbers: [29, 12] Generated Node #0,2,0: 50:[29, 12] Operation: 60/5=12 Exploring Operation: 60-29=31, Resulting Numbers: [5, 31] Generated Node #0,2,1: 50:[5, 31] Operation: 60-29=31 Exploring Operation: 60-5=55, Resulting Numbers: [29, 55] Generated Node #0,2,2: 50:[29, 55] Operation: 60-5=55 Moving to Node #0,2,0 Current State: 50:[29, 12], Operations: ['44-39=5', '60/5=12'] Exploring Operation: 29+12=41, Resulting Numbers: [41] 41,50 unequal: No Solution Exploring Operation: 29-12=17, Resulting Numbers: [17] 17,50 unequal: No Solution Exploring Operation: 29*12=348, Resulting Numbers: [348] 348,50 unequal: No Solution Moving to Node #0,2,1 Current State: 50:[5, 31], Operations: ['44-39=5', '60-29=31'] Exploring Operation: 31-5=26, Resulting Numbers: [26] 26,50 unequal: No Solution Exploring Operation: 5+31=36, Resulting Numbers: [36] 36,50 unequal: No Solution Exploring Operation: 5*31=155, Resulting Numbers: [155] 155,50 unequal: No Solution Moving to Node #0,2,2 Current State: 50:[29, 55], Operations: ['44-39=5', '60-5=55'] Exploring Operation: 29+55=84, Resulting Numbers: [84] 84,50 unequal: No Solution Exploring Operation: 55-29=26, Resulting Numbers: [26] 26,50 unequal: No Solution Exploring Operation: 29*55=1595, Resulting Numbers: [1595] 1595,50 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 50:[44, 60, 10], Operations: ['39-29=10'] Exploring Operation: 60/10=6, Resulting Numbers: [44, 6] Generated Node #0,1,0: 50:[44, 6] Operation: 60/10=6 Exploring Operation: 60-44=16, Resulting Numbers: [10, 16] Generated Node #0,1,1: 50:[10, 16] Operation: 60-44=16 Exploring Operation: 60-10=50, Resulting Numbers: [44, 50] Generated Node #0,1,2: 50:[44, 50] Operation: 60-10=50 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 50:[10, 16], Operations: ['39-29=10', '60-44=16'] Exploring Operation: 16-10=6, Resulting Numbers: [6] 6,50 unequal: No Solution Exploring Operation: 10*16=160, Resulting Numbers: [160] 160,50 unequal: No Solution Exploring Operation: 10+16=26, Resulting Numbers: [26] 26,50 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 50:[44, 50], Operations: ['39-29=10', '60-10=50'] Exploring Operation: 44+50=94, Resulting Numbers: [94] 94,50 unequal: No Solution Exploring Operation: 44*50=2200, Resulting Numbers: [2200] 2200,50 unequal: No Solution Exploring Operation: 50-44=6, Resulting Numbers: [6] 6,50 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 50:[44, 6], Operations: ['39-29=10', '60/10=6'] Exploring Operation: 44-6=38, Resulting Numbers: [38] 38,50 unequal: No Solution Exploring Operation: 44*6=264, Resulting Numbers: [264] 264,50 unequal: No Solution Exploring Operation: 44+6=50, Resulting Numbers: [50] 50,50 equal: Goal Reached Moving to Node #0 Current State: 50:[44, 39, 60, 29], Operations: [] Exploring Operation: 39-29=10, Resulting Numbers: [44, 60, 10] Generated Node #0,1: 50:[44, 60, 10] Operation: 39-29=10 Moving to Node #0,1 Current State: 50:[44, 60, 10], Operations: ['39-29=10'] Exploring Operation: 60/10=6, Resulting Numbers: [44, 6] Generated Node #0,1,0: 50:[44, 6] Operation: 60/10=6 Moving to Node #0,1,0 Current State: 50:[44, 6], Operations: ['39-29=10', '60/10=6'] Exploring Operation: 44+6=50, Resulting Numbers: [50] 50,50 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.962674
hs_3
sum_heuristic
[ 53, 37, 42, 42 ]
15
[ "53-37=16", "42/42=1", "16-1=15" ]
Current State: 15:[53, 37, 42, 42], Operations: [] Exploring Operation: 53-37=16, Resulting Numbers: [42, 42, 16] Generated Node #2: [42, 42, 16] from Operation: 53-37=16 Current State: 15:[42, 42, 16], Operations: ['53-37=16'] Exploring Operation: 42/42=1, Resulting Numbers: [16, 1] Generated Node #3: [16, 1] from Operation: 42/42=1 Current State: 15:[16, 1], Operations: ['53-37=16', '42/42=1'] Exploring Operation: 16-1=15, Resulting Numbers: [15] 15,15 equal: Goal Reached
4
Current State: 15:[53, 37, 42, 42], Operations: [] Exploring Operation: 53-37=16, Resulting Numbers: [42, 42, 16] Generated Node #0,0: 15:[42, 42, 16] Operation: 53-37=16 Exploring Operation: 53-42=11, Resulting Numbers: [37, 42, 11] Generated Node #0,1: 15:[37, 42, 11] Operation: 53-42=11 Exploring Operation: 53-42=11, Resulting Numbers: [37, 42, 11] Generated Node #0,2: 15:[37, 42, 11] Operation: 53-42=11 Moving to Node #0,1 Current State: 15:[37, 42, 11], Operations: ['53-42=11'] Exploring Operation: 42-11=31, Resulting Numbers: [37, 31] Generated Node #0,1,0: 15:[37, 31] Operation: 42-11=31 Exploring Operation: 42-37=5, Resulting Numbers: [11, 5] Generated Node #0,1,1: 15:[11, 5] Operation: 42-37=5 Exploring Operation: 37-11=26, Resulting Numbers: [42, 26] Generated Node #0,1,2: 15:[42, 26] Operation: 37-11=26 Moving to Node #0,2 Current State: 15:[37, 42, 11], Operations: ['53-42=11'] Exploring Operation: 37-11=26, Resulting Numbers: [42, 26] Generated Node #0,2,0: 15:[42, 26] Operation: 37-11=26 Exploring Operation: 42-11=31, Resulting Numbers: [37, 31] Generated Node #0,2,1: 15:[37, 31] Operation: 42-11=31 Exploring Operation: 42-37=5, Resulting Numbers: [11, 5] Generated Node #0,2,2: 15:[11, 5] Operation: 42-37=5 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 15:[11, 5], Operations: ['53-42=11', '42-37=5'] Exploring Operation: 11*5=55, Resulting Numbers: [55] 55,15 unequal: No Solution Exploring Operation: 11-5=6, Resulting Numbers: [6] 6,15 unequal: No Solution Exploring Operation: 11+5=16, Resulting Numbers: [16] 16,15 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 15:[42, 26], Operations: ['53-42=11', '37-11=26'] Exploring Operation: 42+26=68, Resulting Numbers: [68] 68,15 unequal: No Solution Exploring Operation: 42*26=1092, Resulting Numbers: [1092] 1092,15 unequal: No Solution Exploring Operation: 42-26=16, Resulting Numbers: [16] 16,15 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 15:[37, 31], Operations: ['53-42=11', '42-11=31'] Exploring Operation: 37*31=1147, Resulting Numbers: [1147] 1147,15 unequal: No Solution Exploring Operation: 37+31=68, Resulting Numbers: [68] 68,15 unequal: No Solution Exploring Operation: 37-31=6, Resulting Numbers: [6] 6,15 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0 Current State: 15:[42, 42, 16], Operations: ['53-37=16'] Exploring Operation: 42-16=26, Resulting Numbers: [42, 26] Generated Node #0,0,0: 15:[42, 26] Operation: 42-16=26 Exploring Operation: 42/42=1, Resulting Numbers: [16, 1] Generated Node #0,0,1: 15:[16, 1] Operation: 42/42=1 Exploring Operation: 42-42=0, Resulting Numbers: [16, 0] Generated Node #0,0,2: 15:[16, 0] Operation: 42-42=0 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 15:[16, 1], Operations: ['53-37=16', '42/42=1'] Exploring Operation: 16/1=16, Resulting Numbers: [16] 16,15 unequal: No Solution Exploring Operation: 16-1=15, Resulting Numbers: [15] 15,15 equal: Goal Reached Moving to Node #0 Current State: 15:[53, 37, 42, 42], Operations: [] Exploring Operation: 53-37=16, Resulting Numbers: [42, 42, 16] Generated Node #0,0: 15:[42, 42, 16] Operation: 53-37=16 Moving to Node #0,0 Current State: 15:[42, 42, 16], Operations: ['53-37=16'] Exploring Operation: 42/42=1, Resulting Numbers: [16, 1] Generated Node #0,0,1: 15:[16, 1] Operation: 42/42=1 Moving to Node #0,0,1 Current State: 15:[16, 1], Operations: ['53-37=16', '42/42=1'] Exploring Operation: 16-1=15, Resulting Numbers: [15] 15,15 equal: Goal Reached Exit Sub Search at level 1
0.976563
hs_3
sum_heuristic
[ 21, 16, 76, 27 ]
54
[ "21-16=5", "76-27=49", "5+49=54" ]
Current State: 54:[21, 16, 76, 27], Operations: [] Exploring Operation: 21-16=5, Resulting Numbers: [76, 27, 5] Generated Node #2: [76, 27, 5] from Operation: 21-16=5 Current State: 54:[76, 27, 5], Operations: ['21-16=5'] Exploring Operation: 76-27=49, Resulting Numbers: [5, 49] Generated Node #3: [5, 49] from Operation: 76-27=49 Current State: 54:[5, 49], Operations: ['21-16=5', '76-27=49'] Exploring Operation: 5+49=54, Resulting Numbers: [54] 54,54 equal: Goal Reached
4
Current State: 54:[21, 16, 76, 27], Operations: [] Exploring Operation: 76-21=55, Resulting Numbers: [16, 27, 55] Generated Node #0,0: 54:[16, 27, 55] Operation: 76-21=55 Exploring Operation: 76-27=49, Resulting Numbers: [21, 16, 49] Generated Node #0,1: 54:[21, 16, 49] Operation: 76-27=49 Exploring Operation: 76-16=60, Resulting Numbers: [21, 27, 60] Generated Node #0,2: 54:[21, 27, 60] Operation: 76-16=60 Start Sub Search at level 1: Moving to Node #0,0 Current State: 54:[16, 27, 55], Operations: ['76-21=55'] Exploring Operation: 16+27=43, Resulting Numbers: [55, 43] Generated Node #0,0,0: 54:[55, 43] Operation: 16+27=43 Exploring Operation: 27-16=11, Resulting Numbers: [55, 11] Generated Node #0,0,1: 54:[55, 11] Operation: 27-16=11 Exploring Operation: 55-27=28, Resulting Numbers: [16, 28] Generated Node #0,0,2: 54:[16, 28] Operation: 55-27=28 Moving to Node #0,0,1 Current State: 54:[55, 11], Operations: ['76-21=55', '27-16=11'] Exploring Operation: 55-11=44, Resulting Numbers: [44] 44,54 unequal: No Solution Exploring Operation: 55/11=5, Resulting Numbers: [5] 5,54 unequal: No Solution Exploring Operation: 55+11=66, Resulting Numbers: [66] 66,54 unequal: No Solution Moving to Node #0,0,2 Current State: 54:[16, 28], Operations: ['76-21=55', '55-27=28'] Exploring Operation: 16*28=448, Resulting Numbers: [448] 448,54 unequal: No Solution Exploring Operation: 28-16=12, Resulting Numbers: [12] 12,54 unequal: No Solution Exploring Operation: 16+28=44, Resulting Numbers: [44] 44,54 unequal: No Solution Moving to Node #0,0,0 Current State: 54:[55, 43], Operations: ['76-21=55', '16+27=43'] Exploring Operation: 55-43=12, Resulting Numbers: [12] 12,54 unequal: No Solution Exploring Operation: 55*43=2365, Resulting Numbers: [2365] 2365,54 unequal: No Solution Exploring Operation: 55+43=98, Resulting Numbers: [98] 98,54 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 54:[21, 27, 60], Operations: ['76-16=60'] Exploring Operation: 27-21=6, Resulting Numbers: [60, 6] Generated Node #0,2,0: 54:[60, 6] Operation: 27-21=6 Exploring Operation: 60-27=33, Resulting Numbers: [21, 33] Generated Node #0,2,1: 54:[21, 33] Operation: 60-27=33 Exploring Operation: 21+27=48, Resulting Numbers: [60, 48] Generated Node #0,2,2: 54:[60, 48] Operation: 21+27=48 Moving to Node #0,2,0 Current State: 54:[60, 6], Operations: ['76-16=60', '27-21=6'] Exploring Operation: 60/6=10, Resulting Numbers: [10] 10,54 unequal: No Solution Exploring Operation: 60-6=54, Resulting Numbers: [54] 54,54 equal: Goal Reached Moving to Node #0 Current State: 54:[21, 16, 76, 27], Operations: [] Exploring Operation: 76-16=60, Resulting Numbers: [21, 27, 60] Generated Node #0,2: 54:[21, 27, 60] Operation: 76-16=60 Moving to Node #0,2 Current State: 54:[21, 27, 60], Operations: ['76-16=60'] Exploring Operation: 27-21=6, Resulting Numbers: [60, 6] Generated Node #0,2,0: 54:[60, 6] Operation: 27-21=6 Moving to Node #0,2,0 Current State: 54:[60, 6], Operations: ['76-16=60', '27-21=6'] Exploring Operation: 60-6=54, Resulting Numbers: [54] 54,54 equal: Goal Reached Exit Sub Search at level 1
0.979167
hs_3
mult_heuristic
[ 24, 5, 22, 41 ]
23
[ "24-22=2", "5+41=46", "46/2=23" ]
Current State: 23:[24, 5, 22, 41], Operations: [] Exploring Operation: 24-22=2, Resulting Numbers: [5, 41, 2] Generated Node #2: [5, 41, 2] from Operation: 24-22=2 Current State: 23:[5, 41, 2], Operations: ['24-22=2'] Exploring Operation: 5+41=46, Resulting Numbers: [2, 46] Generated Node #3: [2, 46] from Operation: 5+41=46 Current State: 23:[2, 46], Operations: ['24-22=2', '5+41=46'] Exploring Operation: 46/2=23, Resulting Numbers: [23] 23,23 equal: Goal Reached
4
Current State: 23:[24, 5, 22, 41], Operations: [] Exploring Operation: 41-5=36, Resulting Numbers: [24, 22, 36] Generated Node #0,0: 23:[24, 22, 36] Operation: 41-5=36 Exploring Operation: 24-5=19, Resulting Numbers: [22, 41, 19] Generated Node #0,1: 23:[22, 41, 19] Operation: 24-5=19 Moving to Node #0,0 Current State: 23:[24, 22, 36], Operations: ['41-5=36'] Exploring Operation: 36-24=12, Resulting Numbers: [22, 12] Generated Node #0,0,0: 23:[22, 12] Operation: 36-24=12 Exploring Operation: 36-22=14, Resulting Numbers: [24, 14] Generated Node #0,0,1: 23:[24, 14] Operation: 36-22=14 Moving to Node #0,1 Current State: 23:[22, 41, 19], Operations: ['24-5=19'] Exploring Operation: 41-19=22, Resulting Numbers: [22, 22] Generated Node #0,1,0: 23:[22, 22] Operation: 41-19=22 Exploring Operation: 41-22=19, Resulting Numbers: [19, 19] Generated Node #0,1,1: 23:[19, 19] Operation: 41-22=19 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 23:[22, 22], Operations: ['24-5=19', '41-19=22'] Exploring Operation: 22+22=44, Resulting Numbers: [44] 44,23 unequal: No Solution Exploring Operation: 22/22=1, Resulting Numbers: [1] 1,23 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 23:[19, 19], Operations: ['24-5=19', '41-22=19'] Exploring Operation: 19+19=38, Resulting Numbers: [38] 38,23 unequal: No Solution Exploring Operation: 19/19=1, Resulting Numbers: [1] 1,23 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0,1 Current State: 23:[24, 14], Operations: ['41-5=36', '36-22=14'] Exploring Operation: 24+14=38, Resulting Numbers: [38] 38,23 unequal: No Solution Exploring Operation: 24-14=10, Resulting Numbers: [10] 10,23 unequal: No Solution Moving to Node #0,0,0 Current State: 23:[22, 12], Operations: ['41-5=36', '36-24=12'] Exploring Operation: 22+12=34, Resulting Numbers: [34] 34,23 unequal: No Solution Exploring Operation: 22-12=10, Resulting Numbers: [10] 10,23 unequal: No Solution No solution found.
0
hs_2
sum_heuristic
[ 22, 33, 27, 40 ]
58
[ "22*27=594", "594/33=18", "40+18=58" ]
Current State: 58:[22, 33, 27, 40], Operations: [] Exploring Operation: 22*27=594, Resulting Numbers: [33, 40, 594] Generated Node #2: [33, 40, 594] from Operation: 22*27=594 Current State: 58:[33, 40, 594], Operations: ['22*27=594'] Exploring Operation: 594/33=18, Resulting Numbers: [40, 18] Generated Node #3: [40, 18] from Operation: 594/33=18 Current State: 58:[40, 18], Operations: ['22*27=594', '594/33=18'] Exploring Operation: 40+18=58, Resulting Numbers: [58] 58,58 equal: Goal Reached
4
Current State: 58:[22, 33, 27, 40], Operations: [] Exploring Operation: 22+40=62, Resulting Numbers: [33, 27, 62] Generated Node #0,0: 58:[33, 27, 62] Operation: 22+40=62 Moving to Node #0,0 Current State: 58:[33, 27, 62], Operations: ['22+40=62'] Exploring Operation: 62-33=29, Resulting Numbers: [27, 29] Generated Node #0,0,0: 58:[27, 29] Operation: 62-33=29 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 58:[27, 29], Operations: ['22+40=62', '62-33=29'] Exploring Operation: 29-27=2, Resulting Numbers: [2] 2,58 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
sum_heuristic
[ 37, 2, 75, 36 ]
75
[ "37-2=35", "36-35=1", "75*1=75" ]
Current State: 75:[37, 2, 75, 36], Operations: [] Exploring Operation: 37-2=35, Resulting Numbers: [75, 36, 35] Generated Node #2: [75, 36, 35] from Operation: 37-2=35 Current State: 75:[75, 36, 35], Operations: ['37-2=35'] Exploring Operation: 36-35=1, Resulting Numbers: [75, 1] Generated Node #3: [75, 1] from Operation: 36-35=1 Current State: 75:[75, 1], Operations: ['37-2=35', '36-35=1'] Exploring Operation: 75*1=75, Resulting Numbers: [75] 75,75 equal: Goal Reached
4
Current State: 75:[37, 2, 75, 36], Operations: [] Exploring Operation: 37+36=73, Resulting Numbers: [2, 75, 73] Generated Node #0,0: 75:[2, 75, 73] Operation: 37+36=73 Moving to Node #0,0 Current State: 75:[2, 75, 73], Operations: ['37+36=73'] Exploring Operation: 2+73=75, Resulting Numbers: [75, 75] Generated Node #0,0,0: 75:[75, 75] Operation: 2+73=75 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 75:[75, 75], Operations: ['37+36=73', '2+73=75'] Exploring Operation: 75/75=1, Resulting Numbers: [1] 1,75 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
mult_heuristic
[ 80, 69, 38, 43 ]
73
[ "80*38=3040", "69*43=2967", "3040-2967=73" ]
Current State: 73:[80, 69, 38, 43], Operations: [] Exploring Operation: 80*38=3040, Resulting Numbers: [69, 43, 3040] Generated Node #2: [69, 43, 3040] from Operation: 80*38=3040 Current State: 73:[69, 43, 3040], Operations: ['80*38=3040'] Exploring Operation: 69*43=2967, Resulting Numbers: [3040, 2967] Generated Node #3: [3040, 2967] from Operation: 69*43=2967 Current State: 73:[3040, 2967], Operations: ['80*38=3040', '69*43=2967'] Exploring Operation: 3040-2967=73, Resulting Numbers: [73] 73,73 equal: Goal Reached
4
Current State: 73:[80, 69, 38, 43], Operations: [] Exploring Operation: 80-38=42, Resulting Numbers: [69, 43, 42] Generated Node #0,0: 73:[69, 43, 42] Operation: 80-38=42 Exploring Operation: 38+43=81, Resulting Numbers: [80, 69, 81] Generated Node #0,1: 73:[80, 69, 81] Operation: 38+43=81 Exploring Operation: 80-43=37, Resulting Numbers: [69, 38, 37] Generated Node #0,2: 73:[69, 38, 37] Operation: 80-43=37 Exploring Operation: 69+38=107, Resulting Numbers: [80, 43, 107] Generated Node #0,3: 73:[80, 43, 107] Operation: 69+38=107 Exploring Operation: 80+38=118, Resulting Numbers: [69, 43, 118] Generated Node #0,4: 73:[69, 43, 118] Operation: 80+38=118 Moving to Node #0,1 Current State: 73:[80, 69, 81], Operations: ['38+43=81'] Exploring Operation: 81-69=12, Resulting Numbers: [80, 12] Generated Node #0,1,0: 73:[80, 12] Operation: 81-69=12 Exploring Operation: 80-69=11, Resulting Numbers: [81, 11] Generated Node #0,1,1: 73:[81, 11] Operation: 80-69=11 Exploring Operation: 81-80=1, Resulting Numbers: [69, 1] Generated Node #0,1,2: 73:[69, 1] Operation: 81-80=1 Exploring Operation: 69+81=150, Resulting Numbers: [80, 150] Generated Node #0,1,3: 73:[80, 150] Operation: 69+81=150 Exploring Operation: 80+69=149, Resulting Numbers: [81, 149] Generated Node #0,1,4: 73:[81, 149] Operation: 80+69=149 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 73:[80, 12], Operations: ['38+43=81', '81-69=12'] Exploring Operation: 80-12=68, Resulting Numbers: [68] 68,73 unequal: No Solution Exploring Operation: 80+12=92, Resulting Numbers: [92] 92,73 unequal: No Solution Exploring Operation: 80*12=960, Resulting Numbers: [960] 960,73 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 73:[81, 11], Operations: ['38+43=81', '80-69=11'] Exploring Operation: 81*11=891, Resulting Numbers: [891] 891,73 unequal: No Solution Exploring Operation: 81-11=70, Resulting Numbers: [70] 70,73 unequal: No Solution Exploring Operation: 81+11=92, Resulting Numbers: [92] 92,73 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 73:[69, 1], Operations: ['38+43=81', '81-80=1'] Exploring Operation: 69*1=69, Resulting Numbers: [69] 69,73 unequal: No Solution Exploring Operation: 69-1=68, Resulting Numbers: [68] 68,73 unequal: No Solution Exploring Operation: 69+1=70, Resulting Numbers: [70] 70,73 unequal: No Solution Exploring Operation: 69/1=69, Resulting Numbers: [69] 69,73 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 73:[80, 150], Operations: ['38+43=81', '69+81=150'] Exploring Operation: 80+150=230, Resulting Numbers: [230] 230,73 unequal: No Solution Exploring Operation: 80*150=12000, Resulting Numbers: [12000] 12000,73 unequal: No Solution Exploring Operation: 150-80=70, Resulting Numbers: [70] 70,73 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,4 Current State: 73:[81, 149], Operations: ['38+43=81', '80+69=149'] Exploring Operation: 81*149=12069, Resulting Numbers: [12069] 12069,73 unequal: No Solution Exploring Operation: 149-81=68, Resulting Numbers: [68] 68,73 unequal: No Solution Exploring Operation: 81+149=230, Resulting Numbers: [230] 230,73 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0 Current State: 73:[69, 43, 42], Operations: ['80-38=42'] Exploring Operation: 69+42=111, Resulting Numbers: [43, 111] Generated Node #0,0,0: 73:[43, 111] Operation: 69+42=111 Exploring Operation: 69+43=112, Resulting Numbers: [42, 112] Generated Node #0,0,1: 73:[42, 112] Operation: 69+43=112 Exploring Operation: 69-42=27, Resulting Numbers: [43, 27] Generated Node #0,0,2: 73:[43, 27] Operation: 69-42=27 Exploring Operation: 43-42=1, Resulting Numbers: [69, 1] Generated Node #0,0,3: 73:[69, 1] Operation: 43-42=1 Exploring Operation: 43+42=85, Resulting Numbers: [69, 85] Generated Node #0,0,4: 73:[69, 85] Operation: 43+42=85 Moving to Node #0,3 Current State: 73:[80, 43, 107], Operations: ['69+38=107'] Exploring Operation: 107-80=27, Resulting Numbers: [43, 27] Generated Node #0,3,0: 73:[43, 27] Operation: 107-80=27 Exploring Operation: 107-43=64, Resulting Numbers: [80, 64] Generated Node #0,3,1: 73:[80, 64] Operation: 107-43=64 Exploring Operation: 80+43=123, Resulting Numbers: [107, 123] Generated Node #0,3,2: 73:[107, 123] Operation: 80+43=123 Exploring Operation: 43+107=150, Resulting Numbers: [80, 150] Generated Node #0,3,3: 73:[80, 150] Operation: 43+107=150 Exploring Operation: 80-43=37, Resulting Numbers: [107, 37] Generated Node #0,3,4: 73:[107, 37] Operation: 80-43=37 Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 73:[80, 64], Operations: ['69+38=107', '107-43=64'] Exploring Operation: 80+64=144, Resulting Numbers: [144] 144,73 unequal: No Solution Exploring Operation: 80-64=16, Resulting Numbers: [16] 16,73 unequal: No Solution Exploring Operation: 80*64=5120, Resulting Numbers: [5120] 5120,73 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,4 Current State: 73:[107, 37], Operations: ['69+38=107', '80-43=37'] Exploring Operation: 107*37=3959, Resulting Numbers: [3959] 3959,73 unequal: No Solution Exploring Operation: 107-37=70, Resulting Numbers: [70] 70,73 unequal: No Solution Exploring Operation: 107+37=144, Resulting Numbers: [144] 144,73 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 73:[43, 27], Operations: ['69+38=107', '107-80=27'] Exploring Operation: 43+27=70, Resulting Numbers: [70] 70,73 unequal: No Solution Exploring Operation: 43-27=16, Resulting Numbers: [16] 16,73 unequal: No Solution Exploring Operation: 43*27=1161, Resulting Numbers: [1161] 1161,73 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 73:[107, 123], Operations: ['69+38=107', '80+43=123'] Exploring Operation: 123-107=16, Resulting Numbers: [16] 16,73 unequal: No Solution Exploring Operation: 107*123=13161, Resulting Numbers: [13161] 13161,73 unequal: No Solution Exploring Operation: 107+123=230, Resulting Numbers: [230] 230,73 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 73:[80, 150], Operations: ['69+38=107', '43+107=150'] Exploring Operation: 80+150=230, Resulting Numbers: [230] 230,73 unequal: No Solution Exploring Operation: 150-80=70, Resulting Numbers: [70] 70,73 unequal: No Solution Exploring Operation: 80*150=12000, Resulting Numbers: [12000] 12000,73 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2 Current State: 73:[69, 38, 37], Operations: ['80-43=37'] Exploring Operation: 69+37=106, Resulting Numbers: [38, 106] Generated Node #0,2,0: 73:[38, 106] Operation: 69+37=106 Exploring Operation: 38-37=1, Resulting Numbers: [69, 1] Generated Node #0,2,1: 73:[69, 1] Operation: 38-37=1 Exploring Operation: 69+38=107, Resulting Numbers: [37, 107] Generated Node #0,2,2: 73:[37, 107] Operation: 69+38=107 Exploring Operation: 69-37=32, Resulting Numbers: [38, 32] Generated Node #0,2,3: 73:[38, 32] Operation: 69-37=32 Exploring Operation: 38+37=75, Resulting Numbers: [69, 75] Generated Node #0,2,4: 73:[69, 75] Operation: 38+37=75 Moving to Node #0,4 Current State: 73:[69, 43, 118], Operations: ['80+38=118'] Exploring Operation: 43+118=161, Resulting Numbers: [69, 161] Generated Node #0,4,0: 73:[69, 161] Operation: 43+118=161 Exploring Operation: 118-69=49, Resulting Numbers: [43, 49] Generated Node #0,4,1: 73:[43, 49] Operation: 118-69=49 Exploring Operation: 69-43=26, Resulting Numbers: [118, 26] Generated Node #0,4,2: 73:[118, 26] Operation: 69-43=26 Exploring Operation: 118-43=75, Resulting Numbers: [69, 75] Generated Node #0,4,3: 73:[69, 75] Operation: 118-43=75 Exploring Operation: 69+43=112, Resulting Numbers: [118, 112] Generated Node #0,4,4: 73:[118, 112] Operation: 69+43=112 Start Sub Search at level 1: Moving to Node #0,4,3 Current State: 73:[69, 75], Operations: ['80+38=118', '118-43=75'] Exploring Operation: 69+75=144, Resulting Numbers: [144] 144,73 unequal: No Solution Exploring Operation: 69*75=5175, Resulting Numbers: [5175] 5175,73 unequal: No Solution Exploring Operation: 75-69=6, Resulting Numbers: [6] 6,73 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,1 Current State: 73:[43, 49], Operations: ['80+38=118', '118-69=49'] Exploring Operation: 43+49=92, Resulting Numbers: [92] 92,73 unequal: No Solution Exploring Operation: 49-43=6, Resulting Numbers: [6] 6,73 unequal: No Solution Exploring Operation: 43*49=2107, Resulting Numbers: [2107] 2107,73 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,4 Current State: 73:[118, 112], Operations: ['80+38=118', '69+43=112'] Exploring Operation: 118-112=6, Resulting Numbers: [6] 6,73 unequal: No Solution Exploring Operation: 118*112=13216, Resulting Numbers: [13216] 13216,73 unequal: No Solution Exploring Operation: 118+112=230, Resulting Numbers: [230] 230,73 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,0 Current State: 73:[69, 161], Operations: ['80+38=118', '43+118=161'] Exploring Operation: 69*161=11109, Resulting Numbers: [11109] 11109,73 unequal: No Solution Exploring Operation: 69+161=230, Resulting Numbers: [230] 230,73 unequal: No Solution Exploring Operation: 161-69=92, Resulting Numbers: [92] 92,73 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,2 Current State: 73:[118, 26], Operations: ['80+38=118', '69-43=26'] Exploring Operation: 118*26=3068, Resulting Numbers: [3068] 3068,73 unequal: No Solution Exploring Operation: 118+26=144, Resulting Numbers: [144] 144,73 unequal: No Solution Exploring Operation: 118-26=92, Resulting Numbers: [92] 92,73 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2,4 Current State: 73:[69, 75], Operations: ['80-43=37', '38+37=75'] Exploring Operation: 69+75=144, Resulting Numbers: [144] 144,73 unequal: No Solution Exploring Operation: 69*75=5175, Resulting Numbers: [5175] 5175,73 unequal: No Solution Exploring Operation: 75-69=6, Resulting Numbers: [6] 6,73 unequal: No Solution Moving to Node #0,0,4 Current State: 73:[69, 85], Operations: ['80-38=42', '43+42=85'] Exploring Operation: 85-69=16, Resulting Numbers: [16] 16,73 unequal: No Solution Exploring Operation: 69*85=5865, Resulting Numbers: [5865] 5865,73 unequal: No Solution Exploring Operation: 69+85=154, Resulting Numbers: [154] 154,73 unequal: No Solution Moving to Node #0,2,0 Current State: 73:[38, 106], Operations: ['80-43=37', '69+37=106'] Exploring Operation: 106-38=68, Resulting Numbers: [68] 68,73 unequal: No Solution Exploring Operation: 38+106=144, Resulting Numbers: [144] 144,73 unequal: No Solution Exploring Operation: 38*106=4028, Resulting Numbers: [4028] 4028,73 unequal: No Solution Moving to Node #0,0,0 Current State: 73:[43, 111], Operations: ['80-38=42', '69+42=111'] Exploring Operation: 111-43=68, Resulting Numbers: [68] 68,73 unequal: No Solution Exploring Operation: 43*111=4773, Resulting Numbers: [4773] 4773,73 unequal: No Solution Exploring Operation: 43+111=154, Resulting Numbers: [154] 154,73 unequal: No Solution Moving to Node #0,0,1 Current State: 73:[42, 112], Operations: ['80-38=42', '69+43=112'] Exploring Operation: 42+112=154, Resulting Numbers: [154] 154,73 unequal: No Solution Exploring Operation: 112-42=70, Resulting Numbers: [70] 70,73 unequal: No Solution Exploring Operation: 42*112=4704, Resulting Numbers: [4704] 4704,73 unequal: No Solution Moving to Node #0,2,2 Current State: 73:[37, 107], Operations: ['80-43=37', '69+38=107'] Exploring Operation: 37+107=144, Resulting Numbers: [144] 144,73 unequal: No Solution Exploring Operation: 37*107=3959, Resulting Numbers: [3959] 3959,73 unequal: No Solution Exploring Operation: 107-37=70, Resulting Numbers: [70] 70,73 unequal: No Solution Moving to Node #0,2,1 Current State: 73:[69, 1], Operations: ['80-43=37', '38-37=1'] Exploring Operation: 69+1=70, Resulting Numbers: [70] 70,73 unequal: No Solution Exploring Operation: 69/1=69, Resulting Numbers: [69] 69,73 unequal: No Solution Exploring Operation: 69*1=69, Resulting Numbers: [69] 69,73 unequal: No Solution Exploring Operation: 69-1=68, Resulting Numbers: [68] 68,73 unequal: No Solution Moving to Node #0,2,3 Current State: 73:[38, 32], Operations: ['80-43=37', '69-37=32'] Exploring Operation: 38*32=1216, Resulting Numbers: [1216] 1216,73 unequal: No Solution Exploring Operation: 38+32=70, Resulting Numbers: [70] 70,73 unequal: No Solution Exploring Operation: 38-32=6, Resulting Numbers: [6] 6,73 unequal: No Solution Moving to Node #0,0,3 Current State: 73:[69, 1], Operations: ['80-38=42', '43-42=1'] Exploring Operation: 69-1=68, Resulting Numbers: [68] 68,73 unequal: No Solution Exploring Operation: 69*1=69, Resulting Numbers: [69] 69,73 unequal: No Solution Exploring Operation: 69+1=70, Resulting Numbers: [70] 70,73 unequal: No Solution Exploring Operation: 69/1=69, Resulting Numbers: [69] 69,73 unequal: No Solution Moving to Node #0,0,2 Current State: 73:[43, 27], Operations: ['80-38=42', '69-42=27'] Exploring Operation: 43+27=70, Resulting Numbers: [70] 70,73 unequal: No Solution Exploring Operation: 43-27=16, Resulting Numbers: [16] 16,73 unequal: No Solution Exploring Operation: 43*27=1161, Resulting Numbers: [1161] 1161,73 unequal: No Solution No solution found.
0
hs_5
sum_heuristic
[ 93, 13, 43, 56 ]
67
[ "93-13=80", "56-43=13", "80-13=67" ]
Current State: 67:[93, 13, 43, 56], Operations: [] Exploring Operation: 93-13=80, Resulting Numbers: [43, 56, 80] Generated Node #2: [43, 56, 80] from Operation: 93-13=80 Current State: 67:[43, 56, 80], Operations: ['93-13=80'] Exploring Operation: 56-43=13, Resulting Numbers: [80, 13] Generated Node #3: [80, 13] from Operation: 56-43=13 Current State: 67:[80, 13], Operations: ['93-13=80', '56-43=13'] Exploring Operation: 80-13=67, Resulting Numbers: [67] 67,67 equal: Goal Reached
4
Current State: 67:[93, 13, 43, 56], Operations: [] Exploring Operation: 13+56=69, Resulting Numbers: [93, 43, 69] Generated Node #0,0: 67:[93, 43, 69] Operation: 13+56=69 Exploring Operation: 93+13=106, Resulting Numbers: [43, 56, 106] Generated Node #0,1: 67:[43, 56, 106] Operation: 93+13=106 Exploring Operation: 43-13=30, Resulting Numbers: [93, 56, 30] Generated Node #0,2: 67:[93, 56, 30] Operation: 43-13=30 Exploring Operation: 93-13=80, Resulting Numbers: [43, 56, 80] Generated Node #0,3: 67:[43, 56, 80] Operation: 93-13=80 Exploring Operation: 13+43=56, Resulting Numbers: [93, 56, 56] Generated Node #0,4: 67:[93, 56, 56] Operation: 13+43=56 Start Sub Search at level 1: Moving to Node #0,3 Current State: 67:[43, 56, 80], Operations: ['93-13=80'] Exploring Operation: 80-43=37, Resulting Numbers: [56, 37] Generated Node #0,3,0: 67:[56, 37] Operation: 80-43=37 Exploring Operation: 80-56=24, Resulting Numbers: [43, 24] Generated Node #0,3,1: 67:[43, 24] Operation: 80-56=24 Exploring Operation: 43+80=123, Resulting Numbers: [56, 123] Generated Node #0,3,2: 67:[56, 123] Operation: 43+80=123 Exploring Operation: 43+56=99, Resulting Numbers: [80, 99] Generated Node #0,3,3: 67:[80, 99] Operation: 43+56=99 Exploring Operation: 56-43=13, Resulting Numbers: [80, 13] Generated Node #0,3,4: 67:[80, 13] Operation: 56-43=13 Moving to Node #0,3,0 Current State: 67:[56, 37], Operations: ['93-13=80', '80-43=37'] Exploring Operation: 56-37=19, Resulting Numbers: [19] 19,67 unequal: No Solution Exploring Operation: 56*37=2072, Resulting Numbers: [2072] 2072,67 unequal: No Solution Exploring Operation: 56+37=93, Resulting Numbers: [93] 93,67 unequal: No Solution Moving to Node #0,3,3 Current State: 67:[80, 99], Operations: ['93-13=80', '43+56=99'] Exploring Operation: 99-80=19, Resulting Numbers: [19] 19,67 unequal: No Solution Exploring Operation: 80*99=7920, Resulting Numbers: [7920] 7920,67 unequal: No Solution Exploring Operation: 80+99=179, Resulting Numbers: [179] 179,67 unequal: No Solution Moving to Node #0,3,1 Current State: 67:[43, 24], Operations: ['93-13=80', '80-56=24'] Exploring Operation: 43-24=19, Resulting Numbers: [19] 19,67 unequal: No Solution Exploring Operation: 43*24=1032, Resulting Numbers: [1032] 1032,67 unequal: No Solution Exploring Operation: 43+24=67, Resulting Numbers: [67] 67,67 equal: Goal Reached Moving to Node #0 Current State: 67:[93, 13, 43, 56], Operations: [] Exploring Operation: 93-13=80, Resulting Numbers: [43, 56, 80] Generated Node #0,3: 67:[43, 56, 80] Operation: 93-13=80 Moving to Node #0,3 Current State: 67:[43, 56, 80], Operations: ['93-13=80'] Exploring Operation: 80-56=24, Resulting Numbers: [43, 24] Generated Node #0,3,1: 67:[43, 24] Operation: 80-56=24 Moving to Node #0,3,1 Current State: 67:[43, 24], Operations: ['93-13=80', '80-56=24'] Exploring Operation: 43+24=67, Resulting Numbers: [67] 67,67 equal: Goal Reached Exit Sub Search at level 1
0.980035
hs_5
mult_heuristic
[ 86, 64, 87, 36 ]
99
[ "86+64=150", "87-36=51", "150-51=99" ]
Current State: 99:[86, 64, 87, 36], Operations: [] Exploring Operation: 86+64=150, Resulting Numbers: [87, 36, 150] Generated Node #2: [87, 36, 150] from Operation: 86+64=150 Current State: 99:[87, 36, 150], Operations: ['86+64=150'] Exploring Operation: 87-36=51, Resulting Numbers: [150, 51] Generated Node #3: [150, 51] from Operation: 87-36=51 Current State: 99:[150, 51], Operations: ['86+64=150', '87-36=51'] Exploring Operation: 150-51=99, Resulting Numbers: [99] 99,99 equal: Goal Reached
4
Current State: 99:[86, 64, 87, 36], Operations: [] Exploring Operation: 64-36=28, Resulting Numbers: [86, 87, 28] Generated Node #0,0: 99:[86, 87, 28] Operation: 64-36=28 Exploring Operation: 86-64=22, Resulting Numbers: [87, 36, 22] Generated Node #0,1: 99:[87, 36, 22] Operation: 86-64=22 Exploring Operation: 64+36=100, Resulting Numbers: [86, 87, 100] Generated Node #0,2: 99:[86, 87, 100] Operation: 64+36=100 Exploring Operation: 87-64=23, Resulting Numbers: [86, 36, 23] Generated Node #0,3: 99:[86, 36, 23] Operation: 87-64=23 Moving to Node #0,1 Current State: 99:[87, 36, 22], Operations: ['86-64=22'] Exploring Operation: 87+22=109, Resulting Numbers: [36, 109] Generated Node #0,1,0: 99:[36, 109] Operation: 87+22=109 Exploring Operation: 87+36=123, Resulting Numbers: [22, 123] Generated Node #0,1,1: 99:[22, 123] Operation: 87+36=123 Exploring Operation: 87-36=51, Resulting Numbers: [22, 51] Generated Node #0,1,2: 99:[22, 51] Operation: 87-36=51 Exploring Operation: 36-22=14, Resulting Numbers: [87, 14] Generated Node #0,1,3: 99:[87, 14] Operation: 36-22=14 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 99:[36, 109], Operations: ['86-64=22', '87+22=109'] Exploring Operation: 36+109=145, Resulting Numbers: [145] 145,99 unequal: No Solution Exploring Operation: 36*109=3924, Resulting Numbers: [3924] 3924,99 unequal: No Solution Exploring Operation: 109-36=73, Resulting Numbers: [73] 73,99 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 99:[87, 14], Operations: ['86-64=22', '36-22=14'] Exploring Operation: 87+14=101, Resulting Numbers: [101] 101,99 unequal: No Solution Exploring Operation: 87*14=1218, Resulting Numbers: [1218] 1218,99 unequal: No Solution Exploring Operation: 87-14=73, Resulting Numbers: [73] 73,99 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 99:[22, 51], Operations: ['86-64=22', '87-36=51'] Exploring Operation: 51-22=29, Resulting Numbers: [29] 29,99 unequal: No Solution Exploring Operation: 22*51=1122, Resulting Numbers: [1122] 1122,99 unequal: No Solution Exploring Operation: 22+51=73, Resulting Numbers: [73] 73,99 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 99:[22, 123], Operations: ['86-64=22', '87+36=123'] Exploring Operation: 123-22=101, Resulting Numbers: [101] 101,99 unequal: No Solution Exploring Operation: 22*123=2706, Resulting Numbers: [2706] 2706,99 unequal: No Solution Exploring Operation: 22+123=145, Resulting Numbers: [145] 145,99 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,3 Current State: 99:[86, 36, 23], Operations: ['87-64=23'] Exploring Operation: 86-36=50, Resulting Numbers: [23, 50] Generated Node #0,3,0: 99:[23, 50] Operation: 86-36=50 Exploring Operation: 86+23=109, Resulting Numbers: [36, 109] Generated Node #0,3,1: 99:[36, 109] Operation: 86+23=109 Exploring Operation: 86+36=122, Resulting Numbers: [23, 122] Generated Node #0,3,2: 99:[23, 122] Operation: 86+36=122 Exploring Operation: 36-23=13, Resulting Numbers: [86, 13] Generated Node #0,3,3: 99:[86, 13] Operation: 36-23=13 Moving to Node #0,2 Current State: 99:[86, 87, 100], Operations: ['64+36=100'] Exploring Operation: 86+87=173, Resulting Numbers: [100, 173] Generated Node #0,2,0: 99:[100, 173] Operation: 86+87=173 Exploring Operation: 100-86=14, Resulting Numbers: [87, 14] Generated Node #0,2,1: 99:[87, 14] Operation: 100-86=14 Exploring Operation: 87-86=1, Resulting Numbers: [100, 1] Generated Node #0,2,2: 99:[100, 1] Operation: 87-86=1 Exploring Operation: 100-87=13, Resulting Numbers: [86, 13] Generated Node #0,2,3: 99:[86, 13] Operation: 100-87=13 Moving to Node #0,0 Current State: 99:[86, 87, 28], Operations: ['64-36=28'] Exploring Operation: 87+28=115, Resulting Numbers: [86, 115] Generated Node #0,0,0: 99:[86, 115] Operation: 87+28=115 Exploring Operation: 86+28=114, Resulting Numbers: [87, 114] Generated Node #0,0,1: 99:[87, 114] Operation: 86+28=114 Exploring Operation: 86-28=58, Resulting Numbers: [87, 58] Generated Node #0,0,2: 99:[87, 58] Operation: 86-28=58 Exploring Operation: 87-86=1, Resulting Numbers: [28, 1] Generated Node #0,0,3: 99:[28, 1] Operation: 87-86=1 Moving to Node #0,2,2 Current State: 99:[100, 1], Operations: ['64+36=100', '87-86=1'] Exploring Operation: 100/1=100, Resulting Numbers: [100] 100,99 unequal: No Solution Exploring Operation: 100-1=99, Resulting Numbers: [99] 99,99 equal: Goal Reached Moving to Node #0 Current State: 99:[86, 64, 87, 36], Operations: [] Exploring Operation: 64+36=100, Resulting Numbers: [86, 87, 100] Generated Node #0,2: 99:[86, 87, 100] Operation: 64+36=100 Moving to Node #0,2 Current State: 99:[86, 87, 100], Operations: ['64+36=100'] Exploring Operation: 87-86=1, Resulting Numbers: [100, 1] Generated Node #0,2,2: 99:[100, 1] Operation: 87-86=1 Moving to Node #0,2,2 Current State: 99:[100, 1], Operations: ['64+36=100', '87-86=1'] Exploring Operation: 100-1=99, Resulting Numbers: [99] 99,99 equal: Goal Reached
0.967014
hs_4
mult_heuristic
[ 26, 79, 38, 2 ]
73
[ "38-26=12", "12/2=6", "79-6=73" ]
Current State: 73:[26, 79, 38, 2], Operations: [] Exploring Operation: 38-26=12, Resulting Numbers: [79, 2, 12] Generated Node #2: [79, 2, 12] from Operation: 38-26=12 Current State: 73:[79, 2, 12], Operations: ['38-26=12'] Exploring Operation: 12/2=6, Resulting Numbers: [79, 6] Generated Node #3: [79, 6] from Operation: 12/2=6 Current State: 73:[79, 6], Operations: ['38-26=12', '12/2=6'] Exploring Operation: 79-6=73, Resulting Numbers: [73] 73,73 equal: Goal Reached
4
Current State: 73:[26, 79, 38, 2], Operations: [] Exploring Operation: 26*2=52, Resulting Numbers: [79, 38, 52] Generated Node #0,0: 73:[79, 38, 52] Operation: 26*2=52 Exploring Operation: 38*2=76, Resulting Numbers: [26, 79, 76] Generated Node #0,1: 73:[26, 79, 76] Operation: 38*2=76 Start Sub Search at level 1: Moving to Node #0,1 Current State: 73:[26, 79, 76], Operations: ['38*2=76'] Exploring Operation: 76-26=50, Resulting Numbers: [79, 50] Generated Node #0,1,0: 73:[79, 50] Operation: 76-26=50 Exploring Operation: 79-26=53, Resulting Numbers: [76, 53] Generated Node #0,1,1: 73:[76, 53] Operation: 79-26=53 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 73:[76, 53], Operations: ['38*2=76', '79-26=53'] Exploring Operation: 76+53=129, Resulting Numbers: [129] 129,73 unequal: No Solution Exploring Operation: 76-53=23, Resulting Numbers: [23] 23,73 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 73:[79, 50], Operations: ['38*2=76', '76-26=50'] Exploring Operation: 79-50=29, Resulting Numbers: [29] 29,73 unequal: No Solution Exploring Operation: 79+50=129, Resulting Numbers: [129] 129,73 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 73:[79, 38, 52], Operations: ['26*2=52'] Exploring Operation: 79-38=41, Resulting Numbers: [52, 41] Generated Node #0,0,0: 73:[52, 41] Operation: 79-38=41 Exploring Operation: 38+52=90, Resulting Numbers: [79, 90] Generated Node #0,0,1: 73:[79, 90] Operation: 38+52=90 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 73:[79, 90], Operations: ['26*2=52', '38+52=90'] Exploring Operation: 90-79=11, Resulting Numbers: [11] 11,73 unequal: No Solution Exploring Operation: 79+90=169, Resulting Numbers: [169] 169,73 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 73:[52, 41], Operations: ['26*2=52', '79-38=41'] Exploring Operation: 52+41=93, Resulting Numbers: [93] 93,73 unequal: No Solution Exploring Operation: 52-41=11, Resulting Numbers: [11] 11,73 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
mult_heuristic
[ 26, 22, 72, 31 ]
99
[ "26-22=4", "72+31=103", "103-4=99" ]
Current State: 99:[26, 22, 72, 31], Operations: [] Exploring Operation: 26-22=4, Resulting Numbers: [72, 31, 4] Generated Node #2: [72, 31, 4] from Operation: 26-22=4 Current State: 99:[72, 31, 4], Operations: ['26-22=4'] Exploring Operation: 72+31=103, Resulting Numbers: [4, 103] Generated Node #3: [4, 103] from Operation: 72+31=103 Current State: 99:[4, 103], Operations: ['26-22=4', '72+31=103'] Exploring Operation: 103-4=99, Resulting Numbers: [99] 99,99 equal: Goal Reached
4
Current State: 99:[26, 22, 72, 31], Operations: [] Exploring Operation: 26+72=98, Resulting Numbers: [22, 31, 98] Generated Node #0,0: 99:[22, 31, 98] Operation: 26+72=98 Start Sub Search at level 1: Moving to Node #0,0 Current State: 99:[22, 31, 98], Operations: ['26+72=98'] Exploring Operation: 31-22=9, Resulting Numbers: [98, 9] Generated Node #0,0,0: 99:[98, 9] Operation: 31-22=9 Moving to Node #0,0,0 Current State: 99:[98, 9], Operations: ['26+72=98', '31-22=9'] Exploring Operation: 98+9=107, Resulting Numbers: [107] 107,99 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
mult_heuristic
[ 11, 98, 75, 3 ]
37
[ "11+98=109", "75-3=72", "109-72=37" ]
Current State: 37:[11, 98, 75, 3], Operations: [] Exploring Operation: 11+98=109, Resulting Numbers: [75, 3, 109] Generated Node #2: [75, 3, 109] from Operation: 11+98=109 Current State: 37:[75, 3, 109], Operations: ['11+98=109'] Exploring Operation: 75-3=72, Resulting Numbers: [109, 72] Generated Node #3: [109, 72] from Operation: 75-3=72 Current State: 37:[109, 72], Operations: ['11+98=109', '75-3=72'] Exploring Operation: 109-72=37, Resulting Numbers: [37] 37,37 equal: Goal Reached
4
Current State: 37:[11, 98, 75, 3], Operations: [] Exploring Operation: 98-75=23, Resulting Numbers: [11, 3, 23] Generated Node #0,0: 37:[11, 3, 23] Operation: 98-75=23 Start Sub Search at level 1: Moving to Node #0,0 Current State: 37:[11, 3, 23], Operations: ['98-75=23'] Exploring Operation: 11*3=33, Resulting Numbers: [23, 33] Generated Node #0,0,0: 37:[23, 33] Operation: 11*3=33 Moving to Node #0,0,0 Current State: 37:[23, 33], Operations: ['98-75=23', '11*3=33'] Exploring Operation: 23+33=56, Resulting Numbers: [56] 56,37 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
sum_heuristic
[ 27, 35, 32, 34 ]
38
[ "35-27=8", "32/8=4", "34+4=38" ]
Current State: 38:[27, 35, 32, 34], Operations: [] Exploring Operation: 35-27=8, Resulting Numbers: [32, 34, 8] Generated Node #2: [32, 34, 8] from Operation: 35-27=8 Current State: 38:[32, 34, 8], Operations: ['35-27=8'] Exploring Operation: 32/8=4, Resulting Numbers: [34, 4] Generated Node #3: [34, 4] from Operation: 32/8=4 Current State: 38:[34, 4], Operations: ['35-27=8', '32/8=4'] Exploring Operation: 34+4=38, Resulting Numbers: [38] 38,38 equal: Goal Reached
4
Current State: 38:[27, 35, 32, 34], Operations: [] Exploring Operation: 34-32=2, Resulting Numbers: [27, 35, 2] Generated Node #0,0: 38:[27, 35, 2] Operation: 34-32=2 Exploring Operation: 32-27=5, Resulting Numbers: [35, 34, 5] Generated Node #0,1: 38:[35, 34, 5] Operation: 32-27=5 Moving to Node #0,1 Current State: 38:[35, 34, 5], Operations: ['32-27=5'] Exploring Operation: 35-34=1, Resulting Numbers: [5, 1] Generated Node #0,1,0: 38:[5, 1] Operation: 35-34=1 Exploring Operation: 34+5=39, Resulting Numbers: [35, 39] Generated Node #0,1,1: 38:[35, 39] Operation: 34+5=39 Moving to Node #0,0 Current State: 38:[27, 35, 2], Operations: ['34-32=2'] Exploring Operation: 27-2=25, Resulting Numbers: [35, 25] Generated Node #0,0,0: 38:[35, 25] Operation: 27-2=25 Exploring Operation: 35-27=8, Resulting Numbers: [2, 8] Generated Node #0,0,1: 38:[2, 8] Operation: 35-27=8 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 38:[2, 8], Operations: ['34-32=2', '35-27=8'] Exploring Operation: 8/2=4, Resulting Numbers: [4] 4,38 unequal: No Solution Exploring Operation: 2*8=16, Resulting Numbers: [16] 16,38 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 38:[35, 25], Operations: ['34-32=2', '27-2=25'] Exploring Operation: 35+25=60, Resulting Numbers: [60] 60,38 unequal: No Solution Exploring Operation: 35-25=10, Resulting Numbers: [10] 10,38 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1,0 Current State: 38:[5, 1], Operations: ['32-27=5', '35-34=1'] Exploring Operation: 5-1=4, Resulting Numbers: [4] 4,38 unequal: No Solution Exploring Operation: 5*1=5, Resulting Numbers: [5] 5,38 unequal: No Solution Moving to Node #0,1,1 Current State: 38:[35, 39], Operations: ['32-27=5', '34+5=39'] Exploring Operation: 39-35=4, Resulting Numbers: [4] 4,38 unequal: No Solution Exploring Operation: 35+39=74, Resulting Numbers: [74] 74,38 unequal: No Solution No solution found.
0
hs_2
mult_heuristic
[ 22, 58, 70, 10 ]
78
[ "22+58=80", "80/10=8", "70+8=78" ]
Current State: 78:[22, 58, 70, 10], Operations: [] Exploring Operation: 22+58=80, Resulting Numbers: [70, 10, 80] Generated Node #2: [70, 10, 80] from Operation: 22+58=80 Current State: 78:[70, 10, 80], Operations: ['22+58=80'] Exploring Operation: 80/10=8, Resulting Numbers: [70, 8] Generated Node #3: [70, 8] from Operation: 80/10=8 Current State: 78:[70, 8], Operations: ['22+58=80', '80/10=8'] Exploring Operation: 70+8=78, Resulting Numbers: [78] 78,78 equal: Goal Reached
4
Current State: 78:[22, 58, 70, 10], Operations: [] Exploring Operation: 22+58=80, Resulting Numbers: [70, 10, 80] Generated Node #0,0: 78:[70, 10, 80] Operation: 22+58=80 Exploring Operation: 70-58=12, Resulting Numbers: [22, 10, 12] Generated Node #0,1: 78:[22, 10, 12] Operation: 70-58=12 Moving to Node #0,1 Current State: 78:[22, 10, 12], Operations: ['70-58=12'] Exploring Operation: 22-10=12, Resulting Numbers: [12, 12] Generated Node #0,1,0: 78:[12, 12] Operation: 22-10=12 Exploring Operation: 12-10=2, Resulting Numbers: [22, 2] Generated Node #0,1,1: 78:[22, 2] Operation: 12-10=2 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 78:[12, 12], Operations: ['70-58=12', '22-10=12'] Exploring Operation: 12+12=24, Resulting Numbers: [24] 24,78 unequal: No Solution Exploring Operation: 12/12=1, Resulting Numbers: [1] 1,78 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 78:[22, 2], Operations: ['70-58=12', '12-10=2'] Exploring Operation: 22+2=24, Resulting Numbers: [24] 24,78 unequal: No Solution Exploring Operation: 22/2=11, Resulting Numbers: [11] 11,78 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0 Current State: 78:[70, 10, 80], Operations: ['22+58=80'] Exploring Operation: 70/10=7, Resulting Numbers: [80, 7] Generated Node #0,0,0: 78:[80, 7] Operation: 70/10=7 Exploring Operation: 70+10=80, Resulting Numbers: [80, 80] Generated Node #0,0,1: 78:[80, 80] Operation: 70+10=80 Moving to Node #0,0,0 Current State: 78:[80, 7], Operations: ['22+58=80', '70/10=7'] Exploring Operation: 80-7=73, Resulting Numbers: [73] 73,78 unequal: No Solution Exploring Operation: 80+7=87, Resulting Numbers: [87] 87,78 unequal: No Solution Moving to Node #0,0,1 Current State: 78:[80, 80], Operations: ['22+58=80', '70+10=80'] Exploring Operation: 80-80=0, Resulting Numbers: [0] 0,78 unequal: No Solution Exploring Operation: 80/80=1, Resulting Numbers: [1] 1,78 unequal: No Solution No solution found.
0
hs_2
mult_heuristic
[ 34, 47, 45, 81 ]
49
[ "47-34=13", "81-45=36", "13+36=49" ]
Current State: 49:[34, 47, 45, 81], Operations: [] Exploring Operation: 47-34=13, Resulting Numbers: [45, 81, 13] Generated Node #2: [45, 81, 13] from Operation: 47-34=13 Current State: 49:[45, 81, 13], Operations: ['47-34=13'] Exploring Operation: 81-45=36, Resulting Numbers: [13, 36] Generated Node #3: [13, 36] from Operation: 81-45=36 Current State: 49:[13, 36], Operations: ['47-34=13', '81-45=36'] Exploring Operation: 13+36=49, Resulting Numbers: [49] 49,49 equal: Goal Reached
4
Current State: 49:[34, 47, 45, 81], Operations: [] Exploring Operation: 45-34=11, Resulting Numbers: [47, 81, 11] Generated Node #0,0: 49:[47, 81, 11] Operation: 45-34=11 Exploring Operation: 81-34=47, Resulting Numbers: [47, 45, 47] Generated Node #0,1: 49:[47, 45, 47] Operation: 81-34=47 Exploring Operation: 81-45=36, Resulting Numbers: [34, 47, 36] Generated Node #0,2: 49:[34, 47, 36] Operation: 81-45=36 Exploring Operation: 81-47=34, Resulting Numbers: [34, 45, 34] Generated Node #0,3: 49:[34, 45, 34] Operation: 81-47=34 Start Sub Search at level 1: Moving to Node #0,1 Current State: 49:[47, 45, 47], Operations: ['81-34=47'] Exploring Operation: 47-47=0, Resulting Numbers: [45, 0] Generated Node #0,1,0: 49:[45, 0] Operation: 47-47=0 Exploring Operation: 47-45=2, Resulting Numbers: [47, 2] Generated Node #0,1,1: 49:[47, 2] Operation: 47-45=2 Exploring Operation: 47/47=1, Resulting Numbers: [45, 1] Generated Node #0,1,2: 49:[45, 1] Operation: 47/47=1 Exploring Operation: 47-45=2, Resulting Numbers: [47, 2] Generated Node #0,1,3: 49:[47, 2] Operation: 47-45=2 Moving to Node #0,1,1 Current State: 49:[47, 2], Operations: ['81-34=47', '47-45=2'] Exploring Operation: 47+2=49, Resulting Numbers: [49] 49,49 equal: Goal Reached Moving to Node #0 Current State: 49:[34, 47, 45, 81], Operations: [] Exploring Operation: 81-34=47, Resulting Numbers: [47, 45, 47] Generated Node #0,1: 49:[47, 45, 47] Operation: 81-34=47 Moving to Node #0,1 Current State: 49:[47, 45, 47], Operations: ['81-34=47'] Exploring Operation: 47-45=2, Resulting Numbers: [47, 2] Generated Node #0,1,1: 49:[47, 2] Operation: 47-45=2 Moving to Node #0,1,1 Current State: 49:[47, 2], Operations: ['81-34=47', '47-45=2'] Exploring Operation: 47+2=49, Resulting Numbers: [49] 49,49 equal: Goal Reached Exit Sub Search at level 1
0.988715
hs_4
mult_heuristic
[ 46, 57, 44, 52 ]
62
[ "46-44=2", "57*2=114", "114-52=62" ]
Current State: 62:[46, 57, 44, 52], Operations: [] Exploring Operation: 46-44=2, Resulting Numbers: [57, 52, 2] Generated Node #2: [57, 52, 2] from Operation: 46-44=2 Current State: 62:[57, 52, 2], Operations: ['46-44=2'] Exploring Operation: 57*2=114, Resulting Numbers: [52, 114] Generated Node #3: [52, 114] from Operation: 57*2=114 Current State: 62:[52, 114], Operations: ['46-44=2', '57*2=114'] Exploring Operation: 114-52=62, Resulting Numbers: [62] 62,62 equal: Goal Reached
4
Current State: 62:[46, 57, 44, 52], Operations: [] Exploring Operation: 52-46=6, Resulting Numbers: [57, 44, 6] Generated Node #0,0: 62:[57, 44, 6] Operation: 52-46=6 Exploring Operation: 52-44=8, Resulting Numbers: [46, 57, 8] Generated Node #0,1: 62:[46, 57, 8] Operation: 52-44=8 Exploring Operation: 46-44=2, Resulting Numbers: [57, 52, 2] Generated Node #0,2: 62:[57, 52, 2] Operation: 46-44=2 Start Sub Search at level 1: Moving to Node #0,2 Current State: 62:[57, 52, 2], Operations: ['46-44=2'] Exploring Operation: 52/2=26, Resulting Numbers: [57, 26] Generated Node #0,2,0: 62:[57, 26] Operation: 52/2=26 Exploring Operation: 57-52=5, Resulting Numbers: [2, 5] Generated Node #0,2,1: 62:[2, 5] Operation: 57-52=5 Exploring Operation: 57+2=59, Resulting Numbers: [52, 59] Generated Node #0,2,2: 62:[52, 59] Operation: 57+2=59 Moving to Node #0,2,1 Current State: 62:[2, 5], Operations: ['46-44=2', '57-52=5'] Exploring Operation: 2*5=10, Resulting Numbers: [10] 10,62 unequal: No Solution Exploring Operation: 2+5=7, Resulting Numbers: [7] 7,62 unequal: No Solution Exploring Operation: 5-2=3, Resulting Numbers: [3] 3,62 unequal: No Solution Moving to Node #0,2,0 Current State: 62:[57, 26], Operations: ['46-44=2', '52/2=26'] Exploring Operation: 57*26=1482, Resulting Numbers: [1482] 1482,62 unequal: No Solution Exploring Operation: 57+26=83, Resulting Numbers: [83] 83,62 unequal: No Solution Exploring Operation: 57-26=31, Resulting Numbers: [31] 31,62 unequal: No Solution Moving to Node #0,2,2 Current State: 62:[52, 59], Operations: ['46-44=2', '57+2=59'] Exploring Operation: 52*59=3068, Resulting Numbers: [3068] 3068,62 unequal: No Solution Exploring Operation: 59-52=7, Resulting Numbers: [7] 7,62 unequal: No Solution Exploring Operation: 52+59=111, Resulting Numbers: [111] 111,62 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 62:[57, 44, 6], Operations: ['52-46=6'] Exploring Operation: 57-44=13, Resulting Numbers: [6, 13] Generated Node #0,0,0: 62:[6, 13] Operation: 57-44=13 Exploring Operation: 57+6=63, Resulting Numbers: [44, 63] Generated Node #0,0,1: 62:[44, 63] Operation: 57+6=63 Exploring Operation: 44-6=38, Resulting Numbers: [57, 38] Generated Node #0,0,2: 62:[57, 38] Operation: 44-6=38 Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 62:[57, 38], Operations: ['52-46=6', '44-6=38'] Exploring Operation: 57-38=19, Resulting Numbers: [19] 19,62 unequal: No Solution Exploring Operation: 57+38=95, Resulting Numbers: [95] 95,62 unequal: No Solution Exploring Operation: 57*38=2166, Resulting Numbers: [2166] 2166,62 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 62:[44, 63], Operations: ['52-46=6', '57+6=63'] Exploring Operation: 44+63=107, Resulting Numbers: [107] 107,62 unequal: No Solution Exploring Operation: 44*63=2772, Resulting Numbers: [2772] 2772,62 unequal: No Solution Exploring Operation: 63-44=19, Resulting Numbers: [19] 19,62 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 62:[6, 13], Operations: ['52-46=6', '57-44=13'] Exploring Operation: 13-6=7, Resulting Numbers: [7] 7,62 unequal: No Solution Exploring Operation: 6*13=78, Resulting Numbers: [78] 78,62 unequal: No Solution Exploring Operation: 6+13=19, Resulting Numbers: [19] 19,62 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 62:[46, 57, 8], Operations: ['52-44=8'] Exploring Operation: 46-8=38, Resulting Numbers: [57, 38] Generated Node #0,1,0: 62:[57, 38] Operation: 46-8=38 Exploring Operation: 57-46=11, Resulting Numbers: [8, 11] Generated Node #0,1,1: 62:[8, 11] Operation: 57-46=11 Exploring Operation: 46+8=54, Resulting Numbers: [57, 54] Generated Node #0,1,2: 62:[57, 54] Operation: 46+8=54 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 62:[57, 38], Operations: ['52-44=8', '46-8=38'] Exploring Operation: 57+38=95, Resulting Numbers: [95] 95,62 unequal: No Solution Exploring Operation: 57*38=2166, Resulting Numbers: [2166] 2166,62 unequal: No Solution Exploring Operation: 57-38=19, Resulting Numbers: [19] 19,62 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 62:[57, 54], Operations: ['52-44=8', '46+8=54'] Exploring Operation: 57*54=3078, Resulting Numbers: [3078] 3078,62 unequal: No Solution Exploring Operation: 57+54=111, Resulting Numbers: [111] 111,62 unequal: No Solution Exploring Operation: 57-54=3, Resulting Numbers: [3] 3,62 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 62:[8, 11], Operations: ['52-44=8', '57-46=11'] Exploring Operation: 8+11=19, Resulting Numbers: [19] 19,62 unequal: No Solution Exploring Operation: 8*11=88, Resulting Numbers: [88] 88,62 unequal: No Solution Exploring Operation: 11-8=3, Resulting Numbers: [3] 3,62 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_3
mult_heuristic
[ 46, 82, 95, 4 ]
37
[ "46+82=128", "95-4=91", "128-91=37" ]
Current State: 37:[46, 82, 95, 4], Operations: [] Exploring Operation: 46+82=128, Resulting Numbers: [95, 4, 128] Generated Node #2: [95, 4, 128] from Operation: 46+82=128 Current State: 37:[95, 4, 128], Operations: ['46+82=128'] Exploring Operation: 95-4=91, Resulting Numbers: [128, 91] Generated Node #3: [128, 91] from Operation: 95-4=91 Current State: 37:[128, 91], Operations: ['46+82=128', '95-4=91'] Exploring Operation: 128-91=37, Resulting Numbers: [37] 37,37 equal: Goal Reached
4
Current State: 37:[46, 82, 95, 4], Operations: [] Exploring Operation: 95-46=49, Resulting Numbers: [82, 4, 49] Generated Node #0,0: 37:[82, 4, 49] Operation: 95-46=49 Exploring Operation: 95-82=13, Resulting Numbers: [46, 4, 13] Generated Node #0,1: 37:[46, 4, 13] Operation: 95-82=13 Start Sub Search at level 1: Moving to Node #0,1 Current State: 37:[46, 4, 13], Operations: ['95-82=13'] Exploring Operation: 46-4=42, Resulting Numbers: [13, 42] Generated Node #0,1,0: 37:[13, 42] Operation: 46-4=42 Exploring Operation: 4*13=52, Resulting Numbers: [46, 52] Generated Node #0,1,1: 37:[46, 52] Operation: 4*13=52 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 37:[46, 52], Operations: ['95-82=13', '4*13=52'] Exploring Operation: 52-46=6, Resulting Numbers: [6] 6,37 unequal: No Solution Exploring Operation: 46+52=98, Resulting Numbers: [98] 98,37 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 37:[13, 42], Operations: ['95-82=13', '46-4=42'] Exploring Operation: 13+42=55, Resulting Numbers: [55] 55,37 unequal: No Solution Exploring Operation: 42-13=29, Resulting Numbers: [29] 29,37 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 37:[82, 4, 49], Operations: ['95-46=49'] Exploring Operation: 82-4=78, Resulting Numbers: [49, 78] Generated Node #0,0,0: 37:[49, 78] Operation: 82-4=78 Exploring Operation: 82-49=33, Resulting Numbers: [4, 33] Generated Node #0,0,1: 37:[4, 33] Operation: 82-49=33 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 37:[4, 33], Operations: ['95-46=49', '82-49=33'] Exploring Operation: 4+33=37, Resulting Numbers: [37] 37,37 equal: Goal Reached Moving to Node #0 Current State: 37:[46, 82, 95, 4], Operations: [] Exploring Operation: 95-46=49, Resulting Numbers: [82, 4, 49] Generated Node #0,0: 37:[82, 4, 49] Operation: 95-46=49 Moving to Node #0,0 Current State: 37:[82, 4, 49], Operations: ['95-46=49'] Exploring Operation: 82-49=33, Resulting Numbers: [4, 33] Generated Node #0,0,1: 37:[4, 33] Operation: 82-49=33 Moving to Node #0,0,1 Current State: 37:[4, 33], Operations: ['95-46=49', '82-49=33'] Exploring Operation: 4+33=37, Resulting Numbers: [37] 37,37 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.986979
hs_2
mult_heuristic
[ 28, 4, 64, 74 ]
76
[ "28+4=32", "64/32=2", "74+2=76" ]
Current State: 76:[28, 4, 64, 74], Operations: [] Exploring Operation: 28+4=32, Resulting Numbers: [64, 74, 32] Generated Node #2: [64, 74, 32] from Operation: 28+4=32 Current State: 76:[64, 74, 32], Operations: ['28+4=32'] Exploring Operation: 64/32=2, Resulting Numbers: [74, 2] Generated Node #3: [74, 2] from Operation: 64/32=2 Current State: 76:[74, 2], Operations: ['28+4=32', '64/32=2'] Exploring Operation: 74+2=76, Resulting Numbers: [76] 76,76 equal: Goal Reached
4
Current State: 76:[28, 4, 64, 74], Operations: [] Exploring Operation: 74-64=10, Resulting Numbers: [28, 4, 10] Generated Node #0,0: 76:[28, 4, 10] Operation: 74-64=10 Exploring Operation: 64/4=16, Resulting Numbers: [28, 74, 16] Generated Node #0,1: 76:[28, 74, 16] Operation: 64/4=16 Exploring Operation: 64-28=36, Resulting Numbers: [4, 74, 36] Generated Node #0,2: 76:[4, 74, 36] Operation: 64-28=36 Moving to Node #0,2 Current State: 76:[4, 74, 36], Operations: ['64-28=36'] Exploring Operation: 4+36=40, Resulting Numbers: [74, 40] Generated Node #0,2,0: 76:[74, 40] Operation: 4+36=40 Exploring Operation: 74-36=38, Resulting Numbers: [4, 38] Generated Node #0,2,1: 76:[4, 38] Operation: 74-36=38 Exploring Operation: 4+74=78, Resulting Numbers: [36, 78] Generated Node #0,2,2: 76:[36, 78] Operation: 4+74=78 Moving to Node #0,1 Current State: 76:[28, 74, 16], Operations: ['64/4=16'] Exploring Operation: 28-16=12, Resulting Numbers: [74, 12] Generated Node #0,1,0: 76:[74, 12] Operation: 28-16=12 Exploring Operation: 28+16=44, Resulting Numbers: [74, 44] Generated Node #0,1,1: 76:[74, 44] Operation: 28+16=44 Exploring Operation: 74-28=46, Resulting Numbers: [16, 46] Generated Node #0,1,2: 76:[16, 46] Operation: 74-28=46 Moving to Node #0,0 Current State: 76:[28, 4, 10], Operations: ['74-64=10'] Exploring Operation: 28/4=7, Resulting Numbers: [10, 7] Generated Node #0,0,0: 76:[10, 7] Operation: 28/4=7 Exploring Operation: 28+10=38, Resulting Numbers: [4, 38] Generated Node #0,0,1: 76:[4, 38] Operation: 28+10=38 Exploring Operation: 28-10=18, Resulting Numbers: [4, 18] Generated Node #0,0,2: 76:[4, 18] Operation: 28-10=18 Moving to Node #0,2,1 Current State: 76:[4, 38], Operations: ['64-28=36', '74-36=38'] Exploring Operation: 4+38=42, Resulting Numbers: [42] 42,76 unequal: No Solution Exploring Operation: 38-4=34, Resulting Numbers: [34] 34,76 unequal: No Solution Exploring Operation: 4*38=152, Resulting Numbers: [152] 152,76 unequal: No Solution Moving to Node #0,0,1 Current State: 76:[4, 38], Operations: ['74-64=10', '28+10=38'] Exploring Operation: 38-4=34, Resulting Numbers: [34] 34,76 unequal: No Solution Exploring Operation: 4+38=42, Resulting Numbers: [42] 42,76 unequal: No Solution Exploring Operation: 4*38=152, Resulting Numbers: [152] 152,76 unequal: No Solution Moving to Node #0,0,2 Current State: 76:[4, 18], Operations: ['74-64=10', '28-10=18'] Exploring Operation: 18-4=14, Resulting Numbers: [14] 14,76 unequal: No Solution Exploring Operation: 4+18=22, Resulting Numbers: [22] 22,76 unequal: No Solution Exploring Operation: 4*18=72, Resulting Numbers: [72] 72,76 unequal: No Solution Moving to Node #0,2,2 Current State: 76:[36, 78], Operations: ['64-28=36', '4+74=78'] Exploring Operation: 78-36=42, Resulting Numbers: [42] 42,76 unequal: No Solution Exploring Operation: 36+78=114, Resulting Numbers: [114] 114,76 unequal: No Solution Exploring Operation: 36*78=2808, Resulting Numbers: [2808] 2808,76 unequal: No Solution Moving to Node #0,2,0 Current State: 76:[74, 40], Operations: ['64-28=36', '4+36=40'] Exploring Operation: 74-40=34, Resulting Numbers: [34] 34,76 unequal: No Solution Exploring Operation: 74+40=114, Resulting Numbers: [114] 114,76 unequal: No Solution Exploring Operation: 74*40=2960, Resulting Numbers: [2960] 2960,76 unequal: No Solution Moving to Node #0,1,1 Current State: 76:[74, 44], Operations: ['64/4=16', '28+16=44'] Exploring Operation: 74-44=30, Resulting Numbers: [30] 30,76 unequal: No Solution Exploring Operation: 74*44=3256, Resulting Numbers: [3256] 3256,76 unequal: No Solution Exploring Operation: 74+44=118, Resulting Numbers: [118] 118,76 unequal: No Solution Moving to Node #0,0,0 Current State: 76:[10, 7], Operations: ['74-64=10', '28/4=7'] Exploring Operation: 10-7=3, Resulting Numbers: [3] 3,76 unequal: No Solution Exploring Operation: 10*7=70, Resulting Numbers: [70] 70,76 unequal: No Solution Exploring Operation: 10+7=17, Resulting Numbers: [17] 17,76 unequal: No Solution Moving to Node #0,1,0 Current State: 76:[74, 12], Operations: ['64/4=16', '28-16=12'] Exploring Operation: 74+12=86, Resulting Numbers: [86] 86,76 unequal: No Solution Exploring Operation: 74*12=888, Resulting Numbers: [888] 888,76 unequal: No Solution Exploring Operation: 74-12=62, Resulting Numbers: [62] 62,76 unequal: No Solution Moving to Node #0,1,2 Current State: 76:[16, 46], Operations: ['64/4=16', '74-28=46'] Exploring Operation: 46-16=30, Resulting Numbers: [30] 30,76 unequal: No Solution Exploring Operation: 16*46=736, Resulting Numbers: [736] 736,76 unequal: No Solution Exploring Operation: 16+46=62, Resulting Numbers: [62] 62,76 unequal: No Solution No solution found.
0
hs_3
sum_heuristic
[ 65, 85, 43, 34 ]
95
[ "65*43=2795", "85*34=2890", "2890-2795=95" ]
Current State: 95:[65, 85, 43, 34], Operations: [] Exploring Operation: 65*43=2795, Resulting Numbers: [85, 34, 2795] Generated Node #2: [85, 34, 2795] from Operation: 65*43=2795 Current State: 95:[85, 34, 2795], Operations: ['65*43=2795'] Exploring Operation: 85*34=2890, Resulting Numbers: [2795, 2890] Generated Node #3: [2795, 2890] from Operation: 85*34=2890 Current State: 95:[2795, 2890], Operations: ['65*43=2795', '85*34=2890'] Exploring Operation: 2890-2795=95, Resulting Numbers: [95] 95,95 equal: Goal Reached
4
Current State: 95:[65, 85, 43, 34], Operations: [] Exploring Operation: 65-43=22, Resulting Numbers: [85, 34, 22] Generated Node #0,0: 95:[85, 34, 22] Operation: 65-43=22 Exploring Operation: 65+34=99, Resulting Numbers: [85, 43, 99] Generated Node #0,1: 95:[85, 43, 99] Operation: 65+34=99 Exploring Operation: 65+43=108, Resulting Numbers: [85, 34, 108] Generated Node #0,2: 95:[85, 34, 108] Operation: 65+43=108 Moving to Node #0,0 Current State: 95:[85, 34, 22], Operations: ['65-43=22'] Exploring Operation: 34-22=12, Resulting Numbers: [85, 12] Generated Node #0,0,0: 95:[85, 12] Operation: 34-22=12 Exploring Operation: 85+34=119, Resulting Numbers: [22, 119] Generated Node #0,0,1: 95:[22, 119] Operation: 85+34=119 Exploring Operation: 85+22=107, Resulting Numbers: [34, 107] Generated Node #0,0,2: 95:[34, 107] Operation: 85+22=107 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 95:[85, 12], Operations: ['65-43=22', '34-22=12'] Exploring Operation: 85-12=73, Resulting Numbers: [73] 73,95 unequal: No Solution Exploring Operation: 85*12=1020, Resulting Numbers: [1020] 1020,95 unequal: No Solution Exploring Operation: 85+12=97, Resulting Numbers: [97] 97,95 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 95:[22, 119], Operations: ['65-43=22', '85+34=119'] Exploring Operation: 22+119=141, Resulting Numbers: [141] 141,95 unequal: No Solution Exploring Operation: 119-22=97, Resulting Numbers: [97] 97,95 unequal: No Solution Exploring Operation: 22*119=2618, Resulting Numbers: [2618] 2618,95 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 95:[34, 107], Operations: ['65-43=22', '85+22=107'] Exploring Operation: 107-34=73, Resulting Numbers: [73] 73,95 unequal: No Solution Exploring Operation: 34+107=141, Resulting Numbers: [141] 141,95 unequal: No Solution Exploring Operation: 34*107=3638, Resulting Numbers: [3638] 3638,95 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 95:[85, 43, 99], Operations: ['65+34=99'] Exploring Operation: 99-85=14, Resulting Numbers: [43, 14] Generated Node #0,1,0: 95:[43, 14] Operation: 99-85=14 Exploring Operation: 85-43=42, Resulting Numbers: [99, 42] Generated Node #0,1,1: 95:[99, 42] Operation: 85-43=42 Exploring Operation: 85+43=128, Resulting Numbers: [99, 128] Generated Node #0,1,2: 95:[99, 128] Operation: 85+43=128 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 95:[99, 42], Operations: ['65+34=99', '85-43=42'] Exploring Operation: 99+42=141, Resulting Numbers: [141] 141,95 unequal: No Solution Exploring Operation: 99-42=57, Resulting Numbers: [57] 57,95 unequal: No Solution Exploring Operation: 99*42=4158, Resulting Numbers: [4158] 4158,95 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 95:[43, 14], Operations: ['65+34=99', '99-85=14'] Exploring Operation: 43+14=57, Resulting Numbers: [57] 57,95 unequal: No Solution Exploring Operation: 43-14=29, Resulting Numbers: [29] 29,95 unequal: No Solution Exploring Operation: 43*14=602, Resulting Numbers: [602] 602,95 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 95:[99, 128], Operations: ['65+34=99', '85+43=128'] Exploring Operation: 99+128=227, Resulting Numbers: [227] 227,95 unequal: No Solution Exploring Operation: 99*128=12672, Resulting Numbers: [12672] 12672,95 unequal: No Solution Exploring Operation: 128-99=29, Resulting Numbers: [29] 29,95 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2 Current State: 95:[85, 34, 108], Operations: ['65+43=108'] Exploring Operation: 108-85=23, Resulting Numbers: [34, 23] Generated Node #0,2,0: 95:[34, 23] Operation: 108-85=23 Exploring Operation: 108-34=74, Resulting Numbers: [85, 74] Generated Node #0,2,1: 95:[85, 74] Operation: 108-34=74 Exploring Operation: 85+34=119, Resulting Numbers: [108, 119] Generated Node #0,2,2: 95:[108, 119] Operation: 85+34=119 Moving to Node #0,2,0 Current State: 95:[34, 23], Operations: ['65+43=108', '108-85=23'] Exploring Operation: 34*23=782, Resulting Numbers: [782] 782,95 unequal: No Solution Exploring Operation: 34-23=11, Resulting Numbers: [11] 11,95 unequal: No Solution Exploring Operation: 34+23=57, Resulting Numbers: [57] 57,95 unequal: No Solution Moving to Node #0,2,1 Current State: 95:[85, 74], Operations: ['65+43=108', '108-34=74'] Exploring Operation: 85*74=6290, Resulting Numbers: [6290] 6290,95 unequal: No Solution Exploring Operation: 85+74=159, Resulting Numbers: [159] 159,95 unequal: No Solution Exploring Operation: 85-74=11, Resulting Numbers: [11] 11,95 unequal: No Solution Moving to Node #0,2,2 Current State: 95:[108, 119], Operations: ['65+43=108', '85+34=119'] Exploring Operation: 108*119=12852, Resulting Numbers: [12852] 12852,95 unequal: No Solution Exploring Operation: 119-108=11, Resulting Numbers: [11] 11,95 unequal: No Solution Exploring Operation: 108+119=227, Resulting Numbers: [227] 227,95 unequal: No Solution No solution found.
0
hs_3
mult_heuristic
[ 95, 91, 40, 19 ]
25
[ "95-91=4", "40-19=21", "4+21=25" ]
Current State: 25:[95, 91, 40, 19], Operations: [] Exploring Operation: 95-91=4, Resulting Numbers: [40, 19, 4] Generated Node #2: [40, 19, 4] from Operation: 95-91=4 Current State: 25:[40, 19, 4], Operations: ['95-91=4'] Exploring Operation: 40-19=21, Resulting Numbers: [4, 21] Generated Node #3: [4, 21] from Operation: 40-19=21 Current State: 25:[4, 21], Operations: ['95-91=4', '40-19=21'] Exploring Operation: 4+21=25, Resulting Numbers: [25] 25,25 equal: Goal Reached
4
Current State: 25:[95, 91, 40, 19], Operations: [] Exploring Operation: 91-40=51, Resulting Numbers: [95, 19, 51] Generated Node #0,0: 25:[95, 19, 51] Operation: 91-40=51 Exploring Operation: 95/19=5, Resulting Numbers: [91, 40, 5] Generated Node #0,1: 25:[91, 40, 5] Operation: 95/19=5 Exploring Operation: 95-91=4, Resulting Numbers: [40, 19, 4] Generated Node #0,2: 25:[40, 19, 4] Operation: 95-91=4 Exploring Operation: 95-40=55, Resulting Numbers: [91, 19, 55] Generated Node #0,3: 25:[91, 19, 55] Operation: 95-40=55 Start Sub Search at level 1: Moving to Node #0,2 Current State: 25:[40, 19, 4], Operations: ['95-91=4'] Exploring Operation: 40-19=21, Resulting Numbers: [4, 21] Generated Node #0,2,0: 25:[4, 21] Operation: 40-19=21 Exploring Operation: 40/4=10, Resulting Numbers: [19, 10] Generated Node #0,2,1: 25:[19, 10] Operation: 40/4=10 Exploring Operation: 19+4=23, Resulting Numbers: [40, 23] Generated Node #0,2,2: 25:[40, 23] Operation: 19+4=23 Exploring Operation: 40-4=36, Resulting Numbers: [19, 36] Generated Node #0,2,3: 25:[19, 36] Operation: 40-4=36 Moving to Node #0,2,0 Current State: 25:[4, 21], Operations: ['95-91=4', '40-19=21'] Exploring Operation: 4*21=84, Resulting Numbers: [84] 84,25 unequal: No Solution Exploring Operation: 21-4=17, Resulting Numbers: [17] 17,25 unequal: No Solution Exploring Operation: 4+21=25, Resulting Numbers: [25] 25,25 equal: Goal Reached Moving to Node #0 Current State: 25:[95, 91, 40, 19], Operations: [] Exploring Operation: 95-91=4, Resulting Numbers: [40, 19, 4] Generated Node #0,2: 25:[40, 19, 4] Operation: 95-91=4 Moving to Node #0,2 Current State: 25:[40, 19, 4], Operations: ['95-91=4'] Exploring Operation: 40-19=21, Resulting Numbers: [4, 21] Generated Node #0,2,0: 25:[4, 21] Operation: 40-19=21 Moving to Node #0,2,0 Current State: 25:[4, 21], Operations: ['95-91=4', '40-19=21'] Exploring Operation: 4+21=25, Resulting Numbers: [25] 25,25 equal: Goal Reached Exit Sub Search at level 1
0.986979
hs_4
sum_heuristic
[ 67, 39, 80, 81 ]
29
[ "67-39=28", "81-80=1", "28+1=29" ]
Current State: 29:[67, 39, 80, 81], Operations: [] Exploring Operation: 67-39=28, Resulting Numbers: [80, 81, 28] Generated Node #2: [80, 81, 28] from Operation: 67-39=28 Current State: 29:[80, 81, 28], Operations: ['67-39=28'] Exploring Operation: 81-80=1, Resulting Numbers: [28, 1] Generated Node #3: [28, 1] from Operation: 81-80=1 Current State: 29:[28, 1], Operations: ['67-39=28', '81-80=1'] Exploring Operation: 28+1=29, Resulting Numbers: [29] 29,29 equal: Goal Reached
4
Current State: 29:[67, 39, 80, 81], Operations: [] Exploring Operation: 81-67=14, Resulting Numbers: [39, 80, 14] Generated Node #0,0: 29:[39, 80, 14] Operation: 81-67=14 Moving to Node #0,0 Current State: 29:[39, 80, 14], Operations: ['81-67=14'] Exploring Operation: 80-39=41, Resulting Numbers: [14, 41] Generated Node #0,0,0: 29:[14, 41] Operation: 80-39=41 Moving to Node #0,0,0 Current State: 29:[14, 41], Operations: ['81-67=14', '80-39=41'] Exploring Operation: 41-14=27, Resulting Numbers: [27] 27,29 unequal: No Solution No solution found.
0
hs_1
sum_heuristic
[ 96, 72, 50, 48 ]
25
[ "96-72=24", "50*24=1200", "1200/48=25" ]
Current State: 25:[96, 72, 50, 48], Operations: [] Exploring Operation: 96-72=24, Resulting Numbers: [50, 48, 24] Generated Node #2: [50, 48, 24] from Operation: 96-72=24 Current State: 25:[50, 48, 24], Operations: ['96-72=24'] Exploring Operation: 50*24=1200, Resulting Numbers: [48, 1200] Generated Node #3: [48, 1200] from Operation: 50*24=1200 Current State: 25:[48, 1200], Operations: ['96-72=24', '50*24=1200'] Exploring Operation: 1200/48=25, Resulting Numbers: [25] 25,25 equal: Goal Reached
4
Current State: 25:[96, 72, 50, 48], Operations: [] Exploring Operation: 96/48=2, Resulting Numbers: [72, 50, 2] Generated Node #0,0: 25:[72, 50, 2] Operation: 96/48=2 Exploring Operation: 96-72=24, Resulting Numbers: [50, 48, 24] Generated Node #0,1: 25:[50, 48, 24] Operation: 96-72=24 Start Sub Search at level 1: Moving to Node #0,1 Current State: 25:[50, 48, 24], Operations: ['96-72=24'] Exploring Operation: 50-48=2, Resulting Numbers: [24, 2] Generated Node #0,1,0: 25:[24, 2] Operation: 50-48=2 Exploring Operation: 50-24=26, Resulting Numbers: [48, 26] Generated Node #0,1,1: 25:[48, 26] Operation: 50-24=26 Moving to Node #0,1,0 Current State: 25:[24, 2], Operations: ['96-72=24', '50-48=2'] Exploring Operation: 24+2=26, Resulting Numbers: [26] 26,25 unequal: No Solution Exploring Operation: 24-2=22, Resulting Numbers: [22] 22,25 unequal: No Solution Moving to Node #0,1,1 Current State: 25:[48, 26], Operations: ['96-72=24', '50-24=26'] Exploring Operation: 48+26=74, Resulting Numbers: [74] 74,25 unequal: No Solution Exploring Operation: 48-26=22, Resulting Numbers: [22] 22,25 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 25:[72, 50, 2], Operations: ['96/48=2'] Exploring Operation: 72/2=36, Resulting Numbers: [50, 36] Generated Node #0,0,0: 25:[50, 36] Operation: 72/2=36 Exploring Operation: 72-50=22, Resulting Numbers: [2, 22] Generated Node #0,0,1: 25:[2, 22] Operation: 72-50=22 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 25:[2, 22], Operations: ['96/48=2', '72-50=22'] Exploring Operation: 22-2=20, Resulting Numbers: [20] 20,25 unequal: No Solution Exploring Operation: 2+22=24, Resulting Numbers: [24] 24,25 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 25:[50, 36], Operations: ['96/48=2', '72/2=36'] Exploring Operation: 50+36=86, Resulting Numbers: [86] 86,25 unequal: No Solution Exploring Operation: 50-36=14, Resulting Numbers: [14] 14,25 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
sum_heuristic
[ 80, 31, 18, 77 ]
79
[ "80-18=62", "62/31=2", "77+2=79" ]
Current State: 79:[80, 31, 18, 77], Operations: [] Exploring Operation: 80-18=62, Resulting Numbers: [31, 77, 62] Generated Node #2: [31, 77, 62] from Operation: 80-18=62 Current State: 79:[31, 77, 62], Operations: ['80-18=62'] Exploring Operation: 62/31=2, Resulting Numbers: [77, 2] Generated Node #3: [77, 2] from Operation: 62/31=2 Current State: 79:[77, 2], Operations: ['80-18=62', '62/31=2'] Exploring Operation: 77+2=79, Resulting Numbers: [79] 79,79 equal: Goal Reached
4
Current State: 79:[80, 31, 18, 77], Operations: [] Exploring Operation: 80-18=62, Resulting Numbers: [31, 77, 62] Generated Node #0,0: 79:[31, 77, 62] Operation: 80-18=62 Exploring Operation: 18+77=95, Resulting Numbers: [80, 31, 95] Generated Node #0,1: 79:[80, 31, 95] Operation: 18+77=95 Exploring Operation: 31-18=13, Resulting Numbers: [80, 77, 13] Generated Node #0,2: 79:[80, 77, 13] Operation: 31-18=13 Exploring Operation: 31+18=49, Resulting Numbers: [80, 77, 49] Generated Node #0,3: 79:[80, 77, 49] Operation: 31+18=49 Exploring Operation: 80+18=98, Resulting Numbers: [31, 77, 98] Generated Node #0,4: 79:[31, 77, 98] Operation: 80+18=98 Start Sub Search at level 1: Moving to Node #0,3 Current State: 79:[80, 77, 49], Operations: ['31+18=49'] Exploring Operation: 77+49=126, Resulting Numbers: [80, 126] Generated Node #0,3,0: 79:[80, 126] Operation: 77+49=126 Exploring Operation: 80+49=129, Resulting Numbers: [77, 129] Generated Node #0,3,1: 79:[77, 129] Operation: 80+49=129 Exploring Operation: 80-49=31, Resulting Numbers: [77, 31] Generated Node #0,3,2: 79:[77, 31] Operation: 80-49=31 Exploring Operation: 77-49=28, Resulting Numbers: [80, 28] Generated Node #0,3,3: 79:[80, 28] Operation: 77-49=28 Exploring Operation: 80-77=3, Resulting Numbers: [49, 3] Generated Node #0,3,4: 79:[49, 3] Operation: 80-77=3 Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 79:[80, 126], Operations: ['31+18=49', '77+49=126'] Exploring Operation: 80*126=10080, Resulting Numbers: [10080] 10080,79 unequal: No Solution Exploring Operation: 80+126=206, Resulting Numbers: [206] 206,79 unequal: No Solution Exploring Operation: 126-80=46, Resulting Numbers: [46] 46,79 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 79:[77, 31], Operations: ['31+18=49', '80-49=31'] Exploring Operation: 77*31=2387, Resulting Numbers: [2387] 2387,79 unequal: No Solution Exploring Operation: 77+31=108, Resulting Numbers: [108] 108,79 unequal: No Solution Exploring Operation: 77-31=46, Resulting Numbers: [46] 46,79 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 79:[77, 129], Operations: ['31+18=49', '80+49=129'] Exploring Operation: 77+129=206, Resulting Numbers: [206] 206,79 unequal: No Solution Exploring Operation: 129-77=52, Resulting Numbers: [52] 52,79 unequal: No Solution Exploring Operation: 77*129=9933, Resulting Numbers: [9933] 9933,79 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 79:[80, 28], Operations: ['31+18=49', '77-49=28'] Exploring Operation: 80+28=108, Resulting Numbers: [108] 108,79 unequal: No Solution Exploring Operation: 80*28=2240, Resulting Numbers: [2240] 2240,79 unequal: No Solution Exploring Operation: 80-28=52, Resulting Numbers: [52] 52,79 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,4 Current State: 79:[49, 3], Operations: ['31+18=49', '80-77=3'] Exploring Operation: 49+3=52, Resulting Numbers: [52] 52,79 unequal: No Solution Exploring Operation: 49-3=46, Resulting Numbers: [46] 46,79 unequal: No Solution Exploring Operation: 49*3=147, Resulting Numbers: [147] 147,79 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 79:[80, 31, 95], Operations: ['18+77=95'] Exploring Operation: 95-80=15, Resulting Numbers: [31, 15] Generated Node #0,1,0: 79:[31, 15] Operation: 95-80=15 Exploring Operation: 31+95=126, Resulting Numbers: [80, 126] Generated Node #0,1,1: 79:[80, 126] Operation: 31+95=126 Exploring Operation: 80-31=49, Resulting Numbers: [95, 49] Generated Node #0,1,2: 79:[95, 49] Operation: 80-31=49 Exploring Operation: 80+31=111, Resulting Numbers: [95, 111] Generated Node #0,1,3: 79:[95, 111] Operation: 80+31=111 Exploring Operation: 95-31=64, Resulting Numbers: [80, 64] Generated Node #0,1,4: 79:[80, 64] Operation: 95-31=64 Moving to Node #0,1,4 Current State: 79:[80, 64], Operations: ['18+77=95', '95-31=64'] Exploring Operation: 80+64=144, Resulting Numbers: [144] 144,79 unequal: No Solution Exploring Operation: 80*64=5120, Resulting Numbers: [5120] 5120,79 unequal: No Solution Exploring Operation: 80-64=16, Resulting Numbers: [16] 16,79 unequal: No Solution Moving to Node #0,1,2 Current State: 79:[95, 49], Operations: ['18+77=95', '80-31=49'] Exploring Operation: 95-49=46, Resulting Numbers: [46] 46,79 unequal: No Solution Exploring Operation: 95*49=4655, Resulting Numbers: [4655] 4655,79 unequal: No Solution Exploring Operation: 95+49=144, Resulting Numbers: [144] 144,79 unequal: No Solution Moving to Node #0,1,1 Current State: 79:[80, 126], Operations: ['18+77=95', '31+95=126'] Exploring Operation: 80*126=10080, Resulting Numbers: [10080] 10080,79 unequal: No Solution Exploring Operation: 126-80=46, Resulting Numbers: [46] 46,79 unequal: No Solution Exploring Operation: 80+126=206, Resulting Numbers: [206] 206,79 unequal: No Solution Moving to Node #0,1,3 Current State: 79:[95, 111], Operations: ['18+77=95', '80+31=111'] Exploring Operation: 95*111=10545, Resulting Numbers: [10545] 10545,79 unequal: No Solution Exploring Operation: 95+111=206, Resulting Numbers: [206] 206,79 unequal: No Solution Exploring Operation: 111-95=16, Resulting Numbers: [16] 16,79 unequal: No Solution Moving to Node #0,1,0 Current State: 79:[31, 15], Operations: ['18+77=95', '95-80=15'] Exploring Operation: 31*15=465, Resulting Numbers: [465] 465,79 unequal: No Solution Exploring Operation: 31+15=46, Resulting Numbers: [46] 46,79 unequal: No Solution Exploring Operation: 31-15=16, Resulting Numbers: [16] 16,79 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 79:[31, 77, 62], Operations: ['80-18=62'] Exploring Operation: 62/31=2, Resulting Numbers: [77, 2] Generated Node #0,0,0: 79:[77, 2] Operation: 62/31=2 Exploring Operation: 62-31=31, Resulting Numbers: [77, 31] Generated Node #0,0,1: 79:[77, 31] Operation: 62-31=31 Exploring Operation: 77-31=46, Resulting Numbers: [62, 46] Generated Node #0,0,2: 79:[62, 46] Operation: 77-31=46 Exploring Operation: 31+77=108, Resulting Numbers: [62, 108] Generated Node #0,0,3: 79:[62, 108] Operation: 31+77=108 Exploring Operation: 31+62=93, Resulting Numbers: [77, 93] Generated Node #0,0,4: 79:[77, 93] Operation: 31+62=93 Moving to Node #0,0,4 Current State: 79:[77, 93], Operations: ['80-18=62', '31+62=93'] Exploring Operation: 77*93=7161, Resulting Numbers: [7161] 7161,79 unequal: No Solution Exploring Operation: 77+93=170, Resulting Numbers: [170] 170,79 unequal: No Solution Exploring Operation: 93-77=16, Resulting Numbers: [16] 16,79 unequal: No Solution Moving to Node #0,0,3 Current State: 79:[62, 108], Operations: ['80-18=62', '31+77=108'] Exploring Operation: 62*108=6696, Resulting Numbers: [6696] 6696,79 unequal: No Solution Exploring Operation: 62+108=170, Resulting Numbers: [170] 170,79 unequal: No Solution Exploring Operation: 108-62=46, Resulting Numbers: [46] 46,79 unequal: No Solution Moving to Node #0,0,1 Current State: 79:[77, 31], Operations: ['80-18=62', '62-31=31'] Exploring Operation: 77*31=2387, Resulting Numbers: [2387] 2387,79 unequal: No Solution Exploring Operation: 77-31=46, Resulting Numbers: [46] 46,79 unequal: No Solution Exploring Operation: 77+31=108, Resulting Numbers: [108] 108,79 unequal: No Solution Moving to Node #0,0,2 Current State: 79:[62, 46], Operations: ['80-18=62', '77-31=46'] Exploring Operation: 62*46=2852, Resulting Numbers: [2852] 2852,79 unequal: No Solution Exploring Operation: 62+46=108, Resulting Numbers: [108] 108,79 unequal: No Solution Exploring Operation: 62-46=16, Resulting Numbers: [16] 16,79 unequal: No Solution Moving to Node #0,0,0 Current State: 79:[77, 2], Operations: ['80-18=62', '62/31=2'] Exploring Operation: 77-2=75, Resulting Numbers: [75] 75,79 unequal: No Solution Exploring Operation: 77*2=154, Resulting Numbers: [154] 154,79 unequal: No Solution Exploring Operation: 77+2=79, Resulting Numbers: [79] 79,79 equal: Goal Reached Moving to Node #0 Current State: 79:[80, 31, 18, 77], Operations: [] Exploring Operation: 80-18=62, Resulting Numbers: [31, 77, 62] Generated Node #0,0: 79:[31, 77, 62] Operation: 80-18=62 Moving to Node #0,0 Current State: 79:[31, 77, 62], Operations: ['80-18=62'] Exploring Operation: 62/31=2, Resulting Numbers: [77, 2] Generated Node #0,0,0: 79:[77, 2] Operation: 62/31=2 Moving to Node #0,0,0 Current State: 79:[77, 2], Operations: ['80-18=62', '62/31=2'] Exploring Operation: 77+2=79, Resulting Numbers: [79] 79,79 equal: Goal Reached Exit Sub Search at level 1
0.940104
hs_5
mult_heuristic
[ 55, 62, 67, 28 ]
46
[ "62-55=7", "67-28=39", "7+39=46" ]
Current State: 46:[55, 62, 67, 28], Operations: [] Exploring Operation: 62-55=7, Resulting Numbers: [67, 28, 7] Generated Node #2: [67, 28, 7] from Operation: 62-55=7 Current State: 46:[67, 28, 7], Operations: ['62-55=7'] Exploring Operation: 67-28=39, Resulting Numbers: [7, 39] Generated Node #3: [7, 39] from Operation: 67-28=39 Current State: 46:[7, 39], Operations: ['62-55=7', '67-28=39'] Exploring Operation: 7+39=46, Resulting Numbers: [46] 46,46 equal: Goal Reached
4
Current State: 46:[55, 62, 67, 28], Operations: [] Exploring Operation: 62-55=7, Resulting Numbers: [67, 28, 7] Generated Node #0,0: 46:[67, 28, 7] Operation: 62-55=7 Exploring Operation: 67-28=39, Resulting Numbers: [55, 62, 39] Generated Node #0,1: 46:[55, 62, 39] Operation: 67-28=39 Exploring Operation: 67-62=5, Resulting Numbers: [55, 28, 5] Generated Node #0,2: 46:[55, 28, 5] Operation: 67-62=5 Exploring Operation: 67-55=12, Resulting Numbers: [62, 28, 12] Generated Node #0,3: 46:[62, 28, 12] Operation: 67-55=12 Exploring Operation: 55-28=27, Resulting Numbers: [62, 67, 27] Generated Node #0,4: 46:[62, 67, 27] Operation: 55-28=27 Moving to Node #0,2 Current State: 46:[55, 28, 5], Operations: ['67-62=5'] Exploring Operation: 55+5=60, Resulting Numbers: [28, 60] Generated Node #0,2,0: 46:[28, 60] Operation: 55+5=60 Exploring Operation: 55-5=50, Resulting Numbers: [28, 50] Generated Node #0,2,1: 46:[28, 50] Operation: 55-5=50 Exploring Operation: 28-5=23, Resulting Numbers: [55, 23] Generated Node #0,2,2: 46:[55, 23] Operation: 28-5=23 Exploring Operation: 55-28=27, Resulting Numbers: [5, 27] Generated Node #0,2,3: 46:[5, 27] Operation: 55-28=27 Exploring Operation: 55/5=11, Resulting Numbers: [28, 11] Generated Node #0,2,4: 46:[28, 11] Operation: 55/5=11 Moving to Node #0,3 Current State: 46:[62, 28, 12], Operations: ['67-55=12'] Exploring Operation: 62-12=50, Resulting Numbers: [28, 50] Generated Node #0,3,0: 46:[28, 50] Operation: 62-12=50 Exploring Operation: 28+12=40, Resulting Numbers: [62, 40] Generated Node #0,3,1: 46:[62, 40] Operation: 28+12=40 Exploring Operation: 28-12=16, Resulting Numbers: [62, 16] Generated Node #0,3,2: 46:[62, 16] Operation: 28-12=16 Exploring Operation: 62-28=34, Resulting Numbers: [12, 34] Generated Node #0,3,3: 46:[12, 34] Operation: 62-28=34 Exploring Operation: 62+12=74, Resulting Numbers: [28, 74] Generated Node #0,3,4: 46:[28, 74] Operation: 62+12=74 Moving to Node #0,0 Current State: 46:[67, 28, 7], Operations: ['62-55=7'] Exploring Operation: 67-28=39, Resulting Numbers: [7, 39] Generated Node #0,0,0: 46:[7, 39] Operation: 67-28=39 Exploring Operation: 67-7=60, Resulting Numbers: [28, 60] Generated Node #0,0,1: 46:[28, 60] Operation: 67-7=60 Exploring Operation: 28+7=35, Resulting Numbers: [67, 35] Generated Node #0,0,2: 46:[67, 35] Operation: 28+7=35 Exploring Operation: 28/7=4, Resulting Numbers: [67, 4] Generated Node #0,0,3: 46:[67, 4] Operation: 28/7=4 Exploring Operation: 28-7=21, Resulting Numbers: [67, 21] Generated Node #0,0,4: 46:[67, 21] Operation: 28-7=21 Moving to Node #0,1 Current State: 46:[55, 62, 39], Operations: ['67-28=39'] Exploring Operation: 55+39=94, Resulting Numbers: [62, 94] Generated Node #0,1,0: 46:[62, 94] Operation: 55+39=94 Exploring Operation: 62+39=101, Resulting Numbers: [55, 101] Generated Node #0,1,1: 46:[55, 101] Operation: 62+39=101 Exploring Operation: 62-55=7, Resulting Numbers: [39, 7] Generated Node #0,1,2: 46:[39, 7] Operation: 62-55=7 Exploring Operation: 55-39=16, Resulting Numbers: [62, 16] Generated Node #0,1,3: 46:[62, 16] Operation: 55-39=16 Exploring Operation: 62-39=23, Resulting Numbers: [55, 23] Generated Node #0,1,4: 46:[55, 23] Operation: 62-39=23 Moving to Node #0,4 Current State: 46:[62, 67, 27], Operations: ['55-28=27'] Exploring Operation: 67-27=40, Resulting Numbers: [62, 40] Generated Node #0,4,0: 46:[62, 40] Operation: 67-27=40 Exploring Operation: 67-62=5, Resulting Numbers: [27, 5] Generated Node #0,4,1: 46:[27, 5] Operation: 67-62=5 Exploring Operation: 67+27=94, Resulting Numbers: [62, 94] Generated Node #0,4,2: 46:[62, 94] Operation: 67+27=94 Exploring Operation: 62-27=35, Resulting Numbers: [67, 35] Generated Node #0,4,3: 46:[67, 35] Operation: 62-27=35 Exploring Operation: 62+27=89, Resulting Numbers: [67, 89] Generated Node #0,4,4: 46:[67, 89] Operation: 62+27=89 Moving to Node #0,2,3 Current State: 46:[5, 27], Operations: ['67-62=5', '55-28=27'] Exploring Operation: 27-5=22, Resulting Numbers: [22] 22,46 unequal: No Solution Exploring Operation: 5+27=32, Resulting Numbers: [32] 32,46 unequal: No Solution Exploring Operation: 5*27=135, Resulting Numbers: [135] 135,46 unequal: No Solution Moving to Node #0,4,1 Current State: 46:[27, 5], Operations: ['55-28=27', '67-62=5'] Exploring Operation: 27+5=32, Resulting Numbers: [32] 32,46 unequal: No Solution Exploring Operation: 27-5=22, Resulting Numbers: [22] 22,46 unequal: No Solution Exploring Operation: 27*5=135, Resulting Numbers: [135] 135,46 unequal: No Solution Moving to Node #0,2,2 Current State: 46:[55, 23], Operations: ['67-62=5', '28-5=23'] Exploring Operation: 55*23=1265, Resulting Numbers: [1265] 1265,46 unequal: No Solution Exploring Operation: 55+23=78, Resulting Numbers: [78] 78,46 unequal: No Solution Exploring Operation: 55-23=32, Resulting Numbers: [32] 32,46 unequal: No Solution Moving to Node #0,3,0 Current State: 46:[28, 50], Operations: ['67-55=12', '62-12=50'] Exploring Operation: 28+50=78, Resulting Numbers: [78] 78,46 unequal: No Solution Exploring Operation: 28*50=1400, Resulting Numbers: [1400] 1400,46 unequal: No Solution Exploring Operation: 50-28=22, Resulting Numbers: [22] 22,46 unequal: No Solution Moving to Node #0,2,1 Current State: 46:[28, 50], Operations: ['67-62=5', '55-5=50'] Exploring Operation: 28*50=1400, Resulting Numbers: [1400] 1400,46 unequal: No Solution Exploring Operation: 50-28=22, Resulting Numbers: [22] 22,46 unequal: No Solution Exploring Operation: 28+50=78, Resulting Numbers: [78] 78,46 unequal: No Solution Moving to Node #0,1,4 Current State: 46:[55, 23], Operations: ['67-28=39', '62-39=23'] Exploring Operation: 55*23=1265, Resulting Numbers: [1265] 1265,46 unequal: No Solution Exploring Operation: 55+23=78, Resulting Numbers: [78] 78,46 unequal: No Solution Exploring Operation: 55-23=32, Resulting Numbers: [32] 32,46 unequal: No Solution Moving to Node #0,0,0 Current State: 46:[7, 39], Operations: ['62-55=7', '67-28=39'] Exploring Operation: 39-7=32, Resulting Numbers: [32] 32,46 unequal: No Solution Exploring Operation: 7+39=46, Resulting Numbers: [46] 46,46 equal: Goal Reached Moving to Node #0 Current State: 46:[55, 62, 67, 28], Operations: [] Exploring Operation: 62-55=7, Resulting Numbers: [67, 28, 7] Generated Node #0,0: 46:[67, 28, 7] Operation: 62-55=7 Moving to Node #0,0 Current State: 46:[67, 28, 7], Operations: ['62-55=7'] Exploring Operation: 67-28=39, Resulting Numbers: [7, 39] Generated Node #0,0,0: 46:[7, 39] Operation: 67-28=39 Moving to Node #0,0,0 Current State: 46:[7, 39], Operations: ['62-55=7', '67-28=39'] Exploring Operation: 7+39=46, Resulting Numbers: [46] 46,46 equal: Goal Reached
0.953125
hs_5
sum_heuristic
[ 17, 25, 3, 37 ]
23
[ "17+25=42", "42/3=14", "37-14=23" ]
Current State: 23:[17, 25, 3, 37], Operations: [] Exploring Operation: 17+25=42, Resulting Numbers: [3, 37, 42] Generated Node #2: [3, 37, 42] from Operation: 17+25=42 Current State: 23:[3, 37, 42], Operations: ['17+25=42'] Exploring Operation: 42/3=14, Resulting Numbers: [37, 14] Generated Node #3: [37, 14] from Operation: 42/3=14 Current State: 23:[37, 14], Operations: ['17+25=42', '42/3=14'] Exploring Operation: 37-14=23, Resulting Numbers: [23] 23,23 equal: Goal Reached
4
Current State: 23:[17, 25, 3, 37], Operations: [] Exploring Operation: 17+3=20, Resulting Numbers: [25, 37, 20] Generated Node #0,0: 23:[25, 37, 20] Operation: 17+3=20 Start Sub Search at level 1: Moving to Node #0,0 Current State: 23:[25, 37, 20], Operations: ['17+3=20'] Exploring Operation: 37-20=17, Resulting Numbers: [25, 17] Generated Node #0,0,0: 23:[25, 17] Operation: 37-20=17 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 23:[25, 17], Operations: ['17+3=20', '37-20=17'] Exploring Operation: 25-17=8, Resulting Numbers: [8] 8,23 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
mult_heuristic
[ 75, 28, 5, 58 ]
100
[ "75-28=47", "58-5=53", "47+53=100" ]
Current State: 100:[75, 28, 5, 58], Operations: [] Exploring Operation: 75-28=47, Resulting Numbers: [5, 58, 47] Generated Node #2: [5, 58, 47] from Operation: 75-28=47 Current State: 100:[5, 58, 47], Operations: ['75-28=47'] Exploring Operation: 58-5=53, Resulting Numbers: [47, 53] Generated Node #3: [47, 53] from Operation: 58-5=53 Current State: 100:[47, 53], Operations: ['75-28=47', '58-5=53'] Exploring Operation: 47+53=100, Resulting Numbers: [100] 100,100 equal: Goal Reached
4
Current State: 100:[75, 28, 5, 58], Operations: [] Exploring Operation: 75-58=17, Resulting Numbers: [28, 5, 17] Generated Node #0,0: 100:[28, 5, 17] Operation: 75-58=17 Exploring Operation: 75+28=103, Resulting Numbers: [5, 58, 103] Generated Node #0,1: 100:[5, 58, 103] Operation: 75+28=103 Exploring Operation: 75/5=15, Resulting Numbers: [28, 58, 15] Generated Node #0,2: 100:[28, 58, 15] Operation: 75/5=15 Exploring Operation: 75-28=47, Resulting Numbers: [5, 58, 47] Generated Node #0,3: 100:[5, 58, 47] Operation: 75-28=47 Start Sub Search at level 1: Moving to Node #0,0 Current State: 100:[28, 5, 17], Operations: ['75-58=17'] Exploring Operation: 28-17=11, Resulting Numbers: [5, 11] Generated Node #0,0,0: 100:[5, 11] Operation: 28-17=11 Exploring Operation: 28+17=45, Resulting Numbers: [5, 45] Generated Node #0,0,1: 100:[5, 45] Operation: 28+17=45 Exploring Operation: 5+17=22, Resulting Numbers: [28, 22] Generated Node #0,0,2: 100:[28, 22] Operation: 5+17=22 Exploring Operation: 28-5=23, Resulting Numbers: [17, 23] Generated Node #0,0,3: 100:[17, 23] Operation: 28-5=23 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 100:[5, 11], Operations: ['75-58=17', '28-17=11'] Exploring Operation: 11-5=6, Resulting Numbers: [6] 6,100 unequal: No Solution Exploring Operation: 5+11=16, Resulting Numbers: [16] 16,100 unequal: No Solution Exploring Operation: 5*11=55, Resulting Numbers: [55] 55,100 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 100:[5, 45], Operations: ['75-58=17', '28+17=45'] Exploring Operation: 45/5=9, Resulting Numbers: [9] 9,100 unequal: No Solution Exploring Operation: 45-5=40, Resulting Numbers: [40] 40,100 unequal: No Solution Exploring Operation: 5+45=50, Resulting Numbers: [50] 50,100 unequal: No Solution Exploring Operation: 5*45=225, Resulting Numbers: [225] 225,100 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 100:[28, 22], Operations: ['75-58=17', '5+17=22'] Exploring Operation: 28*22=616, Resulting Numbers: [616] 616,100 unequal: No Solution Exploring Operation: 28+22=50, Resulting Numbers: [50] 50,100 unequal: No Solution Exploring Operation: 28-22=6, Resulting Numbers: [6] 6,100 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 100:[17, 23], Operations: ['75-58=17', '28-5=23'] Exploring Operation: 17+23=40, Resulting Numbers: [40] 40,100 unequal: No Solution Exploring Operation: 17*23=391, Resulting Numbers: [391] 391,100 unequal: No Solution Exploring Operation: 23-17=6, Resulting Numbers: [6] 6,100 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 100:[5, 58, 103], Operations: ['75+28=103'] Exploring Operation: 103-5=98, Resulting Numbers: [58, 98] Generated Node #0,1,0: 100:[58, 98] Operation: 103-5=98 Exploring Operation: 58-5=53, Resulting Numbers: [103, 53] Generated Node #0,1,1: 100:[103, 53] Operation: 58-5=53 Exploring Operation: 5+58=63, Resulting Numbers: [103, 63] Generated Node #0,1,2: 100:[103, 63] Operation: 5+58=63 Exploring Operation: 103-58=45, Resulting Numbers: [5, 45] Generated Node #0,1,3: 100:[5, 45] Operation: 103-58=45 Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 100:[5, 45], Operations: ['75+28=103', '103-58=45'] Exploring Operation: 45/5=9, Resulting Numbers: [9] 9,100 unequal: No Solution Exploring Operation: 45-5=40, Resulting Numbers: [40] 40,100 unequal: No Solution Exploring Operation: 5*45=225, Resulting Numbers: [225] 225,100 unequal: No Solution Exploring Operation: 5+45=50, Resulting Numbers: [50] 50,100 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 100:[103, 53], Operations: ['75+28=103', '58-5=53'] Exploring Operation: 103-53=50, Resulting Numbers: [50] 50,100 unequal: No Solution Exploring Operation: 103*53=5459, Resulting Numbers: [5459] 5459,100 unequal: No Solution Exploring Operation: 103+53=156, Resulting Numbers: [156] 156,100 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 100:[58, 98], Operations: ['75+28=103', '103-5=98'] Exploring Operation: 58+98=156, Resulting Numbers: [156] 156,100 unequal: No Solution Exploring Operation: 58*98=5684, Resulting Numbers: [5684] 5684,100 unequal: No Solution Exploring Operation: 98-58=40, Resulting Numbers: [40] 40,100 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 100:[103, 63], Operations: ['75+28=103', '5+58=63'] Exploring Operation: 103-63=40, Resulting Numbers: [40] 40,100 unequal: No Solution Exploring Operation: 103*63=6489, Resulting Numbers: [6489] 6489,100 unequal: No Solution Exploring Operation: 103+63=166, Resulting Numbers: [166] 166,100 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 100:[5, 58, 47], Operations: ['75-28=47'] Exploring Operation: 58-5=53, Resulting Numbers: [47, 53] Generated Node #0,3,0: 100:[47, 53] Operation: 58-5=53 Exploring Operation: 58+47=105, Resulting Numbers: [5, 105] Generated Node #0,3,1: 100:[5, 105] Operation: 58+47=105 Exploring Operation: 58-47=11, Resulting Numbers: [5, 11] Generated Node #0,3,2: 100:[5, 11] Operation: 58-47=11 Exploring Operation: 5+47=52, Resulting Numbers: [58, 52] Generated Node #0,3,3: 100:[58, 52] Operation: 5+47=52 Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 100:[5, 11], Operations: ['75-28=47', '58-47=11'] Exploring Operation: 5+11=16, Resulting Numbers: [16] 16,100 unequal: No Solution Exploring Operation: 5*11=55, Resulting Numbers: [55] 55,100 unequal: No Solution Exploring Operation: 11-5=6, Resulting Numbers: [6] 6,100 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 100:[5, 105], Operations: ['75-28=47', '58+47=105'] Exploring Operation: 5+105=110, Resulting Numbers: [110] 110,100 unequal: No Solution Exploring Operation: 105/5=21, Resulting Numbers: [21] 21,100 unequal: No Solution Exploring Operation: 105-5=100, Resulting Numbers: [100] 100,100 equal: Goal Reached Moving to Node #0 Current State: 100:[75, 28, 5, 58], Operations: [] Exploring Operation: 75-28=47, Resulting Numbers: [5, 58, 47] Generated Node #0,3: 100:[5, 58, 47] Operation: 75-28=47 Moving to Node #0,3 Current State: 100:[5, 58, 47], Operations: ['75-28=47'] Exploring Operation: 58+47=105, Resulting Numbers: [5, 105] Generated Node #0,3,1: 100:[5, 105] Operation: 58+47=105 Moving to Node #0,3,1 Current State: 100:[5, 105], Operations: ['75-28=47', '58+47=105'] Exploring Operation: 105-5=100, Resulting Numbers: [100] 100,100 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.954861
hs_4
mult_heuristic
[ 68, 15, 46, 21 ]
28
[ "68-15=53", "46-21=25", "53-25=28" ]
Current State: 28:[68, 15, 46, 21], Operations: [] Exploring Operation: 68-15=53, Resulting Numbers: [46, 21, 53] Generated Node #2: [46, 21, 53] from Operation: 68-15=53 Current State: 28:[46, 21, 53], Operations: ['68-15=53'] Exploring Operation: 46-21=25, Resulting Numbers: [53, 25] Generated Node #3: [53, 25] from Operation: 46-21=25 Current State: 28:[53, 25], Operations: ['68-15=53', '46-21=25'] Exploring Operation: 53-25=28, Resulting Numbers: [28] 28,28 equal: Goal Reached
4
Current State: 28:[68, 15, 46, 21], Operations: [] Exploring Operation: 68-21=47, Resulting Numbers: [15, 46, 47] Generated Node #0,0: 28:[15, 46, 47] Operation: 68-21=47 Exploring Operation: 68-46=22, Resulting Numbers: [15, 21, 22] Generated Node #0,1: 28:[15, 21, 22] Operation: 68-46=22 Start Sub Search at level 1: Moving to Node #0,1 Current State: 28:[15, 21, 22], Operations: ['68-46=22'] Exploring Operation: 21-15=6, Resulting Numbers: [22, 6] Generated Node #0,1,0: 28:[22, 6] Operation: 21-15=6 Exploring Operation: 22-21=1, Resulting Numbers: [15, 1] Generated Node #0,1,1: 28:[15, 1] Operation: 22-21=1 Moving to Node #0,1,1 Current State: 28:[15, 1], Operations: ['68-46=22', '22-21=1'] Exploring Operation: 15-1=14, Resulting Numbers: [14] 14,28 unequal: No Solution Exploring Operation: 15*1=15, Resulting Numbers: [15] 15,28 unequal: No Solution Moving to Node #0,1,0 Current State: 28:[22, 6], Operations: ['68-46=22', '21-15=6'] Exploring Operation: 22+6=28, Resulting Numbers: [28] 28,28 equal: Goal Reached Moving to Node #0 Current State: 28:[68, 15, 46, 21], Operations: [] Exploring Operation: 68-46=22, Resulting Numbers: [15, 21, 22] Generated Node #0,1: 28:[15, 21, 22] Operation: 68-46=22 Moving to Node #0,1 Current State: 28:[15, 21, 22], Operations: ['68-46=22'] Exploring Operation: 21-15=6, Resulting Numbers: [22, 6] Generated Node #0,1,0: 28:[22, 6] Operation: 21-15=6 Moving to Node #0,1,0 Current State: 28:[22, 6], Operations: ['68-46=22', '21-15=6'] Exploring Operation: 22+6=28, Resulting Numbers: [28] 28,28 equal: Goal Reached Exit Sub Search at level 1
0.990451
hs_2
mult_heuristic
[ 71, 68, 4, 39 ]
96
[ "71+68=139", "4+39=43", "139-43=96" ]
Current State: 96:[71, 68, 4, 39], Operations: [] Exploring Operation: 71+68=139, Resulting Numbers: [4, 39, 139] Generated Node #2: [4, 39, 139] from Operation: 71+68=139 Current State: 96:[4, 39, 139], Operations: ['71+68=139'] Exploring Operation: 4+39=43, Resulting Numbers: [139, 43] Generated Node #3: [139, 43] from Operation: 4+39=43 Current State: 96:[139, 43], Operations: ['71+68=139', '4+39=43'] Exploring Operation: 139-43=96, Resulting Numbers: [96] 96,96 equal: Goal Reached
4
Current State: 96:[71, 68, 4, 39], Operations: [] Exploring Operation: 71-68=3, Resulting Numbers: [4, 39, 3] Generated Node #0,0: 96:[4, 39, 3] Operation: 71-68=3 Start Sub Search at level 1: Moving to Node #0,0 Current State: 96:[4, 39, 3], Operations: ['71-68=3'] Exploring Operation: 39/3=13, Resulting Numbers: [4, 13] Generated Node #0,0,0: 96:[4, 13] Operation: 39/3=13 Moving to Node #0,0,0 Current State: 96:[4, 13], Operations: ['71-68=3', '39/3=13'] Exploring Operation: 4+13=17, Resulting Numbers: [17] 17,96 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
mult_heuristic
[ 23, 2, 36, 84 ]
58
[ "36-23=13", "2*13=26", "84-26=58" ]
Current State: 58:[23, 2, 36, 84], Operations: [] Exploring Operation: 36-23=13, Resulting Numbers: [2, 84, 13] Generated Node #2: [2, 84, 13] from Operation: 36-23=13 Current State: 58:[2, 84, 13], Operations: ['36-23=13'] Exploring Operation: 2*13=26, Resulting Numbers: [84, 26] Generated Node #3: [84, 26] from Operation: 2*13=26 Current State: 58:[84, 26], Operations: ['36-23=13', '2*13=26'] Exploring Operation: 84-26=58, Resulting Numbers: [58] 58,58 equal: Goal Reached
4
Current State: 58:[23, 2, 36, 84], Operations: [] Exploring Operation: 84-23=61, Resulting Numbers: [2, 36, 61] Generated Node #0,0: 58:[2, 36, 61] Operation: 84-23=61 Exploring Operation: 84-36=48, Resulting Numbers: [23, 2, 48] Generated Node #0,1: 58:[23, 2, 48] Operation: 84-36=48 Exploring Operation: 84/2=42, Resulting Numbers: [23, 36, 42] Generated Node #0,2: 58:[23, 36, 42] Operation: 84/2=42 Moving to Node #0,0 Current State: 58:[2, 36, 61], Operations: ['84-23=61'] Exploring Operation: 36-2=34, Resulting Numbers: [61, 34] Generated Node #0,0,0: 58:[61, 34] Operation: 36-2=34 Exploring Operation: 61-36=25, Resulting Numbers: [2, 25] Generated Node #0,0,1: 58:[2, 25] Operation: 61-36=25 Exploring Operation: 61-2=59, Resulting Numbers: [36, 59] Generated Node #0,0,2: 58:[36, 59] Operation: 61-2=59 Moving to Node #0,1 Current State: 58:[23, 2, 48], Operations: ['84-36=48'] Exploring Operation: 48-23=25, Resulting Numbers: [2, 25] Generated Node #0,1,0: 58:[2, 25] Operation: 48-23=25 Exploring Operation: 48/2=24, Resulting Numbers: [23, 24] Generated Node #0,1,1: 58:[23, 24] Operation: 48/2=24 Exploring Operation: 23+48=71, Resulting Numbers: [2, 71] Generated Node #0,1,2: 58:[2, 71] Operation: 23+48=71 Moving to Node #0,2 Current State: 58:[23, 36, 42], Operations: ['84/2=42'] Exploring Operation: 23+42=65, Resulting Numbers: [36, 65] Generated Node #0,2,0: 58:[36, 65] Operation: 23+42=65 Exploring Operation: 42-36=6, Resulting Numbers: [23, 6] Generated Node #0,2,1: 58:[23, 6] Operation: 42-36=6 Exploring Operation: 23+36=59, Resulting Numbers: [42, 59] Generated Node #0,2,2: 58:[42, 59] Operation: 23+36=59 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 58:[23, 6], Operations: ['84/2=42', '42-36=6'] Exploring Operation: 23*6=138, Resulting Numbers: [138] 138,58 unequal: No Solution Exploring Operation: 23+6=29, Resulting Numbers: [29] 29,58 unequal: No Solution Exploring Operation: 23-6=17, Resulting Numbers: [17] 17,58 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 58:[36, 65], Operations: ['84/2=42', '23+42=65'] Exploring Operation: 65-36=29, Resulting Numbers: [29] 29,58 unequal: No Solution Exploring Operation: 36*65=2340, Resulting Numbers: [2340] 2340,58 unequal: No Solution Exploring Operation: 36+65=101, Resulting Numbers: [101] 101,58 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 58:[42, 59], Operations: ['84/2=42', '23+36=59'] Exploring Operation: 42+59=101, Resulting Numbers: [101] 101,58 unequal: No Solution Exploring Operation: 59-42=17, Resulting Numbers: [17] 17,58 unequal: No Solution Exploring Operation: 42*59=2478, Resulting Numbers: [2478] 2478,58 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0,1 Current State: 58:[2, 25], Operations: ['84-23=61', '61-36=25'] Exploring Operation: 25-2=23, Resulting Numbers: [23] 23,58 unequal: No Solution Exploring Operation: 2*25=50, Resulting Numbers: [50] 50,58 unequal: No Solution Exploring Operation: 2+25=27, Resulting Numbers: [27] 27,58 unequal: No Solution Moving to Node #0,1,0 Current State: 58:[2, 25], Operations: ['84-36=48', '48-23=25'] Exploring Operation: 2*25=50, Resulting Numbers: [50] 50,58 unequal: No Solution Exploring Operation: 25-2=23, Resulting Numbers: [23] 23,58 unequal: No Solution Exploring Operation: 2+25=27, Resulting Numbers: [27] 27,58 unequal: No Solution Moving to Node #0,0,2 Current State: 58:[36, 59], Operations: ['84-23=61', '61-2=59'] Exploring Operation: 36+59=95, Resulting Numbers: [95] 95,58 unequal: No Solution Exploring Operation: 36*59=2124, Resulting Numbers: [2124] 2124,58 unequal: No Solution Exploring Operation: 59-36=23, Resulting Numbers: [23] 23,58 unequal: No Solution Moving to Node #0,0,0 Current State: 58:[61, 34], Operations: ['84-23=61', '36-2=34'] Exploring Operation: 61*34=2074, Resulting Numbers: [2074] 2074,58 unequal: No Solution Exploring Operation: 61-34=27, Resulting Numbers: [27] 27,58 unequal: No Solution Exploring Operation: 61+34=95, Resulting Numbers: [95] 95,58 unequal: No Solution Moving to Node #0,1,1 Current State: 58:[23, 24], Operations: ['84-36=48', '48/2=24'] Exploring Operation: 23+24=47, Resulting Numbers: [47] 47,58 unequal: No Solution Exploring Operation: 23*24=552, Resulting Numbers: [552] 552,58 unequal: No Solution Exploring Operation: 24-23=1, Resulting Numbers: [1] 1,58 unequal: No Solution Moving to Node #0,1,2 Current State: 58:[2, 71], Operations: ['84-36=48', '23+48=71'] Exploring Operation: 2+71=73, Resulting Numbers: [73] 73,58 unequal: No Solution Exploring Operation: 2*71=142, Resulting Numbers: [142] 142,58 unequal: No Solution Exploring Operation: 71-2=69, Resulting Numbers: [69] 69,58 unequal: No Solution No solution found.
0
hs_3
sum_heuristic
[ 44, 48, 82, 6 ]
30
[ "82-44=38", "48/6=8", "38-8=30" ]
Current State: 30:[44, 48, 82, 6], Operations: [] Exploring Operation: 82-44=38, Resulting Numbers: [48, 6, 38] Generated Node #2: [48, 6, 38] from Operation: 82-44=38 Current State: 30:[48, 6, 38], Operations: ['82-44=38'] Exploring Operation: 48/6=8, Resulting Numbers: [38, 8] Generated Node #3: [38, 8] from Operation: 48/6=8 Current State: 30:[38, 8], Operations: ['82-44=38', '48/6=8'] Exploring Operation: 38-8=30, Resulting Numbers: [30] 30,30 equal: Goal Reached
4
Current State: 30:[44, 48, 82, 6], Operations: [] Exploring Operation: 44-6=38, Resulting Numbers: [48, 82, 38] Generated Node #0,0: 30:[48, 82, 38] Operation: 44-6=38 Exploring Operation: 82-44=38, Resulting Numbers: [48, 6, 38] Generated Node #0,1: 30:[48, 6, 38] Operation: 82-44=38 Exploring Operation: 48-44=4, Resulting Numbers: [82, 6, 4] Generated Node #0,2: 30:[82, 6, 4] Operation: 48-44=4 Exploring Operation: 82-48=34, Resulting Numbers: [44, 6, 34] Generated Node #0,3: 30:[44, 6, 34] Operation: 82-48=34 Exploring Operation: 48/6=8, Resulting Numbers: [44, 82, 8] Generated Node #0,4: 30:[44, 82, 8] Operation: 48/6=8 Moving to Node #0,3 Current State: 30:[44, 6, 34], Operations: ['82-48=34'] Exploring Operation: 6+34=40, Resulting Numbers: [44, 40] Generated Node #0,3,0: 30:[44, 40] Operation: 6+34=40 Exploring Operation: 34-6=28, Resulting Numbers: [44, 28] Generated Node #0,3,1: 30:[44, 28] Operation: 34-6=28 Exploring Operation: 44-34=10, Resulting Numbers: [6, 10] Generated Node #0,3,2: 30:[6, 10] Operation: 44-34=10 Exploring Operation: 44+6=50, Resulting Numbers: [34, 50] Generated Node #0,3,3: 30:[34, 50] Operation: 44+6=50 Exploring Operation: 44-6=38, Resulting Numbers: [34, 38] Generated Node #0,3,4: 30:[34, 38] Operation: 44-6=38 Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 30:[6, 10], Operations: ['82-48=34', '44-34=10'] Exploring Operation: 10-6=4, Resulting Numbers: [4] 4,30 unequal: No Solution Exploring Operation: 6+10=16, Resulting Numbers: [16] 16,30 unequal: No Solution Exploring Operation: 6*10=60, Resulting Numbers: [60] 60,30 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,4 Current State: 30:[34, 38], Operations: ['82-48=34', '44-6=38'] Exploring Operation: 34*38=1292, Resulting Numbers: [1292] 1292,30 unequal: No Solution Exploring Operation: 38-34=4, Resulting Numbers: [4] 4,30 unequal: No Solution Exploring Operation: 34+38=72, Resulting Numbers: [72] 72,30 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 30:[44, 28], Operations: ['82-48=34', '34-6=28'] Exploring Operation: 44-28=16, Resulting Numbers: [16] 16,30 unequal: No Solution Exploring Operation: 44+28=72, Resulting Numbers: [72] 72,30 unequal: No Solution Exploring Operation: 44*28=1232, Resulting Numbers: [1232] 1232,30 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 30:[44, 40], Operations: ['82-48=34', '6+34=40'] Exploring Operation: 44*40=1760, Resulting Numbers: [1760] 1760,30 unequal: No Solution Exploring Operation: 44+40=84, Resulting Numbers: [84] 84,30 unequal: No Solution Exploring Operation: 44-40=4, Resulting Numbers: [4] 4,30 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 30:[34, 50], Operations: ['82-48=34', '44+6=50'] Exploring Operation: 50-34=16, Resulting Numbers: [16] 16,30 unequal: No Solution Exploring Operation: 34*50=1700, Resulting Numbers: [1700] 1700,30 unequal: No Solution Exploring Operation: 34+50=84, Resulting Numbers: [84] 84,30 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 30:[48, 6, 38], Operations: ['82-44=38'] Exploring Operation: 48-38=10, Resulting Numbers: [6, 10] Generated Node #0,1,0: 30:[6, 10] Operation: 48-38=10 Exploring Operation: 48+6=54, Resulting Numbers: [38, 54] Generated Node #0,1,1: 30:[38, 54] Operation: 48+6=54 Exploring Operation: 48/6=8, Resulting Numbers: [38, 8] Generated Node #0,1,2: 30:[38, 8] Operation: 48/6=8 Exploring Operation: 38-6=32, Resulting Numbers: [48, 32] Generated Node #0,1,3: 30:[48, 32] Operation: 38-6=32 Exploring Operation: 48-6=42, Resulting Numbers: [38, 42] Generated Node #0,1,4: 30:[38, 42] Operation: 48-6=42 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 30:[6, 10], Operations: ['82-44=38', '48-38=10'] Exploring Operation: 6+10=16, Resulting Numbers: [16] 16,30 unequal: No Solution Exploring Operation: 10-6=4, Resulting Numbers: [4] 4,30 unequal: No Solution Exploring Operation: 6*10=60, Resulting Numbers: [60] 60,30 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 30:[38, 8], Operations: ['82-44=38', '48/6=8'] Exploring Operation: 38-8=30, Resulting Numbers: [30] 30,30 equal: Goal Reached Moving to Node #0 Current State: 30:[44, 48, 82, 6], Operations: [] Exploring Operation: 82-44=38, Resulting Numbers: [48, 6, 38] Generated Node #0,1: 30:[48, 6, 38] Operation: 82-44=38 Moving to Node #0,1 Current State: 30:[48, 6, 38], Operations: ['82-44=38'] Exploring Operation: 48/6=8, Resulting Numbers: [38, 8] Generated Node #0,1,2: 30:[38, 8] Operation: 48/6=8 Moving to Node #0,1,2 Current State: 30:[38, 8], Operations: ['82-44=38', '48/6=8'] Exploring Operation: 38-8=30, Resulting Numbers: [30] 30,30 equal: Goal Reached Exit Sub Search at level 1
0.967014
hs_5
mult_heuristic
[ 95, 38, 12, 19 ]
62
[ "95*12=1140", "38+1140=1178", "1178/19=62" ]
Current State: 62:[95, 38, 12, 19], Operations: [] Exploring Operation: 95*12=1140, Resulting Numbers: [38, 19, 1140] Generated Node #2: [38, 19, 1140] from Operation: 95*12=1140 Current State: 62:[38, 19, 1140], Operations: ['95*12=1140'] Exploring Operation: 38+1140=1178, Resulting Numbers: [19, 1178] Generated Node #3: [19, 1178] from Operation: 38+1140=1178 Current State: 62:[19, 1178], Operations: ['95*12=1140', '38+1140=1178'] Exploring Operation: 1178/19=62, Resulting Numbers: [62] 62,62 equal: Goal Reached
4
Current State: 62:[95, 38, 12, 19], Operations: [] Exploring Operation: 95/19=5, Resulting Numbers: [38, 12, 5] Generated Node #0,0: 62:[38, 12, 5] Operation: 95/19=5 Exploring Operation: 95-38=57, Resulting Numbers: [12, 19, 57] Generated Node #0,1: 62:[12, 19, 57] Operation: 95-38=57 Moving to Node #0,0 Current State: 62:[38, 12, 5], Operations: ['95/19=5'] Exploring Operation: 38-12=26, Resulting Numbers: [5, 26] Generated Node #0,0,0: 62:[5, 26] Operation: 38-12=26 Exploring Operation: 12*5=60, Resulting Numbers: [38, 60] Generated Node #0,0,1: 62:[38, 60] Operation: 12*5=60 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 62:[5, 26], Operations: ['95/19=5', '38-12=26'] Exploring Operation: 5+26=31, Resulting Numbers: [31] 31,62 unequal: No Solution Exploring Operation: 26-5=21, Resulting Numbers: [21] 21,62 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 62:[38, 60], Operations: ['95/19=5', '12*5=60'] Exploring Operation: 38+60=98, Resulting Numbers: [98] 98,62 unequal: No Solution Exploring Operation: 60-38=22, Resulting Numbers: [22] 22,62 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 62:[12, 19, 57], Operations: ['95-38=57'] Exploring Operation: 19-12=7, Resulting Numbers: [57, 7] Generated Node #0,1,0: 62:[57, 7] Operation: 19-12=7 Exploring Operation: 12+19=31, Resulting Numbers: [57, 31] Generated Node #0,1,1: 62:[57, 31] Operation: 12+19=31 Moving to Node #0,1,1 Current State: 62:[57, 31], Operations: ['95-38=57', '12+19=31'] Exploring Operation: 57-31=26, Resulting Numbers: [26] 26,62 unequal: No Solution Exploring Operation: 57+31=88, Resulting Numbers: [88] 88,62 unequal: No Solution Moving to Node #0,1,0 Current State: 62:[57, 7], Operations: ['95-38=57', '19-12=7'] Exploring Operation: 57-7=50, Resulting Numbers: [50] 50,62 unequal: No Solution Exploring Operation: 57+7=64, Resulting Numbers: [64] 64,62 unequal: No Solution No solution found.
0
hs_2
sum_heuristic
[ 54, 43, 50, 84 ]
37
[ "54+43=97", "50+84=134", "134-97=37" ]
Current State: 37:[54, 43, 50, 84], Operations: [] Exploring Operation: 54+43=97, Resulting Numbers: [50, 84, 97] Generated Node #2: [50, 84, 97] from Operation: 54+43=97 Current State: 37:[50, 84, 97], Operations: ['54+43=97'] Exploring Operation: 50+84=134, Resulting Numbers: [97, 134] Generated Node #3: [97, 134] from Operation: 50+84=134 Current State: 37:[97, 134], Operations: ['54+43=97', '50+84=134'] Exploring Operation: 134-97=37, Resulting Numbers: [37] 37,37 equal: Goal Reached
4
Current State: 37:[54, 43, 50, 84], Operations: [] Exploring Operation: 84-50=34, Resulting Numbers: [54, 43, 34] Generated Node #0,0: 37:[54, 43, 34] Operation: 84-50=34 Exploring Operation: 84-54=30, Resulting Numbers: [43, 50, 30] Generated Node #0,1: 37:[43, 50, 30] Operation: 84-54=30 Exploring Operation: 84-43=41, Resulting Numbers: [54, 50, 41] Generated Node #0,2: 37:[54, 50, 41] Operation: 84-43=41 Exploring Operation: 54-43=11, Resulting Numbers: [50, 84, 11] Generated Node #0,3: 37:[50, 84, 11] Operation: 54-43=11 Moving to Node #0,0 Current State: 37:[54, 43, 34], Operations: ['84-50=34'] Exploring Operation: 43-34=9, Resulting Numbers: [54, 9] Generated Node #0,0,0: 37:[54, 9] Operation: 43-34=9 Exploring Operation: 54-34=20, Resulting Numbers: [43, 20] Generated Node #0,0,1: 37:[43, 20] Operation: 54-34=20 Exploring Operation: 54+34=88, Resulting Numbers: [43, 88] Generated Node #0,0,2: 37:[43, 88] Operation: 54+34=88 Exploring Operation: 54-43=11, Resulting Numbers: [34, 11] Generated Node #0,0,3: 37:[34, 11] Operation: 54-43=11 Moving to Node #0,1 Current State: 37:[43, 50, 30], Operations: ['84-54=30'] Exploring Operation: 50-30=20, Resulting Numbers: [43, 20] Generated Node #0,1,0: 37:[43, 20] Operation: 50-30=20 Exploring Operation: 50-43=7, Resulting Numbers: [30, 7] Generated Node #0,1,1: 37:[30, 7] Operation: 50-43=7 Exploring Operation: 43-30=13, Resulting Numbers: [50, 13] Generated Node #0,1,2: 37:[50, 13] Operation: 43-30=13 Exploring Operation: 43+30=73, Resulting Numbers: [50, 73] Generated Node #0,1,3: 37:[50, 73] Operation: 43+30=73 Moving to Node #0,2 Current State: 37:[54, 50, 41], Operations: ['84-43=41'] Exploring Operation: 54-50=4, Resulting Numbers: [41, 4] Generated Node #0,2,0: 37:[41, 4] Operation: 54-50=4 Exploring Operation: 54+50=104, Resulting Numbers: [41, 104] Generated Node #0,2,1: 37:[41, 104] Operation: 54+50=104 Exploring Operation: 50-41=9, Resulting Numbers: [54, 9] Generated Node #0,2,2: 37:[54, 9] Operation: 50-41=9 Exploring Operation: 54-41=13, Resulting Numbers: [50, 13] Generated Node #0,2,3: 37:[50, 13] Operation: 54-41=13 Moving to Node #0,3 Current State: 37:[50, 84, 11], Operations: ['54-43=11'] Exploring Operation: 84-50=34, Resulting Numbers: [11, 34] Generated Node #0,3,0: 37:[11, 34] Operation: 84-50=34 Exploring Operation: 50-11=39, Resulting Numbers: [84, 39] Generated Node #0,3,1: 37:[84, 39] Operation: 50-11=39 Exploring Operation: 50+11=61, Resulting Numbers: [84, 61] Generated Node #0,3,2: 37:[84, 61] Operation: 50+11=61 Exploring Operation: 84-11=73, Resulting Numbers: [50, 73] Generated Node #0,3,3: 37:[50, 73] Operation: 84-11=73 Moving to Node #0,0,1 Current State: 37:[43, 20], Operations: ['84-50=34', '54-34=20'] Exploring Operation: 43*20=860, Resulting Numbers: [860] 860,37 unequal: No Solution Exploring Operation: 43+20=63, Resulting Numbers: [63] 63,37 unequal: No Solution Exploring Operation: 43-20=23, Resulting Numbers: [23] 23,37 unequal: No Solution Moving to Node #0,1,0 Current State: 37:[43, 20], Operations: ['84-54=30', '50-30=20'] Exploring Operation: 43+20=63, Resulting Numbers: [63] 63,37 unequal: No Solution Exploring Operation: 43-20=23, Resulting Numbers: [23] 23,37 unequal: No Solution Exploring Operation: 43*20=860, Resulting Numbers: [860] 860,37 unequal: No Solution Moving to Node #0,3,0 Current State: 37:[11, 34], Operations: ['54-43=11', '84-50=34'] Exploring Operation: 11*34=374, Resulting Numbers: [374] 374,37 unequal: No Solution Exploring Operation: 34-11=23, Resulting Numbers: [23] 23,37 unequal: No Solution Exploring Operation: 11+34=45, Resulting Numbers: [45] 45,37 unequal: No Solution Moving to Node #0,0,3 Current State: 37:[34, 11], Operations: ['84-50=34', '54-43=11'] Exploring Operation: 34*11=374, Resulting Numbers: [374] 374,37 unequal: No Solution Exploring Operation: 34-11=23, Resulting Numbers: [23] 23,37 unequal: No Solution Exploring Operation: 34+11=45, Resulting Numbers: [45] 45,37 unequal: No Solution Moving to Node #0,1,2 Current State: 37:[50, 13], Operations: ['84-54=30', '43-30=13'] Exploring Operation: 50+13=63, Resulting Numbers: [63] 63,37 unequal: No Solution Exploring Operation: 50-13=37, Resulting Numbers: [37] 37,37 equal: Goal Reached Moving to Node #0 Current State: 37:[54, 43, 50, 84], Operations: [] Exploring Operation: 84-54=30, Resulting Numbers: [43, 50, 30] Generated Node #0,1: 37:[43, 50, 30] Operation: 84-54=30 Moving to Node #0,1 Current State: 37:[43, 50, 30], Operations: ['84-54=30'] Exploring Operation: 43-30=13, Resulting Numbers: [50, 13] Generated Node #0,1,2: 37:[50, 13] Operation: 43-30=13 Moving to Node #0,1,2 Current State: 37:[50, 13], Operations: ['84-54=30', '43-30=13'] Exploring Operation: 50-13=37, Resulting Numbers: [37] 37,37 equal: Goal Reached
0.967014
hs_4
mult_heuristic
[ 80, 48, 26, 96 ]
14
[ "80*48=3840", "3840/96=40", "40-26=14" ]
Current State: 14:[80, 48, 26, 96], Operations: [] Exploring Operation: 80*48=3840, Resulting Numbers: [26, 96, 3840] Generated Node #2: [26, 96, 3840] from Operation: 80*48=3840 Current State: 14:[26, 96, 3840], Operations: ['80*48=3840'] Exploring Operation: 3840/96=40, Resulting Numbers: [26, 40] Generated Node #3: [26, 40] from Operation: 3840/96=40 Current State: 14:[26, 40], Operations: ['80*48=3840', '3840/96=40'] Exploring Operation: 40-26=14, Resulting Numbers: [14] 14,14 equal: Goal Reached
4
Current State: 14:[80, 48, 26, 96], Operations: [] Exploring Operation: 96-48=48, Resulting Numbers: [80, 26, 48] Generated Node #0,0: 14:[80, 26, 48] Operation: 96-48=48 Exploring Operation: 80-48=32, Resulting Numbers: [26, 96, 32] Generated Node #0,1: 14:[26, 96, 32] Operation: 80-48=32 Exploring Operation: 96-80=16, Resulting Numbers: [48, 26, 16] Generated Node #0,2: 14:[48, 26, 16] Operation: 96-80=16 Exploring Operation: 96/48=2, Resulting Numbers: [80, 26, 2] Generated Node #0,3: 14:[80, 26, 2] Operation: 96/48=2 Moving to Node #0,2 Current State: 14:[48, 26, 16], Operations: ['96-80=16'] Exploring Operation: 48-16=32, Resulting Numbers: [26, 32] Generated Node #0,2,0: 14:[26, 32] Operation: 48-16=32 Exploring Operation: 48/16=3, Resulting Numbers: [26, 3] Generated Node #0,2,1: 14:[26, 3] Operation: 48/16=3 Exploring Operation: 48-26=22, Resulting Numbers: [16, 22] Generated Node #0,2,2: 14:[16, 22] Operation: 48-26=22 Exploring Operation: 26-16=10, Resulting Numbers: [48, 10] Generated Node #0,2,3: 14:[48, 10] Operation: 26-16=10 Moving to Node #0,3 Current State: 14:[80, 26, 2], Operations: ['96/48=2'] Exploring Operation: 80/2=40, Resulting Numbers: [26, 40] Generated Node #0,3,0: 14:[26, 40] Operation: 80/2=40 Exploring Operation: 26/2=13, Resulting Numbers: [80, 13] Generated Node #0,3,1: 14:[80, 13] Operation: 26/2=13 Exploring Operation: 80-2=78, Resulting Numbers: [26, 78] Generated Node #0,3,2: 14:[26, 78] Operation: 80-2=78 Exploring Operation: 80-26=54, Resulting Numbers: [2, 54] Generated Node #0,3,3: 14:[2, 54] Operation: 80-26=54 Moving to Node #0,1 Current State: 14:[26, 96, 32], Operations: ['80-48=32'] Exploring Operation: 96-26=70, Resulting Numbers: [32, 70] Generated Node #0,1,0: 14:[32, 70] Operation: 96-26=70 Exploring Operation: 32-26=6, Resulting Numbers: [96, 6] Generated Node #0,1,1: 14:[96, 6] Operation: 32-26=6 Exploring Operation: 96-32=64, Resulting Numbers: [26, 64] Generated Node #0,1,2: 14:[26, 64] Operation: 96-32=64 Exploring Operation: 96/32=3, Resulting Numbers: [26, 3] Generated Node #0,1,3: 14:[26, 3] Operation: 96/32=3 Moving to Node #0,0 Current State: 14:[80, 26, 48], Operations: ['96-48=48'] Exploring Operation: 48-26=22, Resulting Numbers: [80, 22] Generated Node #0,0,0: 14:[80, 22] Operation: 48-26=22 Exploring Operation: 80+26=106, Resulting Numbers: [48, 106] Generated Node #0,0,1: 14:[48, 106] Operation: 80+26=106 Exploring Operation: 80-26=54, Resulting Numbers: [48, 54] Generated Node #0,0,2: 14:[48, 54] Operation: 80-26=54 Exploring Operation: 80-48=32, Resulting Numbers: [26, 32] Generated Node #0,0,3: 14:[26, 32] Operation: 80-48=32 Moving to Node #0,2,2 Current State: 14:[16, 22], Operations: ['96-80=16', '48-26=22'] Exploring Operation: 22-16=6, Resulting Numbers: [6] 6,14 unequal: No Solution Exploring Operation: 16*22=352, Resulting Numbers: [352] 352,14 unequal: No Solution Exploring Operation: 16+22=38, Resulting Numbers: [38] 38,14 unequal: No Solution Moving to Node #0,2,1 Current State: 14:[26, 3], Operations: ['96-80=16', '48/16=3'] Exploring Operation: 26-3=23, Resulting Numbers: [23] 23,14 unequal: No Solution Exploring Operation: 26*3=78, Resulting Numbers: [78] 78,14 unequal: No Solution Exploring Operation: 26+3=29, Resulting Numbers: [29] 29,14 unequal: No Solution Moving to Node #0,1,3 Current State: 14:[26, 3], Operations: ['80-48=32', '96/32=3'] Exploring Operation: 26+3=29, Resulting Numbers: [29] 29,14 unequal: No Solution Exploring Operation: 26-3=23, Resulting Numbers: [23] 23,14 unequal: No Solution Exploring Operation: 26*3=78, Resulting Numbers: [78] 78,14 unequal: No Solution Moving to Node #0,2,0 Current State: 14:[26, 32], Operations: ['96-80=16', '48-16=32'] Exploring Operation: 26+32=58, Resulting Numbers: [58] 58,14 unequal: No Solution Exploring Operation: 26*32=832, Resulting Numbers: [832] 832,14 unequal: No Solution Exploring Operation: 32-26=6, Resulting Numbers: [6] 6,14 unequal: No Solution Moving to Node #0,0,3 Current State: 14:[26, 32], Operations: ['96-48=48', '80-48=32'] Exploring Operation: 32-26=6, Resulting Numbers: [6] 6,14 unequal: No Solution Exploring Operation: 26*32=832, Resulting Numbers: [832] 832,14 unequal: No Solution Exploring Operation: 26+32=58, Resulting Numbers: [58] 58,14 unequal: No Solution Moving to Node #0,2,3 Current State: 14:[48, 10], Operations: ['96-80=16', '26-16=10'] Exploring Operation: 48-10=38, Resulting Numbers: [38] 38,14 unequal: No Solution Exploring Operation: 48*10=480, Resulting Numbers: [480] 480,14 unequal: No Solution Exploring Operation: 48+10=58, Resulting Numbers: [58] 58,14 unequal: No Solution Moving to Node #0,3,0 Current State: 14:[26, 40], Operations: ['96/48=2', '80/2=40'] Exploring Operation: 26*40=1040, Resulting Numbers: [1040] 1040,14 unequal: No Solution Exploring Operation: 40-26=14, Resulting Numbers: [14] 14,14 equal: Goal Reached Moving to Node #0 Current State: 14:[80, 48, 26, 96], Operations: [] Exploring Operation: 96/48=2, Resulting Numbers: [80, 26, 2] Generated Node #0,3: 14:[80, 26, 2] Operation: 96/48=2 Moving to Node #0,3 Current State: 14:[80, 26, 2], Operations: ['96/48=2'] Exploring Operation: 80/2=40, Resulting Numbers: [26, 40] Generated Node #0,3,0: 14:[26, 40] Operation: 80/2=40 Moving to Node #0,3,0 Current State: 14:[26, 40], Operations: ['96/48=2', '80/2=40'] Exploring Operation: 40-26=14, Resulting Numbers: [14] 14,14 equal: Goal Reached
0.961806
hs_4
sum_heuristic
[ 86, 10, 40, 28 ]
45
[ "86+40=126", "10*126=1260", "1260/28=45" ]
Current State: 45:[86, 10, 40, 28], Operations: [] Exploring Operation: 86+40=126, Resulting Numbers: [10, 28, 126] Generated Node #2: [10, 28, 126] from Operation: 86+40=126 Current State: 45:[10, 28, 126], Operations: ['86+40=126'] Exploring Operation: 10*126=1260, Resulting Numbers: [28, 1260] Generated Node #3: [28, 1260] from Operation: 10*126=1260 Current State: 45:[28, 1260], Operations: ['86+40=126', '10*126=1260'] Exploring Operation: 1260/28=45, Resulting Numbers: [45] 45,45 equal: Goal Reached
4
Current State: 45:[86, 10, 40, 28], Operations: [] Exploring Operation: 28-10=18, Resulting Numbers: [86, 40, 18] Generated Node #0,0: 45:[86, 40, 18] Operation: 28-10=18 Exploring Operation: 40-28=12, Resulting Numbers: [86, 10, 12] Generated Node #0,1: 45:[86, 10, 12] Operation: 40-28=12 Exploring Operation: 86-28=58, Resulting Numbers: [10, 40, 58] Generated Node #0,2: 45:[10, 40, 58] Operation: 86-28=58 Exploring Operation: 86-40=46, Resulting Numbers: [10, 28, 46] Generated Node #0,3: 45:[10, 28, 46] Operation: 86-40=46 Exploring Operation: 86-10=76, Resulting Numbers: [40, 28, 76] Generated Node #0,4: 45:[40, 28, 76] Operation: 86-10=76 Start Sub Search at level 1: Moving to Node #0,3 Current State: 45:[10, 28, 46], Operations: ['86-40=46'] Exploring Operation: 28-10=18, Resulting Numbers: [46, 18] Generated Node #0,3,0: 45:[46, 18] Operation: 28-10=18 Exploring Operation: 46-10=36, Resulting Numbers: [28, 36] Generated Node #0,3,1: 45:[28, 36] Operation: 46-10=36 Exploring Operation: 10+46=56, Resulting Numbers: [28, 56] Generated Node #0,3,2: 45:[28, 56] Operation: 10+46=56 Exploring Operation: 10+28=38, Resulting Numbers: [46, 38] Generated Node #0,3,3: 45:[46, 38] Operation: 10+28=38 Exploring Operation: 46-28=18, Resulting Numbers: [10, 18] Generated Node #0,3,4: 45:[10, 18] Operation: 46-28=18 Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 45:[46, 18], Operations: ['86-40=46', '28-10=18'] Exploring Operation: 46-18=28, Resulting Numbers: [28] 28,45 unequal: No Solution Exploring Operation: 46+18=64, Resulting Numbers: [64] 64,45 unequal: No Solution Exploring Operation: 46*18=828, Resulting Numbers: [828] 828,45 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,4 Current State: 45:[10, 18], Operations: ['86-40=46', '46-28=18'] Exploring Operation: 18-10=8, Resulting Numbers: [8] 8,45 unequal: No Solution Exploring Operation: 10+18=28, Resulting Numbers: [28] 28,45 unequal: No Solution Exploring Operation: 10*18=180, Resulting Numbers: [180] 180,45 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 45:[46, 38], Operations: ['86-40=46', '10+28=38'] Exploring Operation: 46*38=1748, Resulting Numbers: [1748] 1748,45 unequal: No Solution Exploring Operation: 46+38=84, Resulting Numbers: [84] 84,45 unequal: No Solution Exploring Operation: 46-38=8, Resulting Numbers: [8] 8,45 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 45:[28, 36], Operations: ['86-40=46', '46-10=36'] Exploring Operation: 36-28=8, Resulting Numbers: [8] 8,45 unequal: No Solution Exploring Operation: 28*36=1008, Resulting Numbers: [1008] 1008,45 unequal: No Solution Exploring Operation: 28+36=64, Resulting Numbers: [64] 64,45 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 45:[28, 56], Operations: ['86-40=46', '10+46=56'] Exploring Operation: 56-28=28, Resulting Numbers: [28] 28,45 unequal: No Solution Exploring Operation: 28+56=84, Resulting Numbers: [84] 84,45 unequal: No Solution Exploring Operation: 56/28=2, Resulting Numbers: [2] 2,45 unequal: No Solution Exploring Operation: 28*56=1568, Resulting Numbers: [1568] 1568,45 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 45:[10, 40, 58], Operations: ['86-28=58'] Exploring Operation: 10+40=50, Resulting Numbers: [58, 50] Generated Node #0,2,0: 45:[58, 50] Operation: 10+40=50 Exploring Operation: 58-40=18, Resulting Numbers: [10, 18] Generated Node #0,2,1: 45:[10, 18] Operation: 58-40=18 Exploring Operation: 40/10=4, Resulting Numbers: [58, 4] Generated Node #0,2,2: 45:[58, 4] Operation: 40/10=4 Exploring Operation: 40-10=30, Resulting Numbers: [58, 30] Generated Node #0,2,3: 45:[58, 30] Operation: 40-10=30 Exploring Operation: 58-10=48, Resulting Numbers: [40, 48] Generated Node #0,2,4: 45:[40, 48] Operation: 58-10=48 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 45:[10, 18], Operations: ['86-28=58', '58-40=18'] Exploring Operation: 10*18=180, Resulting Numbers: [180] 180,45 unequal: No Solution Exploring Operation: 10+18=28, Resulting Numbers: [28] 28,45 unequal: No Solution Exploring Operation: 18-10=8, Resulting Numbers: [8] 8,45 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,4 Current State: 45:[40, 48], Operations: ['86-28=58', '58-10=48'] Exploring Operation: 48-40=8, Resulting Numbers: [8] 8,45 unequal: No Solution Exploring Operation: 40+48=88, Resulting Numbers: [88] 88,45 unequal: No Solution Exploring Operation: 40*48=1920, Resulting Numbers: [1920] 1920,45 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 45:[58, 4], Operations: ['86-28=58', '40/10=4'] Exploring Operation: 58-4=54, Resulting Numbers: [54] 54,45 unequal: No Solution Exploring Operation: 58*4=232, Resulting Numbers: [232] 232,45 unequal: No Solution Exploring Operation: 58+4=62, Resulting Numbers: [62] 62,45 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 45:[58, 50], Operations: ['86-28=58', '10+40=50'] Exploring Operation: 58+50=108, Resulting Numbers: [108] 108,45 unequal: No Solution Exploring Operation: 58-50=8, Resulting Numbers: [8] 8,45 unequal: No Solution Exploring Operation: 58*50=2900, Resulting Numbers: [2900] 2900,45 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 45:[58, 30], Operations: ['86-28=58', '40-10=30'] Exploring Operation: 58+30=88, Resulting Numbers: [88] 88,45 unequal: No Solution Exploring Operation: 58-30=28, Resulting Numbers: [28] 28,45 unequal: No Solution Exploring Operation: 58*30=1740, Resulting Numbers: [1740] 1740,45 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 45:[86, 10, 12], Operations: ['40-28=12'] Exploring Operation: 86-12=74, Resulting Numbers: [10, 74] Generated Node #0,1,0: 45:[10, 74] Operation: 86-12=74 Exploring Operation: 12-10=2, Resulting Numbers: [86, 2] Generated Node #0,1,1: 45:[86, 2] Operation: 12-10=2 Exploring Operation: 10+12=22, Resulting Numbers: [86, 22] Generated Node #0,1,2: 45:[86, 22] Operation: 10+12=22 Exploring Operation: 86-10=76, Resulting Numbers: [12, 76] Generated Node #0,1,3: 45:[12, 76] Operation: 86-10=76 Exploring Operation: 86+10=96, Resulting Numbers: [12, 96] Generated Node #0,1,4: 45:[12, 96] Operation: 86+10=96 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 45:[10, 74], Operations: ['40-28=12', '86-12=74'] Exploring Operation: 10*74=740, Resulting Numbers: [740] 740,45 unequal: No Solution Exploring Operation: 74-10=64, Resulting Numbers: [64] 64,45 unequal: No Solution Exploring Operation: 10+74=84, Resulting Numbers: [84] 84,45 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 45:[12, 76], Operations: ['40-28=12', '86-10=76'] Exploring Operation: 12+76=88, Resulting Numbers: [88] 88,45 unequal: No Solution Exploring Operation: 76-12=64, Resulting Numbers: [64] 64,45 unequal: No Solution Exploring Operation: 12*76=912, Resulting Numbers: [912] 912,45 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 45:[86, 2], Operations: ['40-28=12', '12-10=2'] Exploring Operation: 86/2=43, Resulting Numbers: [43] 43,45 unequal: No Solution Exploring Operation: 86*2=172, Resulting Numbers: [172] 172,45 unequal: No Solution Exploring Operation: 86+2=88, Resulting Numbers: [88] 88,45 unequal: No Solution Exploring Operation: 86-2=84, Resulting Numbers: [84] 84,45 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 45:[86, 22], Operations: ['40-28=12', '10+12=22'] Exploring Operation: 86+22=108, Resulting Numbers: [108] 108,45 unequal: No Solution Exploring Operation: 86*22=1892, Resulting Numbers: [1892] 1892,45 unequal: No Solution Exploring Operation: 86-22=64, Resulting Numbers: [64] 64,45 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,4 Current State: 45:[12, 96], Operations: ['40-28=12', '86+10=96'] Exploring Operation: 96-12=84, Resulting Numbers: [84] 84,45 unequal: No Solution Exploring Operation: 12+96=108, Resulting Numbers: [108] 108,45 unequal: No Solution Exploring Operation: 96/12=8, Resulting Numbers: [8] 8,45 unequal: No Solution Exploring Operation: 12*96=1152, Resulting Numbers: [1152] 1152,45 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 45:[86, 40, 18], Operations: ['28-10=18'] Exploring Operation: 40+18=58, Resulting Numbers: [86, 58] Generated Node #0,0,0: 45:[86, 58] Operation: 40+18=58 Exploring Operation: 86+18=104, Resulting Numbers: [40, 104] Generated Node #0,0,1: 45:[40, 104] Operation: 86+18=104 Exploring Operation: 40-18=22, Resulting Numbers: [86, 22] Generated Node #0,0,2: 45:[86, 22] Operation: 40-18=22 Exploring Operation: 86-40=46, Resulting Numbers: [18, 46] Generated Node #0,0,3: 45:[18, 46] Operation: 86-40=46 Exploring Operation: 86-18=68, Resulting Numbers: [40, 68] Generated Node #0,0,4: 45:[40, 68] Operation: 86-18=68 Moving to Node #0,0,3 Current State: 45:[18, 46], Operations: ['28-10=18', '86-40=46'] Exploring Operation: 18+46=64, Resulting Numbers: [64] 64,45 unequal: No Solution Exploring Operation: 18*46=828, Resulting Numbers: [828] 828,45 unequal: No Solution Exploring Operation: 46-18=28, Resulting Numbers: [28] 28,45 unequal: No Solution Moving to Node #0,0,4 Current State: 45:[40, 68], Operations: ['28-10=18', '86-18=68'] Exploring Operation: 68-40=28, Resulting Numbers: [28] 28,45 unequal: No Solution Exploring Operation: 40*68=2720, Resulting Numbers: [2720] 2720,45 unequal: No Solution Exploring Operation: 40+68=108, Resulting Numbers: [108] 108,45 unequal: No Solution Moving to Node #0,0,2 Current State: 45:[86, 22], Operations: ['28-10=18', '40-18=22'] Exploring Operation: 86+22=108, Resulting Numbers: [108] 108,45 unequal: No Solution Exploring Operation: 86*22=1892, Resulting Numbers: [1892] 1892,45 unequal: No Solution Exploring Operation: 86-22=64, Resulting Numbers: [64] 64,45 unequal: No Solution Moving to Node #0,0,0 Current State: 45:[86, 58], Operations: ['28-10=18', '40+18=58'] Exploring Operation: 86+58=144, Resulting Numbers: [144] 144,45 unequal: No Solution Exploring Operation: 86*58=4988, Resulting Numbers: [4988] 4988,45 unequal: No Solution Exploring Operation: 86-58=28, Resulting Numbers: [28] 28,45 unequal: No Solution Moving to Node #0,0,1 Current State: 45:[40, 104], Operations: ['28-10=18', '86+18=104'] Exploring Operation: 40*104=4160, Resulting Numbers: [4160] 4160,45 unequal: No Solution Exploring Operation: 104-40=64, Resulting Numbers: [64] 64,45 unequal: No Solution Exploring Operation: 40+104=144, Resulting Numbers: [144] 144,45 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4 Current State: 45:[40, 28, 76], Operations: ['86-10=76'] Exploring Operation: 76-28=48, Resulting Numbers: [40, 48] Generated Node #0,4,0: 45:[40, 48] Operation: 76-28=48 Exploring Operation: 76-40=36, Resulting Numbers: [28, 36] Generated Node #0,4,1: 45:[28, 36] Operation: 76-40=36 Exploring Operation: 40-28=12, Resulting Numbers: [76, 12] Generated Node #0,4,2: 45:[76, 12] Operation: 40-28=12 Exploring Operation: 40+28=68, Resulting Numbers: [76, 68] Generated Node #0,4,3: 45:[76, 68] Operation: 40+28=68 Exploring Operation: 28+76=104, Resulting Numbers: [40, 104] Generated Node #0,4,4: 45:[40, 104] Operation: 28+76=104 Moving to Node #0,4,0 Current State: 45:[40, 48], Operations: ['86-10=76', '76-28=48'] Exploring Operation: 48-40=8, Resulting Numbers: [8] 8,45 unequal: No Solution Exploring Operation: 40*48=1920, Resulting Numbers: [1920] 1920,45 unequal: No Solution Exploring Operation: 40+48=88, Resulting Numbers: [88] 88,45 unequal: No Solution Moving to Node #0,4,1 Current State: 45:[28, 36], Operations: ['86-10=76', '76-40=36'] Exploring Operation: 28+36=64, Resulting Numbers: [64] 64,45 unequal: No Solution Exploring Operation: 36-28=8, Resulting Numbers: [8] 8,45 unequal: No Solution Exploring Operation: 28*36=1008, Resulting Numbers: [1008] 1008,45 unequal: No Solution Moving to Node #0,4,2 Current State: 45:[76, 12], Operations: ['86-10=76', '40-28=12'] Exploring Operation: 76+12=88, Resulting Numbers: [88] 88,45 unequal: No Solution Exploring Operation: 76*12=912, Resulting Numbers: [912] 912,45 unequal: No Solution Exploring Operation: 76-12=64, Resulting Numbers: [64] 64,45 unequal: No Solution Moving to Node #0,4,3 Current State: 45:[76, 68], Operations: ['86-10=76', '40+28=68'] Exploring Operation: 76*68=5168, Resulting Numbers: [5168] 5168,45 unequal: No Solution Exploring Operation: 76-68=8, Resulting Numbers: [8] 8,45 unequal: No Solution Exploring Operation: 76+68=144, Resulting Numbers: [144] 144,45 unequal: No Solution Moving to Node #0,4,4 Current State: 45:[40, 104], Operations: ['86-10=76', '28+76=104'] Exploring Operation: 104-40=64, Resulting Numbers: [64] 64,45 unequal: No Solution Exploring Operation: 40*104=4160, Resulting Numbers: [4160] 4160,45 unequal: No Solution Exploring Operation: 40+104=144, Resulting Numbers: [144] 144,45 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_5
sum_heuristic
[ 81, 57, 54, 18 ]
46
[ "81+57=138", "54/18=3", "138/3=46" ]
Current State: 46:[81, 57, 54, 18], Operations: [] Exploring Operation: 81+57=138, Resulting Numbers: [54, 18, 138] Generated Node #2: [54, 18, 138] from Operation: 81+57=138 Current State: 46:[54, 18, 138], Operations: ['81+57=138'] Exploring Operation: 54/18=3, Resulting Numbers: [138, 3] Generated Node #3: [138, 3] from Operation: 54/18=3 Current State: 46:[138, 3], Operations: ['81+57=138', '54/18=3'] Exploring Operation: 138/3=46, Resulting Numbers: [46] 46,46 equal: Goal Reached
4
Current State: 46:[81, 57, 54, 18], Operations: [] Exploring Operation: 81-57=24, Resulting Numbers: [54, 18, 24] Generated Node #0,0: 46:[54, 18, 24] Operation: 81-57=24 Exploring Operation: 57-54=3, Resulting Numbers: [81, 18, 3] Generated Node #0,1: 46:[81, 18, 3] Operation: 57-54=3 Exploring Operation: 81-18=63, Resulting Numbers: [57, 54, 63] Generated Node #0,2: 46:[57, 54, 63] Operation: 81-18=63 Exploring Operation: 81-54=27, Resulting Numbers: [57, 18, 27] Generated Node #0,3: 46:[57, 18, 27] Operation: 81-54=27 Start Sub Search at level 1: Moving to Node #0,0 Current State: 46:[54, 18, 24], Operations: ['81-57=24'] Exploring Operation: 54-18=36, Resulting Numbers: [24, 36] Generated Node #0,0,0: 46:[24, 36] Operation: 54-18=36 Exploring Operation: 54-24=30, Resulting Numbers: [18, 30] Generated Node #0,0,1: 46:[18, 30] Operation: 54-24=30 Exploring Operation: 54/18=3, Resulting Numbers: [24, 3] Generated Node #0,0,2: 46:[24, 3] Operation: 54/18=3 Exploring Operation: 18+24=42, Resulting Numbers: [54, 42] Generated Node #0,0,3: 46:[54, 42] Operation: 18+24=42 Moving to Node #0,0,2 Current State: 46:[24, 3], Operations: ['81-57=24', '54/18=3'] Exploring Operation: 24/3=8, Resulting Numbers: [8] 8,46 unequal: No Solution Exploring Operation: 24-3=21, Resulting Numbers: [21] 21,46 unequal: No Solution Exploring Operation: 24*3=72, Resulting Numbers: [72] 72,46 unequal: No Solution Exploring Operation: 24+3=27, Resulting Numbers: [27] 27,46 unequal: No Solution Moving to Node #0,0,0 Current State: 46:[24, 36], Operations: ['81-57=24', '54-18=36'] Exploring Operation: 24+36=60, Resulting Numbers: [60] 60,46 unequal: No Solution Exploring Operation: 36-24=12, Resulting Numbers: [12] 12,46 unequal: No Solution Exploring Operation: 24*36=864, Resulting Numbers: [864] 864,46 unequal: No Solution Moving to Node #0,0,3 Current State: 46:[54, 42], Operations: ['81-57=24', '18+24=42'] Exploring Operation: 54-42=12, Resulting Numbers: [12] 12,46 unequal: No Solution Exploring Operation: 54+42=96, Resulting Numbers: [96] 96,46 unequal: No Solution Exploring Operation: 54*42=2268, Resulting Numbers: [2268] 2268,46 unequal: No Solution Moving to Node #0,0,1 Current State: 46:[18, 30], Operations: ['81-57=24', '54-24=30'] Exploring Operation: 18*30=540, Resulting Numbers: [540] 540,46 unequal: No Solution Exploring Operation: 18+30=48, Resulting Numbers: [48] 48,46 unequal: No Solution Exploring Operation: 30-18=12, Resulting Numbers: [12] 12,46 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 46:[57, 18, 27], Operations: ['81-54=27'] Exploring Operation: 57-27=30, Resulting Numbers: [18, 30] Generated Node #0,3,0: 46:[18, 30] Operation: 57-27=30 Exploring Operation: 57-18=39, Resulting Numbers: [27, 39] Generated Node #0,3,1: 46:[27, 39] Operation: 57-18=39 Exploring Operation: 18+27=45, Resulting Numbers: [57, 45] Generated Node #0,3,2: 46:[57, 45] Operation: 18+27=45 Exploring Operation: 27-18=9, Resulting Numbers: [57, 9] Generated Node #0,3,3: 46:[57, 9] Operation: 27-18=9 Moving to Node #0,3,1 Current State: 46:[27, 39], Operations: ['81-54=27', '57-18=39'] Exploring Operation: 39-27=12, Resulting Numbers: [12] 12,46 unequal: No Solution Exploring Operation: 27*39=1053, Resulting Numbers: [1053] 1053,46 unequal: No Solution Exploring Operation: 27+39=66, Resulting Numbers: [66] 66,46 unequal: No Solution Moving to Node #0,3,2 Current State: 46:[57, 45], Operations: ['81-54=27', '18+27=45'] Exploring Operation: 57*45=2565, Resulting Numbers: [2565] 2565,46 unequal: No Solution Exploring Operation: 57+45=102, Resulting Numbers: [102] 102,46 unequal: No Solution Exploring Operation: 57-45=12, Resulting Numbers: [12] 12,46 unequal: No Solution Moving to Node #0,3,0 Current State: 46:[18, 30], Operations: ['81-54=27', '57-27=30'] Exploring Operation: 18+30=48, Resulting Numbers: [48] 48,46 unequal: No Solution Exploring Operation: 30-18=12, Resulting Numbers: [12] 12,46 unequal: No Solution Exploring Operation: 18*30=540, Resulting Numbers: [540] 540,46 unequal: No Solution Moving to Node #0,3,3 Current State: 46:[57, 9], Operations: ['81-54=27', '27-18=9'] Exploring Operation: 57-9=48, Resulting Numbers: [48] 48,46 unequal: No Solution Exploring Operation: 57+9=66, Resulting Numbers: [66] 66,46 unequal: No Solution Exploring Operation: 57*9=513, Resulting Numbers: [513] 513,46 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 46:[57, 54, 63], Operations: ['81-18=63'] Exploring Operation: 63-57=6, Resulting Numbers: [54, 6] Generated Node #0,2,0: 46:[54, 6] Operation: 63-57=6 Exploring Operation: 63-54=9, Resulting Numbers: [57, 9] Generated Node #0,2,1: 46:[57, 9] Operation: 63-54=9 Exploring Operation: 57-54=3, Resulting Numbers: [63, 3] Generated Node #0,2,2: 46:[63, 3] Operation: 57-54=3 Exploring Operation: 57+54=111, Resulting Numbers: [63, 111] Generated Node #0,2,3: 46:[63, 111] Operation: 57+54=111 Moving to Node #0,2,0 Current State: 46:[54, 6], Operations: ['81-18=63', '63-57=6'] Exploring Operation: 54+6=60, Resulting Numbers: [60] 60,46 unequal: No Solution Exploring Operation: 54-6=48, Resulting Numbers: [48] 48,46 unequal: No Solution Exploring Operation: 54*6=324, Resulting Numbers: [324] 324,46 unequal: No Solution Exploring Operation: 54/6=9, Resulting Numbers: [9] 9,46 unequal: No Solution Moving to Node #0,2,2 Current State: 46:[63, 3], Operations: ['81-18=63', '57-54=3'] Exploring Operation: 63*3=189, Resulting Numbers: [189] 189,46 unequal: No Solution Exploring Operation: 63/3=21, Resulting Numbers: [21] 21,46 unequal: No Solution Exploring Operation: 63-3=60, Resulting Numbers: [60] 60,46 unequal: No Solution Exploring Operation: 63+3=66, Resulting Numbers: [66] 66,46 unequal: No Solution Moving to Node #0,2,1 Current State: 46:[57, 9], Operations: ['81-18=63', '63-54=9'] Exploring Operation: 57+9=66, Resulting Numbers: [66] 66,46 unequal: No Solution Exploring Operation: 57-9=48, Resulting Numbers: [48] 48,46 unequal: No Solution Exploring Operation: 57*9=513, Resulting Numbers: [513] 513,46 unequal: No Solution Moving to Node #0,2,3 Current State: 46:[63, 111], Operations: ['81-18=63', '57+54=111'] Exploring Operation: 111-63=48, Resulting Numbers: [48] 48,46 unequal: No Solution Exploring Operation: 63*111=6993, Resulting Numbers: [6993] 6993,46 unequal: No Solution Exploring Operation: 63+111=174, Resulting Numbers: [174] 174,46 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 46:[81, 18, 3], Operations: ['57-54=3'] Exploring Operation: 18+3=21, Resulting Numbers: [81, 21] Generated Node #0,1,0: 46:[81, 21] Operation: 18+3=21 Exploring Operation: 81-18=63, Resulting Numbers: [3, 63] Generated Node #0,1,1: 46:[3, 63] Operation: 81-18=63 Exploring Operation: 81/3=27, Resulting Numbers: [18, 27] Generated Node #0,1,2: 46:[18, 27] Operation: 81/3=27 Exploring Operation: 81-3=78, Resulting Numbers: [18, 78] Generated Node #0,1,3: 46:[18, 78] Operation: 81-3=78 Moving to Node #0,1,2 Current State: 46:[18, 27], Operations: ['57-54=3', '81/3=27'] Exploring Operation: 18*27=486, Resulting Numbers: [486] 486,46 unequal: No Solution Exploring Operation: 27-18=9, Resulting Numbers: [9] 9,46 unequal: No Solution Exploring Operation: 18+27=45, Resulting Numbers: [45] 45,46 unequal: No Solution Moving to Node #0,1,1 Current State: 46:[3, 63], Operations: ['57-54=3', '81-18=63'] Exploring Operation: 63-3=60, Resulting Numbers: [60] 60,46 unequal: No Solution Exploring Operation: 3+63=66, Resulting Numbers: [66] 66,46 unequal: No Solution Exploring Operation: 63/3=21, Resulting Numbers: [21] 21,46 unequal: No Solution Exploring Operation: 3*63=189, Resulting Numbers: [189] 189,46 unequal: No Solution Moving to Node #0,1,3 Current State: 46:[18, 78], Operations: ['57-54=3', '81-3=78'] Exploring Operation: 78-18=60, Resulting Numbers: [60] 60,46 unequal: No Solution Exploring Operation: 18*78=1404, Resulting Numbers: [1404] 1404,46 unequal: No Solution Exploring Operation: 18+78=96, Resulting Numbers: [96] 96,46 unequal: No Solution Moving to Node #0,1,0 Current State: 46:[81, 21], Operations: ['57-54=3', '18+3=21'] Exploring Operation: 81*21=1701, Resulting Numbers: [1701] 1701,46 unequal: No Solution Exploring Operation: 81+21=102, Resulting Numbers: [102] 102,46 unequal: No Solution Exploring Operation: 81-21=60, Resulting Numbers: [60] 60,46 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_4
mult_heuristic
[ 97, 72, 35, 43 ]
91
[ "97+72=169", "35+43=78", "169-78=91" ]
Current State: 91:[97, 72, 35, 43], Operations: [] Exploring Operation: 97+72=169, Resulting Numbers: [35, 43, 169] Generated Node #2: [35, 43, 169] from Operation: 97+72=169 Current State: 91:[35, 43, 169], Operations: ['97+72=169'] Exploring Operation: 35+43=78, Resulting Numbers: [169, 78] Generated Node #3: [169, 78] from Operation: 35+43=78 Current State: 91:[169, 78], Operations: ['97+72=169', '35+43=78'] Exploring Operation: 169-78=91, Resulting Numbers: [91] 91,91 equal: Goal Reached
4
Current State: 91:[97, 72, 35, 43], Operations: [] Exploring Operation: 43-35=8, Resulting Numbers: [97, 72, 8] Generated Node #0,0: 91:[97, 72, 8] Operation: 43-35=8 Exploring Operation: 35+43=78, Resulting Numbers: [97, 72, 78] Generated Node #0,1: 91:[97, 72, 78] Operation: 35+43=78 Exploring Operation: 72-43=29, Resulting Numbers: [97, 35, 29] Generated Node #0,2: 91:[97, 35, 29] Operation: 72-43=29 Start Sub Search at level 1: Moving to Node #0,0 Current State: 91:[97, 72, 8], Operations: ['43-35=8'] Exploring Operation: 72+8=80, Resulting Numbers: [97, 80] Generated Node #0,0,0: 91:[97, 80] Operation: 72+8=80 Exploring Operation: 72/8=9, Resulting Numbers: [97, 9] Generated Node #0,0,1: 91:[97, 9] Operation: 72/8=9 Exploring Operation: 97-72=25, Resulting Numbers: [8, 25] Generated Node #0,0,2: 91:[8, 25] Operation: 97-72=25 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 91:[97, 9], Operations: ['43-35=8', '72/8=9'] Exploring Operation: 97+9=106, Resulting Numbers: [106] 106,91 unequal: No Solution Exploring Operation: 97-9=88, Resulting Numbers: [88] 88,91 unequal: No Solution Exploring Operation: 97*9=873, Resulting Numbers: [873] 873,91 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 91:[8, 25], Operations: ['43-35=8', '97-72=25'] Exploring Operation: 8+25=33, Resulting Numbers: [33] 33,91 unequal: No Solution Exploring Operation: 8*25=200, Resulting Numbers: [200] 200,91 unequal: No Solution Exploring Operation: 25-8=17, Resulting Numbers: [17] 17,91 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 91:[97, 80], Operations: ['43-35=8', '72+8=80'] Exploring Operation: 97+80=177, Resulting Numbers: [177] 177,91 unequal: No Solution Exploring Operation: 97*80=7760, Resulting Numbers: [7760] 7760,91 unequal: No Solution Exploring Operation: 97-80=17, Resulting Numbers: [17] 17,91 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 91:[97, 72, 78], Operations: ['35+43=78'] Exploring Operation: 78-72=6, Resulting Numbers: [97, 6] Generated Node #0,1,0: 91:[97, 6] Operation: 78-72=6 Exploring Operation: 97-78=19, Resulting Numbers: [72, 19] Generated Node #0,1,1: 91:[72, 19] Operation: 97-78=19 Exploring Operation: 97-72=25, Resulting Numbers: [78, 25] Generated Node #0,1,2: 91:[78, 25] Operation: 97-72=25 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 91:[97, 6], Operations: ['35+43=78', '78-72=6'] Exploring Operation: 97*6=582, Resulting Numbers: [582] 582,91 unequal: No Solution Exploring Operation: 97-6=91, Resulting Numbers: [91] 91,91 equal: Goal Reached Moving to Node #0 Current State: 91:[97, 72, 35, 43], Operations: [] Exploring Operation: 35+43=78, Resulting Numbers: [97, 72, 78] Generated Node #0,1: 91:[97, 72, 78] Operation: 35+43=78 Moving to Node #0,1 Current State: 91:[97, 72, 78], Operations: ['35+43=78'] Exploring Operation: 78-72=6, Resulting Numbers: [97, 6] Generated Node #0,1,0: 91:[97, 6] Operation: 78-72=6 Moving to Node #0,1,0 Current State: 91:[97, 6], Operations: ['35+43=78', '78-72=6'] Exploring Operation: 97-6=91, Resulting Numbers: [91] 91,91 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.979167
hs_3
mult_heuristic
[ 14, 41, 33, 67 ]
98
[ "41+33=74", "74-67=7", "14*7=98" ]
Current State: 98:[14, 41, 33, 67], Operations: [] Exploring Operation: 41+33=74, Resulting Numbers: [14, 67, 74] Generated Node #2: [14, 67, 74] from Operation: 41+33=74 Current State: 98:[14, 67, 74], Operations: ['41+33=74'] Exploring Operation: 74-67=7, Resulting Numbers: [14, 7] Generated Node #3: [14, 7] from Operation: 74-67=7 Current State: 98:[14, 7], Operations: ['41+33=74', '74-67=7'] Exploring Operation: 14*7=98, Resulting Numbers: [98] 98,98 equal: Goal Reached
4
Current State: 98:[14, 41, 33, 67], Operations: [] Exploring Operation: 41-33=8, Resulting Numbers: [14, 67, 8] Generated Node #0,0: 98:[14, 67, 8] Operation: 41-33=8 Exploring Operation: 67-33=34, Resulting Numbers: [14, 41, 34] Generated Node #0,1: 98:[14, 41, 34] Operation: 67-33=34 Exploring Operation: 33+67=100, Resulting Numbers: [14, 41, 100] Generated Node #0,2: 98:[14, 41, 100] Operation: 33+67=100 Start Sub Search at level 1: Moving to Node #0,2 Current State: 98:[14, 41, 100], Operations: ['33+67=100'] Exploring Operation: 14+41=55, Resulting Numbers: [100, 55] Generated Node #0,2,0: 98:[100, 55] Operation: 14+41=55 Exploring Operation: 41-14=27, Resulting Numbers: [100, 27] Generated Node #0,2,1: 98:[100, 27] Operation: 41-14=27 Exploring Operation: 100-41=59, Resulting Numbers: [14, 59] Generated Node #0,2,2: 98:[14, 59] Operation: 100-41=59 Moving to Node #0,2,0 Current State: 98:[100, 55], Operations: ['33+67=100', '14+41=55'] Exploring Operation: 100-55=45, Resulting Numbers: [45] 45,98 unequal: No Solution Exploring Operation: 100+55=155, Resulting Numbers: [155] 155,98 unequal: No Solution Exploring Operation: 100*55=5500, Resulting Numbers: [5500] 5500,98 unequal: No Solution Moving to Node #0,2,2 Current State: 98:[14, 59], Operations: ['33+67=100', '100-41=59'] Exploring Operation: 14+59=73, Resulting Numbers: [73] 73,98 unequal: No Solution Exploring Operation: 14*59=826, Resulting Numbers: [826] 826,98 unequal: No Solution Exploring Operation: 59-14=45, Resulting Numbers: [45] 45,98 unequal: No Solution Moving to Node #0,2,1 Current State: 98:[100, 27], Operations: ['33+67=100', '41-14=27'] Exploring Operation: 100-27=73, Resulting Numbers: [73] 73,98 unequal: No Solution Exploring Operation: 100*27=2700, Resulting Numbers: [2700] 2700,98 unequal: No Solution Exploring Operation: 100+27=127, Resulting Numbers: [127] 127,98 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 98:[14, 67, 8], Operations: ['41-33=8'] Exploring Operation: 67-8=59, Resulting Numbers: [14, 59] Generated Node #0,0,0: 98:[14, 59] Operation: 67-8=59 Exploring Operation: 14+67=81, Resulting Numbers: [8, 81] Generated Node #0,0,1: 98:[8, 81] Operation: 14+67=81 Exploring Operation: 67-14=53, Resulting Numbers: [8, 53] Generated Node #0,0,2: 98:[8, 53] Operation: 67-14=53 Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 98:[8, 53], Operations: ['41-33=8', '67-14=53'] Exploring Operation: 8+53=61, Resulting Numbers: [61] 61,98 unequal: No Solution Exploring Operation: 53-8=45, Resulting Numbers: [45] 45,98 unequal: No Solution Exploring Operation: 8*53=424, Resulting Numbers: [424] 424,98 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 98:[14, 59], Operations: ['41-33=8', '67-8=59'] Exploring Operation: 59-14=45, Resulting Numbers: [45] 45,98 unequal: No Solution Exploring Operation: 14*59=826, Resulting Numbers: [826] 826,98 unequal: No Solution Exploring Operation: 14+59=73, Resulting Numbers: [73] 73,98 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 98:[8, 81], Operations: ['41-33=8', '14+67=81'] Exploring Operation: 8+81=89, Resulting Numbers: [89] 89,98 unequal: No Solution Exploring Operation: 8*81=648, Resulting Numbers: [648] 648,98 unequal: No Solution Exploring Operation: 81-8=73, Resulting Numbers: [73] 73,98 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 98:[14, 41, 34], Operations: ['67-33=34'] Exploring Operation: 41-34=7, Resulting Numbers: [14, 7] Generated Node #0,1,0: 98:[14, 7] Operation: 41-34=7 Exploring Operation: 34-14=20, Resulting Numbers: [41, 20] Generated Node #0,1,1: 98:[41, 20] Operation: 34-14=20 Exploring Operation: 14+34=48, Resulting Numbers: [41, 48] Generated Node #0,1,2: 98:[41, 48] Operation: 14+34=48 Moving to Node #0,1,0 Current State: 98:[14, 7], Operations: ['67-33=34', '41-34=7'] Exploring Operation: 14-7=7, Resulting Numbers: [7] 7,98 unequal: No Solution Exploring Operation: 14*7=98, Resulting Numbers: [98] 98,98 equal: Goal Reached Moving to Node #0 Current State: 98:[14, 41, 33, 67], Operations: [] Exploring Operation: 67-33=34, Resulting Numbers: [14, 41, 34] Generated Node #0,1: 98:[14, 41, 34] Operation: 67-33=34 Moving to Node #0,1 Current State: 98:[14, 41, 34], Operations: ['67-33=34'] Exploring Operation: 41-34=7, Resulting Numbers: [14, 7] Generated Node #0,1,0: 98:[14, 7] Operation: 41-34=7 Moving to Node #0,1,0 Current State: 98:[14, 7], Operations: ['67-33=34', '41-34=7'] Exploring Operation: 14*7=98, Resulting Numbers: [98] 98,98 equal: Goal Reached Exit Sub Search at level 1
0.96875
hs_3
sum_heuristic
[ 38, 73, 93, 21 ]
39
[ "38+73=111", "93-21=72", "111-72=39" ]
Current State: 39:[38, 73, 93, 21], Operations: [] Exploring Operation: 38+73=111, Resulting Numbers: [93, 21, 111] Generated Node #2: [93, 21, 111] from Operation: 38+73=111 Current State: 39:[93, 21, 111], Operations: ['38+73=111'] Exploring Operation: 93-21=72, Resulting Numbers: [111, 72] Generated Node #3: [111, 72] from Operation: 93-21=72 Current State: 39:[111, 72], Operations: ['38+73=111', '93-21=72'] Exploring Operation: 111-72=39, Resulting Numbers: [39] 39,39 equal: Goal Reached
4
Current State: 39:[38, 73, 93, 21], Operations: [] Exploring Operation: 93-73=20, Resulting Numbers: [38, 21, 20] Generated Node #0,0: 39:[38, 21, 20] Operation: 93-73=20 Exploring Operation: 93-38=55, Resulting Numbers: [73, 21, 55] Generated Node #0,1: 39:[73, 21, 55] Operation: 93-38=55 Exploring Operation: 73-38=35, Resulting Numbers: [93, 21, 35] Generated Node #0,2: 39:[93, 21, 35] Operation: 73-38=35 Exploring Operation: 73-21=52, Resulting Numbers: [38, 93, 52] Generated Node #0,3: 39:[38, 93, 52] Operation: 73-21=52 Start Sub Search at level 1: Moving to Node #0,0 Current State: 39:[38, 21, 20], Operations: ['93-73=20'] Exploring Operation: 21-20=1, Resulting Numbers: [38, 1] Generated Node #0,0,0: 39:[38, 1] Operation: 21-20=1 Exploring Operation: 38-21=17, Resulting Numbers: [20, 17] Generated Node #0,0,1: 39:[20, 17] Operation: 38-21=17 Exploring Operation: 21+20=41, Resulting Numbers: [38, 41] Generated Node #0,0,2: 39:[38, 41] Operation: 21+20=41 Exploring Operation: 38-20=18, Resulting Numbers: [21, 18] Generated Node #0,0,3: 39:[21, 18] Operation: 38-20=18 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 39:[38, 1], Operations: ['93-73=20', '21-20=1'] Exploring Operation: 38/1=38, Resulting Numbers: [38] 38,39 unequal: No Solution Exploring Operation: 38+1=39, Resulting Numbers: [39] 39,39 equal: Goal Reached Moving to Node #0 Current State: 39:[38, 73, 93, 21], Operations: [] Exploring Operation: 93-73=20, Resulting Numbers: [38, 21, 20] Generated Node #0,0: 39:[38, 21, 20] Operation: 93-73=20 Moving to Node #0,0 Current State: 39:[38, 21, 20], Operations: ['93-73=20'] Exploring Operation: 21-20=1, Resulting Numbers: [38, 1] Generated Node #0,0,0: 39:[38, 1] Operation: 21-20=1 Moving to Node #0,0,0 Current State: 39:[38, 1], Operations: ['93-73=20', '21-20=1'] Exploring Operation: 38+1=39, Resulting Numbers: [39] 39,39 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.987847
hs_4
sum_heuristic
[ 64, 45, 34, 66 ]
22
[ "66-64=2", "45-34=11", "2*11=22" ]
Current State: 22:[64, 45, 34, 66], Operations: [] Exploring Operation: 66-64=2, Resulting Numbers: [45, 34, 2] Generated Node #2: [45, 34, 2] from Operation: 66-64=2 Current State: 22:[45, 34, 2], Operations: ['66-64=2'] Exploring Operation: 45-34=11, Resulting Numbers: [2, 11] Generated Node #3: [2, 11] from Operation: 45-34=11 Current State: 22:[2, 11], Operations: ['66-64=2', '45-34=11'] Exploring Operation: 2*11=22, Resulting Numbers: [22] 22,22 equal: Goal Reached
4
Current State: 22:[64, 45, 34, 66], Operations: [] Exploring Operation: 66-64=2, Resulting Numbers: [45, 34, 2] Generated Node #0,0: 22:[45, 34, 2] Operation: 66-64=2 Exploring Operation: 66-45=21, Resulting Numbers: [64, 34, 21] Generated Node #0,1: 22:[64, 34, 21] Operation: 66-45=21 Moving to Node #0,0 Current State: 22:[45, 34, 2], Operations: ['66-64=2'] Exploring Operation: 45-34=11, Resulting Numbers: [2, 11] Generated Node #0,0,0: 22:[2, 11] Operation: 45-34=11 Exploring Operation: 34/2=17, Resulting Numbers: [45, 17] Generated Node #0,0,1: 22:[45, 17] Operation: 34/2=17 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 22:[2, 11], Operations: ['66-64=2', '45-34=11'] Exploring Operation: 2*11=22, Resulting Numbers: [22] 22,22 equal: Goal Reached Moving to Node #0 Current State: 22:[64, 45, 34, 66], Operations: [] Exploring Operation: 66-64=2, Resulting Numbers: [45, 34, 2] Generated Node #0,0: 22:[45, 34, 2] Operation: 66-64=2 Moving to Node #0,0 Current State: 22:[45, 34, 2], Operations: ['66-64=2'] Exploring Operation: 45-34=11, Resulting Numbers: [2, 11] Generated Node #0,0,0: 22:[2, 11] Operation: 45-34=11 Moving to Node #0,0,0 Current State: 22:[2, 11], Operations: ['66-64=2', '45-34=11'] Exploring Operation: 2*11=22, Resulting Numbers: [22] 22,22 equal: Goal Reached Exit Sub Search at level 1
0.992188
hs_2
mult_heuristic
[ 86, 10, 37, 41 ]
100
[ "86+10=96", "41-37=4", "96+4=100" ]
Current State: 100:[86, 10, 37, 41], Operations: [] Exploring Operation: 86+10=96, Resulting Numbers: [37, 41, 96] Generated Node #2: [37, 41, 96] from Operation: 86+10=96 Current State: 100:[37, 41, 96], Operations: ['86+10=96'] Exploring Operation: 41-37=4, Resulting Numbers: [96, 4] Generated Node #3: [96, 4] from Operation: 41-37=4 Current State: 100:[96, 4], Operations: ['86+10=96', '41-37=4'] Exploring Operation: 96+4=100, Resulting Numbers: [100] 100,100 equal: Goal Reached
4
Current State: 100:[86, 10, 37, 41], Operations: [] Exploring Operation: 86-41=45, Resulting Numbers: [10, 37, 45] Generated Node #0,0: 100:[10, 37, 45] Operation: 86-41=45 Exploring Operation: 86-37=49, Resulting Numbers: [10, 41, 49] Generated Node #0,1: 100:[10, 41, 49] Operation: 86-37=49 Exploring Operation: 41-37=4, Resulting Numbers: [86, 10, 4] Generated Node #0,2: 100:[86, 10, 4] Operation: 41-37=4 Start Sub Search at level 1: Moving to Node #0,1 Current State: 100:[10, 41, 49], Operations: ['86-37=49'] Exploring Operation: 10+41=51, Resulting Numbers: [49, 51] Generated Node #0,1,0: 100:[49, 51] Operation: 10+41=51 Exploring Operation: 49-41=8, Resulting Numbers: [10, 8] Generated Node #0,1,1: 100:[10, 8] Operation: 49-41=8 Exploring Operation: 41-10=31, Resulting Numbers: [49, 31] Generated Node #0,1,2: 100:[49, 31] Operation: 41-10=31 Moving to Node #0,1,0 Current State: 100:[49, 51], Operations: ['86-37=49', '10+41=51'] Exploring Operation: 49+51=100, Resulting Numbers: [100] 100,100 equal: Goal Reached Moving to Node #0 Current State: 100:[86, 10, 37, 41], Operations: [] Exploring Operation: 86-37=49, Resulting Numbers: [10, 41, 49] Generated Node #0,1: 100:[10, 41, 49] Operation: 86-37=49 Moving to Node #0,1 Current State: 100:[10, 41, 49], Operations: ['86-37=49'] Exploring Operation: 10+41=51, Resulting Numbers: [49, 51] Generated Node #0,1,0: 100:[49, 51] Operation: 10+41=51 Moving to Node #0,1,0 Current State: 100:[49, 51], Operations: ['86-37=49', '10+41=51'] Exploring Operation: 49+51=100, Resulting Numbers: [100] 100,100 equal: Goal Reached Exit Sub Search at level 1
0.990451
hs_3
mult_heuristic
[ 35, 24, 28, 24 ]
41
[ "35-24=11", "28+24=52", "52-11=41" ]
Current State: 41:[35, 24, 28, 24], Operations: [] Exploring Operation: 35-24=11, Resulting Numbers: [28, 11] Generated Node #2: [28, 11] from Operation: 35-24=11 Current State: 41:[28, 11], Operations: ['35-24=11'] Exploring Operation: 28+24=52, Resulting Numbers: [11, 52] Generated Node #3: [11, 52] from Operation: 28+24=52 Current State: 41:[11, 52], Operations: ['35-24=11', '28+24=52'] Exploring Operation: 52-11=41, Resulting Numbers: [41] 41,41 equal: Goal Reached
4
Current State: 41:[35, 24, 28, 24], Operations: [] Exploring Operation: 24+24=48, Resulting Numbers: [35, 28, 48] Generated Node #0,0: 41:[35, 28, 48] Operation: 24+24=48 Moving to Node #0,0 Current State: 41:[35, 28, 48], Operations: ['24+24=48'] Exploring Operation: 48-28=20, Resulting Numbers: [35, 20] Generated Node #0,0,0: 41:[35, 20] Operation: 48-28=20 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 41:[35, 20], Operations: ['24+24=48', '48-28=20'] Exploring Operation: 35+20=55, Resulting Numbers: [55] 55,41 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
sum_heuristic
[ 57, 5, 70, 19 ]
90
[ "57+19=76", "70/5=14", "76+14=90" ]
Current State: 90:[57, 5, 70, 19], Operations: [] Exploring Operation: 57+19=76, Resulting Numbers: [5, 70, 76] Generated Node #2: [5, 70, 76] from Operation: 57+19=76 Current State: 90:[5, 70, 76], Operations: ['57+19=76'] Exploring Operation: 70/5=14, Resulting Numbers: [76, 14] Generated Node #3: [76, 14] from Operation: 70/5=14 Current State: 90:[76, 14], Operations: ['57+19=76', '70/5=14'] Exploring Operation: 76+14=90, Resulting Numbers: [90] 90,90 equal: Goal Reached
4
Current State: 90:[57, 5, 70, 19], Operations: [] Exploring Operation: 70-57=13, Resulting Numbers: [5, 19, 13] Generated Node #0,0: 90:[5, 19, 13] Operation: 70-57=13 Exploring Operation: 70+19=89, Resulting Numbers: [57, 5, 89] Generated Node #0,1: 90:[57, 5, 89] Operation: 70+19=89 Start Sub Search at level 1: Moving to Node #0,0 Current State: 90:[5, 19, 13], Operations: ['70-57=13'] Exploring Operation: 5+13=18, Resulting Numbers: [19, 18] Generated Node #0,0,0: 90:[19, 18] Operation: 5+13=18 Exploring Operation: 19-13=6, Resulting Numbers: [5, 6] Generated Node #0,0,1: 90:[5, 6] Operation: 19-13=6 Moving to Node #0,0,1 Current State: 90:[5, 6], Operations: ['70-57=13', '19-13=6'] Exploring Operation: 5*6=30, Resulting Numbers: [30] 30,90 unequal: No Solution Exploring Operation: 5+6=11, Resulting Numbers: [11] 11,90 unequal: No Solution Moving to Node #0,0,0 Current State: 90:[19, 18], Operations: ['70-57=13', '5+13=18'] Exploring Operation: 19-18=1, Resulting Numbers: [1] 1,90 unequal: No Solution Exploring Operation: 19+18=37, Resulting Numbers: [37] 37,90 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 90:[57, 5, 89], Operations: ['70+19=89'] Exploring Operation: 89-57=32, Resulting Numbers: [5, 32] Generated Node #0,1,0: 90:[5, 32] Operation: 89-57=32 Exploring Operation: 57-5=52, Resulting Numbers: [89, 52] Generated Node #0,1,1: 90:[89, 52] Operation: 57-5=52 Moving to Node #0,1,0 Current State: 90:[5, 32], Operations: ['70+19=89', '89-57=32'] Exploring Operation: 32-5=27, Resulting Numbers: [27] 27,90 unequal: No Solution Exploring Operation: 5+32=37, Resulting Numbers: [37] 37,90 unequal: No Solution Moving to Node #0,1,1 Current State: 90:[89, 52], Operations: ['70+19=89', '57-5=52'] Exploring Operation: 89+52=141, Resulting Numbers: [141] 141,90 unequal: No Solution Exploring Operation: 89-52=37, Resulting Numbers: [37] 37,90 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
sum_heuristic
[ 73, 37, 21, 6 ]
23
[ "37-21=16", "6*16=96", "96-73=23" ]
Current State: 23:[73, 37, 21, 6], Operations: [] Exploring Operation: 37-21=16, Resulting Numbers: [73, 6, 16] Generated Node #2: [73, 6, 16] from Operation: 37-21=16 Current State: 23:[73, 6, 16], Operations: ['37-21=16'] Exploring Operation: 6*16=96, Resulting Numbers: [73, 96] Generated Node #3: [73, 96] from Operation: 6*16=96 Current State: 23:[73, 96], Operations: ['37-21=16', '6*16=96'] Exploring Operation: 96-73=23, Resulting Numbers: [23] 23,23 equal: Goal Reached
4
Current State: 23:[73, 37, 21, 6], Operations: [] Exploring Operation: 73-6=67, Resulting Numbers: [37, 21, 67] Generated Node #0,0: 23:[37, 21, 67] Operation: 73-6=67 Exploring Operation: 37-6=31, Resulting Numbers: [73, 21, 31] Generated Node #0,1: 23:[73, 21, 31] Operation: 37-6=31 Exploring Operation: 73-21=52, Resulting Numbers: [37, 6, 52] Generated Node #0,2: 23:[37, 6, 52] Operation: 73-21=52 Exploring Operation: 73-37=36, Resulting Numbers: [21, 6, 36] Generated Node #0,3: 23:[21, 6, 36] Operation: 73-37=36 Exploring Operation: 21+6=27, Resulting Numbers: [73, 37, 27] Generated Node #0,4: 23:[73, 37, 27] Operation: 21+6=27 Moving to Node #0,3 Current State: 23:[21, 6, 36], Operations: ['73-37=36'] Exploring Operation: 36-6=30, Resulting Numbers: [21, 30] Generated Node #0,3,0: 23:[21, 30] Operation: 36-6=30 Exploring Operation: 21+6=27, Resulting Numbers: [36, 27] Generated Node #0,3,1: 23:[36, 27] Operation: 21+6=27 Exploring Operation: 21-6=15, Resulting Numbers: [36, 15] Generated Node #0,3,2: 23:[36, 15] Operation: 21-6=15 Exploring Operation: 36/6=6, Resulting Numbers: [21, 6] Generated Node #0,3,3: 23:[21, 6] Operation: 36/6=6 Exploring Operation: 6+36=42, Resulting Numbers: [21, 42] Generated Node #0,3,4: 23:[21, 42] Operation: 6+36=42 Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 23:[21, 30], Operations: ['73-37=36', '36-6=30'] Exploring Operation: 30-21=9, Resulting Numbers: [9] 9,23 unequal: No Solution Exploring Operation: 21*30=630, Resulting Numbers: [630] 630,23 unequal: No Solution Exploring Operation: 21+30=51, Resulting Numbers: [51] 51,23 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 23:[36, 27], Operations: ['73-37=36', '21+6=27'] Exploring Operation: 36+27=63, Resulting Numbers: [63] 63,23 unequal: No Solution Exploring Operation: 36*27=972, Resulting Numbers: [972] 972,23 unequal: No Solution Exploring Operation: 36-27=9, Resulting Numbers: [9] 9,23 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 23:[21, 6], Operations: ['73-37=36', '36/6=6'] Exploring Operation: 21-6=15, Resulting Numbers: [15] 15,23 unequal: No Solution Exploring Operation: 21*6=126, Resulting Numbers: [126] 126,23 unequal: No Solution Exploring Operation: 21+6=27, Resulting Numbers: [27] 27,23 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 23:[36, 15], Operations: ['73-37=36', '21-6=15'] Exploring Operation: 36+15=51, Resulting Numbers: [51] 51,23 unequal: No Solution Exploring Operation: 36-15=21, Resulting Numbers: [21] 21,23 unequal: No Solution Exploring Operation: 36*15=540, Resulting Numbers: [540] 540,23 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,4 Current State: 23:[21, 42], Operations: ['73-37=36', '6+36=42'] Exploring Operation: 42-21=21, Resulting Numbers: [21] 21,23 unequal: No Solution Exploring Operation: 21*42=882, Resulting Numbers: [882] 882,23 unequal: No Solution Exploring Operation: 42/21=2, Resulting Numbers: [2] 2,23 unequal: No Solution Exploring Operation: 21+42=63, Resulting Numbers: [63] 63,23 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 23:[73, 21, 31], Operations: ['37-6=31'] Exploring Operation: 31-21=10, Resulting Numbers: [73, 10] Generated Node #0,1,0: 23:[73, 10] Operation: 31-21=10 Exploring Operation: 21+31=52, Resulting Numbers: [73, 52] Generated Node #0,1,1: 23:[73, 52] Operation: 21+31=52 Exploring Operation: 73-21=52, Resulting Numbers: [31, 52] Generated Node #0,1,2: 23:[31, 52] Operation: 73-21=52 Exploring Operation: 73+21=94, Resulting Numbers: [31, 94] Generated Node #0,1,3: 23:[31, 94] Operation: 73+21=94 Exploring Operation: 73-31=42, Resulting Numbers: [21, 42] Generated Node #0,1,4: 23:[21, 42] Operation: 73-31=42 Start Sub Search at level 1: Moving to Node #0,1,4 Current State: 23:[21, 42], Operations: ['37-6=31', '73-31=42'] Exploring Operation: 21+42=63, Resulting Numbers: [63] 63,23 unequal: No Solution Exploring Operation: 21*42=882, Resulting Numbers: [882] 882,23 unequal: No Solution Exploring Operation: 42-21=21, Resulting Numbers: [21] 21,23 unequal: No Solution Exploring Operation: 42/21=2, Resulting Numbers: [2] 2,23 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 23:[31, 52], Operations: ['37-6=31', '73-21=52'] Exploring Operation: 31*52=1612, Resulting Numbers: [1612] 1612,23 unequal: No Solution Exploring Operation: 52-31=21, Resulting Numbers: [21] 21,23 unequal: No Solution Exploring Operation: 31+52=83, Resulting Numbers: [83] 83,23 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 23:[73, 10], Operations: ['37-6=31', '31-21=10'] Exploring Operation: 73-10=63, Resulting Numbers: [63] 63,23 unequal: No Solution Exploring Operation: 73+10=83, Resulting Numbers: [83] 83,23 unequal: No Solution Exploring Operation: 73*10=730, Resulting Numbers: [730] 730,23 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 23:[73, 52], Operations: ['37-6=31', '21+31=52'] Exploring Operation: 73*52=3796, Resulting Numbers: [3796] 3796,23 unequal: No Solution Exploring Operation: 73-52=21, Resulting Numbers: [21] 21,23 unequal: No Solution Exploring Operation: 73+52=125, Resulting Numbers: [125] 125,23 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 23:[31, 94], Operations: ['37-6=31', '73+21=94'] Exploring Operation: 94-31=63, Resulting Numbers: [63] 63,23 unequal: No Solution Exploring Operation: 31*94=2914, Resulting Numbers: [2914] 2914,23 unequal: No Solution Exploring Operation: 31+94=125, Resulting Numbers: [125] 125,23 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0 Current State: 23:[37, 21, 67], Operations: ['73-6=67'] Exploring Operation: 37+21=58, Resulting Numbers: [67, 58] Generated Node #0,0,0: 23:[67, 58] Operation: 37+21=58 Exploring Operation: 21+67=88, Resulting Numbers: [37, 88] Generated Node #0,0,1: 23:[37, 88] Operation: 21+67=88 Exploring Operation: 37-21=16, Resulting Numbers: [67, 16] Generated Node #0,0,2: 23:[67, 16] Operation: 37-21=16 Exploring Operation: 67-21=46, Resulting Numbers: [37, 46] Generated Node #0,0,3: 23:[37, 46] Operation: 67-21=46 Exploring Operation: 67-37=30, Resulting Numbers: [21, 30] Generated Node #0,0,4: 23:[21, 30] Operation: 67-37=30 Moving to Node #0,2 Current State: 23:[37, 6, 52], Operations: ['73-21=52'] Exploring Operation: 37+6=43, Resulting Numbers: [52, 43] Generated Node #0,2,0: 23:[52, 43] Operation: 37+6=43 Exploring Operation: 37-6=31, Resulting Numbers: [52, 31] Generated Node #0,2,1: 23:[52, 31] Operation: 37-6=31 Exploring Operation: 52-37=15, Resulting Numbers: [6, 15] Generated Node #0,2,2: 23:[6, 15] Operation: 52-37=15 Exploring Operation: 52-6=46, Resulting Numbers: [37, 46] Generated Node #0,2,3: 23:[37, 46] Operation: 52-6=46 Exploring Operation: 6+52=58, Resulting Numbers: [37, 58] Generated Node #0,2,4: 23:[37, 58] Operation: 6+52=58 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 23:[6, 15], Operations: ['73-21=52', '52-37=15'] Exploring Operation: 6*15=90, Resulting Numbers: [90] 90,23 unequal: No Solution Exploring Operation: 15-6=9, Resulting Numbers: [9] 9,23 unequal: No Solution Exploring Operation: 6+15=21, Resulting Numbers: [21] 21,23 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 23:[52, 31], Operations: ['73-21=52', '37-6=31'] Exploring Operation: 52-31=21, Resulting Numbers: [21] 21,23 unequal: No Solution Exploring Operation: 52+31=83, Resulting Numbers: [83] 83,23 unequal: No Solution Exploring Operation: 52*31=1612, Resulting Numbers: [1612] 1612,23 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 23:[37, 46], Operations: ['73-21=52', '52-6=46'] Exploring Operation: 46-37=9, Resulting Numbers: [9] 9,23 unequal: No Solution Exploring Operation: 37+46=83, Resulting Numbers: [83] 83,23 unequal: No Solution Exploring Operation: 37*46=1702, Resulting Numbers: [1702] 1702,23 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 23:[52, 43], Operations: ['73-21=52', '37+6=43'] Exploring Operation: 52-43=9, Resulting Numbers: [9] 9,23 unequal: No Solution Exploring Operation: 52+43=95, Resulting Numbers: [95] 95,23 unequal: No Solution Exploring Operation: 52*43=2236, Resulting Numbers: [2236] 2236,23 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,4 Current State: 23:[37, 58], Operations: ['73-21=52', '6+52=58'] Exploring Operation: 37+58=95, Resulting Numbers: [95] 95,23 unequal: No Solution Exploring Operation: 37*58=2146, Resulting Numbers: [2146] 2146,23 unequal: No Solution Exploring Operation: 58-37=21, Resulting Numbers: [21] 21,23 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,4 Current State: 23:[73, 37, 27], Operations: ['21+6=27'] Exploring Operation: 37-27=10, Resulting Numbers: [73, 10] Generated Node #0,4,0: 23:[73, 10] Operation: 37-27=10 Exploring Operation: 73+27=100, Resulting Numbers: [37, 100] Generated Node #0,4,1: 23:[37, 100] Operation: 73+27=100 Exploring Operation: 73-37=36, Resulting Numbers: [27, 36] Generated Node #0,4,2: 23:[27, 36] Operation: 73-37=36 Exploring Operation: 73+37=110, Resulting Numbers: [27, 110] Generated Node #0,4,3: 23:[27, 110] Operation: 73+37=110 Exploring Operation: 73-27=46, Resulting Numbers: [37, 46] Generated Node #0,4,4: 23:[37, 46] Operation: 73-27=46 Moving to Node #0,0,4 Current State: 23:[21, 30], Operations: ['73-6=67', '67-37=30'] Exploring Operation: 21+30=51, Resulting Numbers: [51] 51,23 unequal: No Solution Exploring Operation: 30-21=9, Resulting Numbers: [9] 9,23 unequal: No Solution Exploring Operation: 21*30=630, Resulting Numbers: [630] 630,23 unequal: No Solution Moving to Node #0,4,2 Current State: 23:[27, 36], Operations: ['21+6=27', '73-37=36'] Exploring Operation: 36-27=9, Resulting Numbers: [9] 9,23 unequal: No Solution Exploring Operation: 27*36=972, Resulting Numbers: [972] 972,23 unequal: No Solution Exploring Operation: 27+36=63, Resulting Numbers: [63] 63,23 unequal: No Solution Moving to Node #0,4,4 Current State: 23:[37, 46], Operations: ['21+6=27', '73-27=46'] Exploring Operation: 46-37=9, Resulting Numbers: [9] 9,23 unequal: No Solution Exploring Operation: 37*46=1702, Resulting Numbers: [1702] 1702,23 unequal: No Solution Exploring Operation: 37+46=83, Resulting Numbers: [83] 83,23 unequal: No Solution Moving to Node #0,0,3 Current State: 23:[37, 46], Operations: ['73-6=67', '67-21=46'] Exploring Operation: 37+46=83, Resulting Numbers: [83] 83,23 unequal: No Solution Exploring Operation: 46-37=9, Resulting Numbers: [9] 9,23 unequal: No Solution Exploring Operation: 37*46=1702, Resulting Numbers: [1702] 1702,23 unequal: No Solution Moving to Node #0,0,2 Current State: 23:[67, 16], Operations: ['73-6=67', '37-21=16'] Exploring Operation: 67*16=1072, Resulting Numbers: [1072] 1072,23 unequal: No Solution Exploring Operation: 67+16=83, Resulting Numbers: [83] 83,23 unequal: No Solution Exploring Operation: 67-16=51, Resulting Numbers: [51] 51,23 unequal: No Solution Moving to Node #0,4,0 Current State: 23:[73, 10], Operations: ['21+6=27', '37-27=10'] Exploring Operation: 73*10=730, Resulting Numbers: [730] 730,23 unequal: No Solution Exploring Operation: 73+10=83, Resulting Numbers: [83] 83,23 unequal: No Solution Exploring Operation: 73-10=63, Resulting Numbers: [63] 63,23 unequal: No Solution Moving to Node #0,0,1 Current State: 23:[37, 88], Operations: ['73-6=67', '21+67=88'] Exploring Operation: 37+88=125, Resulting Numbers: [125] 125,23 unequal: No Solution Exploring Operation: 88-37=51, Resulting Numbers: [51] 51,23 unequal: No Solution Exploring Operation: 37*88=3256, Resulting Numbers: [3256] 3256,23 unequal: No Solution Moving to Node #0,0,0 Current State: 23:[67, 58], Operations: ['73-6=67', '37+21=58'] Exploring Operation: 67+58=125, Resulting Numbers: [125] 125,23 unequal: No Solution Exploring Operation: 67*58=3886, Resulting Numbers: [3886] 3886,23 unequal: No Solution Exploring Operation: 67-58=9, Resulting Numbers: [9] 9,23 unequal: No Solution Moving to Node #0,4,3 Current State: 23:[27, 110], Operations: ['21+6=27', '73+37=110'] Exploring Operation: 27+110=137, Resulting Numbers: [137] 137,23 unequal: No Solution Exploring Operation: 27*110=2970, Resulting Numbers: [2970] 2970,23 unequal: No Solution Exploring Operation: 110-27=83, Resulting Numbers: [83] 83,23 unequal: No Solution Moving to Node #0,4,1 Current State: 23:[37, 100], Operations: ['21+6=27', '73+27=100'] Exploring Operation: 100-37=63, Resulting Numbers: [63] 63,23 unequal: No Solution Exploring Operation: 37*100=3700, Resulting Numbers: [3700] 3700,23 unequal: No Solution Exploring Operation: 37+100=137, Resulting Numbers: [137] 137,23 unequal: No Solution No solution found.
0
hs_5
sum_heuristic
[ 76, 92, 90, 15 ]
89
[ "92-76=16", "90+15=105", "105-16=89" ]
Current State: 89:[76, 92, 90, 15], Operations: [] Exploring Operation: 92-76=16, Resulting Numbers: [90, 15, 16] Generated Node #2: [90, 15, 16] from Operation: 92-76=16 Current State: 89:[90, 15, 16], Operations: ['92-76=16'] Exploring Operation: 90+15=105, Resulting Numbers: [16, 105] Generated Node #3: [16, 105] from Operation: 90+15=105 Current State: 89:[16, 105], Operations: ['92-76=16', '90+15=105'] Exploring Operation: 105-16=89, Resulting Numbers: [89] 89,89 equal: Goal Reached
4
Current State: 89:[76, 92, 90, 15], Operations: [] Exploring Operation: 92-15=77, Resulting Numbers: [76, 90, 77] Generated Node #0,0: 89:[76, 90, 77] Operation: 92-15=77 Exploring Operation: 76+15=91, Resulting Numbers: [92, 90, 91] Generated Node #0,1: 89:[92, 90, 91] Operation: 76+15=91 Exploring Operation: 76-15=61, Resulting Numbers: [92, 90, 61] Generated Node #0,2: 89:[92, 90, 61] Operation: 76-15=61 Exploring Operation: 92+15=107, Resulting Numbers: [76, 90, 107] Generated Node #0,3: 89:[76, 90, 107] Operation: 92+15=107 Exploring Operation: 90-15=75, Resulting Numbers: [76, 92, 75] Generated Node #0,4: 89:[76, 92, 75] Operation: 90-15=75 Moving to Node #0,1 Current State: 89:[92, 90, 91], Operations: ['76+15=91'] Exploring Operation: 92+90=182, Resulting Numbers: [91, 182] Generated Node #0,1,0: 89:[91, 182] Operation: 92+90=182 Exploring Operation: 92-91=1, Resulting Numbers: [90, 1] Generated Node #0,1,1: 89:[90, 1] Operation: 92-91=1 Exploring Operation: 92+91=183, Resulting Numbers: [90, 183] Generated Node #0,1,2: 89:[90, 183] Operation: 92+91=183 Exploring Operation: 91-90=1, Resulting Numbers: [92, 1] Generated Node #0,1,3: 89:[92, 1] Operation: 91-90=1 Exploring Operation: 92-90=2, Resulting Numbers: [91, 2] Generated Node #0,1,4: 89:[91, 2] Operation: 92-90=2 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 89:[90, 1], Operations: ['76+15=91', '92-91=1'] Exploring Operation: 90/1=90, Resulting Numbers: [90] 90,89 unequal: No Solution Exploring Operation: 90-1=89, Resulting Numbers: [89] 89,89 equal: Goal Reached Moving to Node #0 Current State: 89:[76, 92, 90, 15], Operations: [] Exploring Operation: 76+15=91, Resulting Numbers: [92, 90, 91] Generated Node #0,1: 89:[92, 90, 91] Operation: 76+15=91 Moving to Node #0,1 Current State: 89:[92, 90, 91], Operations: ['76+15=91'] Exploring Operation: 92-91=1, Resulting Numbers: [90, 1] Generated Node #0,1,1: 89:[90, 1] Operation: 92-91=1 Moving to Node #0,1,1 Current State: 89:[90, 1], Operations: ['76+15=91', '92-91=1'] Exploring Operation: 90-1=89, Resulting Numbers: [89] 89,89 equal: Goal Reached Exit Sub Search at level 1
0.986111
hs_5
sum_heuristic
[ 10, 70, 78, 84 ]
62
[ "84-70=14", "10*14=140", "140-78=62" ]
Current State: 62:[10, 70, 78, 84], Operations: [] Exploring Operation: 84-70=14, Resulting Numbers: [10, 78, 14] Generated Node #2: [10, 78, 14] from Operation: 84-70=14 Current State: 62:[10, 78, 14], Operations: ['84-70=14'] Exploring Operation: 10*14=140, Resulting Numbers: [78, 140] Generated Node #3: [78, 140] from Operation: 10*14=140 Current State: 62:[78, 140], Operations: ['84-70=14', '10*14=140'] Exploring Operation: 140-78=62, Resulting Numbers: [62] 62,62 equal: Goal Reached
4
Current State: 62:[10, 70, 78, 84], Operations: [] Exploring Operation: 84-78=6, Resulting Numbers: [10, 70, 6] Generated Node #0,0: 62:[10, 70, 6] Operation: 84-78=6 Start Sub Search at level 1: Moving to Node #0,0 Current State: 62:[10, 70, 6], Operations: ['84-78=6'] Exploring Operation: 70-10=60, Resulting Numbers: [6, 60] Generated Node #0,0,0: 62:[6, 60] Operation: 70-10=60 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 62:[6, 60], Operations: ['84-78=6', '70-10=60'] Exploring Operation: 6+60=66, Resulting Numbers: [66] 66,62 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
sum_heuristic
[ 83, 55, 5, 71 ]
94
[ "83-55=28", "71-5=66", "28+66=94" ]
Current State: 94:[83, 55, 5, 71], Operations: [] Exploring Operation: 83-55=28, Resulting Numbers: [5, 71, 28] Generated Node #2: [5, 71, 28] from Operation: 83-55=28 Current State: 94:[5, 71, 28], Operations: ['83-55=28'] Exploring Operation: 71-5=66, Resulting Numbers: [28, 66] Generated Node #3: [28, 66] from Operation: 71-5=66 Current State: 94:[28, 66], Operations: ['83-55=28', '71-5=66'] Exploring Operation: 28+66=94, Resulting Numbers: [94] 94,94 equal: Goal Reached
4
Current State: 94:[83, 55, 5, 71], Operations: [] Exploring Operation: 71-55=16, Resulting Numbers: [83, 5, 16] Generated Node #0,0: 94:[83, 5, 16] Operation: 71-55=16 Exploring Operation: 55-5=50, Resulting Numbers: [83, 71, 50] Generated Node #0,1: 94:[83, 71, 50] Operation: 55-5=50 Exploring Operation: 5+71=76, Resulting Numbers: [83, 55, 76] Generated Node #0,2: 94:[83, 55, 76] Operation: 5+71=76 Exploring Operation: 83-71=12, Resulting Numbers: [55, 5, 12] Generated Node #0,3: 94:[55, 5, 12] Operation: 83-71=12 Exploring Operation: 83+5=88, Resulting Numbers: [55, 71, 88] Generated Node #0,4: 94:[55, 71, 88] Operation: 83+5=88 Start Sub Search at level 1: Moving to Node #0,3 Current State: 94:[55, 5, 12], Operations: ['83-71=12'] Exploring Operation: 55-12=43, Resulting Numbers: [5, 43] Generated Node #0,3,0: 94:[5, 43] Operation: 55-12=43 Exploring Operation: 5*12=60, Resulting Numbers: [55, 60] Generated Node #0,3,1: 94:[55, 60] Operation: 5*12=60 Exploring Operation: 55-5=50, Resulting Numbers: [12, 50] Generated Node #0,3,2: 94:[12, 50] Operation: 55-5=50 Exploring Operation: 55/5=11, Resulting Numbers: [12, 11] Generated Node #0,3,3: 94:[12, 11] Operation: 55/5=11 Exploring Operation: 12-5=7, Resulting Numbers: [55, 7] Generated Node #0,3,4: 94:[55, 7] Operation: 12-5=7 Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 94:[5, 43], Operations: ['83-71=12', '55-12=43'] Exploring Operation: 5*43=215, Resulting Numbers: [215] 215,94 unequal: No Solution Exploring Operation: 5+43=48, Resulting Numbers: [48] 48,94 unequal: No Solution Exploring Operation: 43-5=38, Resulting Numbers: [38] 38,94 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 94:[12, 50], Operations: ['83-71=12', '55-5=50'] Exploring Operation: 12+50=62, Resulting Numbers: [62] 62,94 unequal: No Solution Exploring Operation: 12*50=600, Resulting Numbers: [600] 600,94 unequal: No Solution Exploring Operation: 50-12=38, Resulting Numbers: [38] 38,94 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,4 Current State: 94:[55, 7], Operations: ['83-71=12', '12-5=7'] Exploring Operation: 55-7=48, Resulting Numbers: [48] 48,94 unequal: No Solution Exploring Operation: 55*7=385, Resulting Numbers: [385] 385,94 unequal: No Solution Exploring Operation: 55+7=62, Resulting Numbers: [62] 62,94 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 94:[12, 11], Operations: ['83-71=12', '55/5=11'] Exploring Operation: 12-11=1, Resulting Numbers: [1] 1,94 unequal: No Solution Exploring Operation: 12*11=132, Resulting Numbers: [132] 132,94 unequal: No Solution Exploring Operation: 12+11=23, Resulting Numbers: [23] 23,94 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 94:[55, 60], Operations: ['83-71=12', '5*12=60'] Exploring Operation: 55+60=115, Resulting Numbers: [115] 115,94 unequal: No Solution Exploring Operation: 55*60=3300, Resulting Numbers: [3300] 3300,94 unequal: No Solution Exploring Operation: 60-55=5, Resulting Numbers: [5] 5,94 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 94:[83, 5, 16], Operations: ['71-55=16'] Exploring Operation: 16-5=11, Resulting Numbers: [83, 11] Generated Node #0,0,0: 94:[83, 11] Operation: 16-5=11 Exploring Operation: 83+5=88, Resulting Numbers: [16, 88] Generated Node #0,0,1: 94:[16, 88] Operation: 83+5=88 Exploring Operation: 5*16=80, Resulting Numbers: [83, 80] Generated Node #0,0,2: 94:[83, 80] Operation: 5*16=80 Exploring Operation: 83-16=67, Resulting Numbers: [5, 67] Generated Node #0,0,3: 94:[5, 67] Operation: 83-16=67 Exploring Operation: 83+16=99, Resulting Numbers: [5, 99] Generated Node #0,0,4: 94:[5, 99] Operation: 83+16=99 Moving to Node #0,0,4 Current State: 94:[5, 99], Operations: ['71-55=16', '83+16=99'] Exploring Operation: 5*99=495, Resulting Numbers: [495] 495,94 unequal: No Solution Exploring Operation: 5+99=104, Resulting Numbers: [104] 104,94 unequal: No Solution Exploring Operation: 99-5=94, Resulting Numbers: [94] 94,94 equal: Goal Reached Moving to Node #0 Current State: 94:[83, 55, 5, 71], Operations: [] Exploring Operation: 71-55=16, Resulting Numbers: [83, 5, 16] Generated Node #0,0: 94:[83, 5, 16] Operation: 71-55=16 Moving to Node #0,0 Current State: 94:[83, 5, 16], Operations: ['71-55=16'] Exploring Operation: 83+16=99, Resulting Numbers: [5, 99] Generated Node #0,0,4: 94:[5, 99] Operation: 83+16=99 Moving to Node #0,0,4 Current State: 94:[5, 99], Operations: ['71-55=16', '83+16=99'] Exploring Operation: 99-5=94, Resulting Numbers: [94] 94,94 equal: Goal Reached Exit Sub Search at level 1
0.967882
hs_5
sum_heuristic
[ 85, 39, 61, 5 ]
75
[ "85-39=46", "61-46=15", "5*15=75" ]
Current State: 75:[85, 39, 61, 5], Operations: [] Exploring Operation: 85-39=46, Resulting Numbers: [61, 5, 46] Generated Node #2: [61, 5, 46] from Operation: 85-39=46 Current State: 75:[61, 5, 46], Operations: ['85-39=46'] Exploring Operation: 61-46=15, Resulting Numbers: [5, 15] Generated Node #3: [5, 15] from Operation: 61-46=15 Current State: 75:[5, 15], Operations: ['85-39=46', '61-46=15'] Exploring Operation: 5*15=75, Resulting Numbers: [75] 75,75 equal: Goal Reached
4
Current State: 75:[85, 39, 61, 5], Operations: [] Exploring Operation: 61-39=22, Resulting Numbers: [85, 5, 22] Generated Node #0,0: 75:[85, 5, 22] Operation: 61-39=22 Exploring Operation: 85-61=24, Resulting Numbers: [39, 5, 24] Generated Node #0,1: 75:[39, 5, 24] Operation: 85-61=24 Exploring Operation: 85-5=80, Resulting Numbers: [39, 61, 80] Generated Node #0,2: 75:[39, 61, 80] Operation: 85-5=80 Exploring Operation: 85/5=17, Resulting Numbers: [39, 61, 17] Generated Node #0,3: 75:[39, 61, 17] Operation: 85/5=17 Moving to Node #0,0 Current State: 75:[85, 5, 22], Operations: ['61-39=22'] Exploring Operation: 85-22=63, Resulting Numbers: [5, 63] Generated Node #0,0,0: 75:[5, 63] Operation: 85-22=63 Exploring Operation: 85-5=80, Resulting Numbers: [22, 80] Generated Node #0,0,1: 75:[22, 80] Operation: 85-5=80 Exploring Operation: 5+22=27, Resulting Numbers: [85, 27] Generated Node #0,0,2: 75:[85, 27] Operation: 5+22=27 Exploring Operation: 85/5=17, Resulting Numbers: [22, 17] Generated Node #0,0,3: 75:[22, 17] Operation: 85/5=17 Moving to Node #0,1 Current State: 75:[39, 5, 24], Operations: ['85-61=24'] Exploring Operation: 39+24=63, Resulting Numbers: [5, 63] Generated Node #0,1,0: 75:[5, 63] Operation: 39+24=63 Exploring Operation: 5+24=29, Resulting Numbers: [39, 29] Generated Node #0,1,1: 75:[39, 29] Operation: 5+24=29 Exploring Operation: 39-24=15, Resulting Numbers: [5, 15] Generated Node #0,1,2: 75:[5, 15] Operation: 39-24=15 Exploring Operation: 39-5=34, Resulting Numbers: [24, 34] Generated Node #0,1,3: 75:[24, 34] Operation: 39-5=34 Moving to Node #0,3 Current State: 75:[39, 61, 17], Operations: ['85/5=17'] Exploring Operation: 39+61=100, Resulting Numbers: [17, 100] Generated Node #0,3,0: 75:[17, 100] Operation: 39+61=100 Exploring Operation: 39-17=22, Resulting Numbers: [61, 22] Generated Node #0,3,1: 75:[61, 22] Operation: 39-17=22 Exploring Operation: 61-39=22, Resulting Numbers: [17, 22] Generated Node #0,3,2: 75:[17, 22] Operation: 61-39=22 Exploring Operation: 61+17=78, Resulting Numbers: [39, 78] Generated Node #0,3,3: 75:[39, 78] Operation: 61+17=78 Moving to Node #0,2 Current State: 75:[39, 61, 80], Operations: ['85-5=80'] Exploring Operation: 39+61=100, Resulting Numbers: [80, 100] Generated Node #0,2,0: 75:[80, 100] Operation: 39+61=100 Exploring Operation: 61-39=22, Resulting Numbers: [80, 22] Generated Node #0,2,1: 75:[80, 22] Operation: 61-39=22 Exploring Operation: 80-39=41, Resulting Numbers: [61, 41] Generated Node #0,2,2: 75:[61, 41] Operation: 80-39=41 Exploring Operation: 80-61=19, Resulting Numbers: [39, 19] Generated Node #0,2,3: 75:[39, 19] Operation: 80-61=19 Moving to Node #0,1,2 Current State: 75:[5, 15], Operations: ['85-61=24', '39-24=15'] Exploring Operation: 5+15=20, Resulting Numbers: [20] 20,75 unequal: No Solution Exploring Operation: 5*15=75, Resulting Numbers: [75] 75,75 equal: Goal Reached Moving to Node #0 Current State: 75:[85, 39, 61, 5], Operations: [] Exploring Operation: 85-61=24, Resulting Numbers: [39, 5, 24] Generated Node #0,1: 75:[39, 5, 24] Operation: 85-61=24 Moving to Node #0,1 Current State: 75:[39, 5, 24], Operations: ['85-61=24'] Exploring Operation: 39-24=15, Resulting Numbers: [5, 15] Generated Node #0,1,2: 75:[5, 15] Operation: 39-24=15 Moving to Node #0,1,2 Current State: 75:[5, 15], Operations: ['85-61=24', '39-24=15'] Exploring Operation: 5*15=75, Resulting Numbers: [75] 75,75 equal: Goal Reached
0.977431
hs_4
mult_heuristic
[ 23, 70, 11, 35 ]
24
[ "23-11=12", "70/35=2", "12*2=24" ]
Current State: 24:[23, 70, 11, 35], Operations: [] Exploring Operation: 23-11=12, Resulting Numbers: [70, 35, 12] Generated Node #2: [70, 35, 12] from Operation: 23-11=12 Current State: 24:[70, 35, 12], Operations: ['23-11=12'] Exploring Operation: 70/35=2, Resulting Numbers: [12, 2] Generated Node #3: [12, 2] from Operation: 70/35=2 Current State: 24:[12, 2], Operations: ['23-11=12', '70/35=2'] Exploring Operation: 12*2=24, Resulting Numbers: [24] 24,24 equal: Goal Reached
4
Current State: 24:[23, 70, 11, 35], Operations: [] Exploring Operation: 70/35=2, Resulting Numbers: [23, 11, 2] Generated Node #0,0: 24:[23, 11, 2] Operation: 70/35=2 Exploring Operation: 70-35=35, Resulting Numbers: [23, 11, 35] Generated Node #0,1: 24:[23, 11, 35] Operation: 70-35=35 Moving to Node #0,0 Current State: 24:[23, 11, 2], Operations: ['70/35=2'] Exploring Operation: 23+2=25, Resulting Numbers: [11, 25] Generated Node #0,0,0: 24:[11, 25] Operation: 23+2=25 Exploring Operation: 23-11=12, Resulting Numbers: [2, 12] Generated Node #0,0,1: 24:[2, 12] Operation: 23-11=12 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 24:[2, 12], Operations: ['70/35=2', '23-11=12'] Exploring Operation: 2*12=24, Resulting Numbers: [24] 24,24 equal: Goal Reached Moving to Node #0 Current State: 24:[23, 70, 11, 35], Operations: [] Exploring Operation: 70/35=2, Resulting Numbers: [23, 11, 2] Generated Node #0,0: 24:[23, 11, 2] Operation: 70/35=2 Moving to Node #0,0 Current State: 24:[23, 11, 2], Operations: ['70/35=2'] Exploring Operation: 23-11=12, Resulting Numbers: [2, 12] Generated Node #0,0,1: 24:[2, 12] Operation: 23-11=12 Moving to Node #0,0,1 Current State: 24:[2, 12], Operations: ['70/35=2', '23-11=12'] Exploring Operation: 2*12=24, Resulting Numbers: [24] 24,24 equal: Goal Reached Exit Sub Search at level 1
0.992188
hs_2
sum_heuristic
[ 96, 52, 4, 48 ]
80
[ "52-48=4", "4*4=16", "96-16=80" ]
Current State: 80:[96, 52, 4, 48], Operations: [] Exploring Operation: 52-48=4, Resulting Numbers: [96, 4, 4] Generated Node #2: [96, 4, 4] from Operation: 52-48=4 Current State: 80:[96, 4, 4], Operations: ['52-48=4'] Exploring Operation: 4*4=16, Resulting Numbers: [96, 16] Generated Node #3: [96, 16] from Operation: 4*4=16 Current State: 80:[96, 16], Operations: ['52-48=4', '4*4=16'] Exploring Operation: 96-16=80, Resulting Numbers: [80] 80,80 equal: Goal Reached
4
Current State: 80:[96, 52, 4, 48], Operations: [] Exploring Operation: 96-52=44, Resulting Numbers: [4, 48, 44] Generated Node #0,0: 80:[4, 48, 44] Operation: 96-52=44 Moving to Node #0,0 Current State: 80:[4, 48, 44], Operations: ['96-52=44'] Exploring Operation: 48-44=4, Resulting Numbers: [4, 4] Generated Node #0,0,0: 80:[4, 4] Operation: 48-44=4 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 80:[4, 4], Operations: ['96-52=44', '48-44=4'] Exploring Operation: 4+4=8, Resulting Numbers: [8] 8,80 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
sum_heuristic
[ 67, 2, 99, 34 ]
30
[ "99-67=32", "2*32=64", "64-34=30" ]
Current State: 30:[67, 2, 99, 34], Operations: [] Exploring Operation: 99-67=32, Resulting Numbers: [2, 34, 32] Generated Node #2: [2, 34, 32] from Operation: 99-67=32 Current State: 30:[2, 34, 32], Operations: ['99-67=32'] Exploring Operation: 2*32=64, Resulting Numbers: [34, 64] Generated Node #3: [34, 64] from Operation: 2*32=64 Current State: 30:[34, 64], Operations: ['99-67=32', '2*32=64'] Exploring Operation: 64-34=30, Resulting Numbers: [30] 30,30 equal: Goal Reached
4
Current State: 30:[67, 2, 99, 34], Operations: [] Exploring Operation: 99-67=32, Resulting Numbers: [2, 34, 32] Generated Node #0,0: 30:[2, 34, 32] Operation: 99-67=32 Exploring Operation: 67-34=33, Resulting Numbers: [2, 99, 33] Generated Node #0,1: 30:[2, 99, 33] Operation: 67-34=33 Start Sub Search at level 1: Moving to Node #0,0 Current State: 30:[2, 34, 32], Operations: ['99-67=32'] Exploring Operation: 34-32=2, Resulting Numbers: [2, 2] Generated Node #0,0,0: 30:[2, 2] Operation: 34-32=2 Exploring Operation: 34-2=32, Resulting Numbers: [32, 32] Generated Node #0,0,1: 30:[32, 32] Operation: 34-2=32 Moving to Node #0,0,0 Current State: 30:[2, 2], Operations: ['99-67=32', '34-32=2'] Exploring Operation: 2+2=4, Resulting Numbers: [4] 4,30 unequal: No Solution Exploring Operation: 2*2=4, Resulting Numbers: [4] 4,30 unequal: No Solution Moving to Node #0,0,1 Current State: 30:[32, 32], Operations: ['99-67=32', '34-2=32'] Exploring Operation: 32/32=1, Resulting Numbers: [1] 1,30 unequal: No Solution Exploring Operation: 32-32=0, Resulting Numbers: [0] 0,30 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 30:[2, 99, 33], Operations: ['67-34=33'] Exploring Operation: 99-33=66, Resulting Numbers: [2, 66] Generated Node #0,1,0: 30:[2, 66] Operation: 99-33=66 Exploring Operation: 99/33=3, Resulting Numbers: [2, 3] Generated Node #0,1,1: 30:[2, 3] Operation: 99/33=3 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 30:[2, 3], Operations: ['67-34=33', '99/33=3'] Exploring Operation: 2+3=5, Resulting Numbers: [5] 5,30 unequal: No Solution Exploring Operation: 2*3=6, Resulting Numbers: [6] 6,30 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 30:[2, 66], Operations: ['67-34=33', '99-33=66'] Exploring Operation: 66/2=33, Resulting Numbers: [33] 33,30 unequal: No Solution Exploring Operation: 66-2=64, Resulting Numbers: [64] 64,30 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
sum_heuristic
[ 32, 78, 62, 15 ]
17
[ "78-62=16", "32/16=2", "15+2=17" ]
Current State: 17:[32, 78, 62, 15], Operations: [] Exploring Operation: 78-62=16, Resulting Numbers: [32, 15, 16] Generated Node #2: [32, 15, 16] from Operation: 78-62=16 Current State: 17:[32, 15, 16], Operations: ['78-62=16'] Exploring Operation: 32/16=2, Resulting Numbers: [15, 2] Generated Node #3: [15, 2] from Operation: 32/16=2 Current State: 17:[15, 2], Operations: ['78-62=16', '32/16=2'] Exploring Operation: 15+2=17, Resulting Numbers: [17] 17,17 equal: Goal Reached
4
Current State: 17:[32, 78, 62, 15], Operations: [] Exploring Operation: 78-32=46, Resulting Numbers: [62, 15, 46] Generated Node #0,0: 17:[62, 15, 46] Operation: 78-32=46 Exploring Operation: 78-62=16, Resulting Numbers: [32, 15, 16] Generated Node #0,1: 17:[32, 15, 16] Operation: 78-62=16 Exploring Operation: 32-15=17, Resulting Numbers: [78, 62, 17] Generated Node #0,2: 17:[78, 62, 17] Operation: 32-15=17 Exploring Operation: 62-32=30, Resulting Numbers: [78, 15, 30] Generated Node #0,3: 17:[78, 15, 30] Operation: 62-32=30 Moving to Node #0,1 Current State: 17:[32, 15, 16], Operations: ['78-62=16'] Exploring Operation: 15+16=31, Resulting Numbers: [32, 31] Generated Node #0,1,0: 17:[32, 31] Operation: 15+16=31 Exploring Operation: 32-16=16, Resulting Numbers: [15, 16] Generated Node #0,1,1: 17:[15, 16] Operation: 32-16=16 Exploring Operation: 32/16=2, Resulting Numbers: [15, 2] Generated Node #0,1,2: 17:[15, 2] Operation: 32/16=2 Exploring Operation: 32-15=17, Resulting Numbers: [16, 17] Generated Node #0,1,3: 17:[16, 17] Operation: 32-15=17 Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 17:[16, 17], Operations: ['78-62=16', '32-15=17'] Exploring Operation: 16+17=33, Resulting Numbers: [33] 33,17 unequal: No Solution Exploring Operation: 16*17=272, Resulting Numbers: [272] 272,17 unequal: No Solution Exploring Operation: 17-16=1, Resulting Numbers: [1] 1,17 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 17:[15, 16], Operations: ['78-62=16', '32-16=16'] Exploring Operation: 15*16=240, Resulting Numbers: [240] 240,17 unequal: No Solution Exploring Operation: 15+16=31, Resulting Numbers: [31] 31,17 unequal: No Solution Exploring Operation: 16-15=1, Resulting Numbers: [1] 1,17 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 17:[15, 2], Operations: ['78-62=16', '32/16=2'] Exploring Operation: 15*2=30, Resulting Numbers: [30] 30,17 unequal: No Solution Exploring Operation: 15+2=17, Resulting Numbers: [17] 17,17 equal: Goal Reached Moving to Node #0 Current State: 17:[32, 78, 62, 15], Operations: [] Exploring Operation: 78-62=16, Resulting Numbers: [32, 15, 16] Generated Node #0,1: 17:[32, 15, 16] Operation: 78-62=16 Moving to Node #0,1 Current State: 17:[32, 15, 16], Operations: ['78-62=16'] Exploring Operation: 32/16=2, Resulting Numbers: [15, 2] Generated Node #0,1,2: 17:[15, 2] Operation: 32/16=2 Moving to Node #0,1,2 Current State: 17:[15, 2], Operations: ['78-62=16', '32/16=2'] Exploring Operation: 15+2=17, Resulting Numbers: [17] 17,17 equal: Goal Reached Exit Sub Search at level 1
0.982639
hs_4
mult_heuristic
[ 1, 5, 80, 23 ]
38
[ "23-1=22", "80/5=16", "22+16=38" ]
Current State: 38:[1, 5, 80, 23], Operations: [] Exploring Operation: 23-1=22, Resulting Numbers: [5, 80, 22] Generated Node #2: [5, 80, 22] from Operation: 23-1=22 Current State: 38:[5, 80, 22], Operations: ['23-1=22'] Exploring Operation: 80/5=16, Resulting Numbers: [22, 16] Generated Node #3: [22, 16] from Operation: 80/5=16 Current State: 38:[22, 16], Operations: ['23-1=22', '80/5=16'] Exploring Operation: 22+16=38, Resulting Numbers: [38] 38,38 equal: Goal Reached
4
Current State: 38:[1, 5, 80, 23], Operations: [] Exploring Operation: 80-23=57, Resulting Numbers: [1, 5, 57] Generated Node #0,0: 38:[1, 5, 57] Operation: 80-23=57 Exploring Operation: 23-5=18, Resulting Numbers: [1, 80, 18] Generated Node #0,1: 38:[1, 80, 18] Operation: 23-5=18 Exploring Operation: 5-1=4, Resulting Numbers: [80, 23, 4] Generated Node #0,2: 38:[80, 23, 4] Operation: 5-1=4 Exploring Operation: 80-5=75, Resulting Numbers: [1, 23, 75] Generated Node #0,3: 38:[1, 23, 75] Operation: 80-5=75 Exploring Operation: 80/5=16, Resulting Numbers: [1, 23, 16] Generated Node #0,4: 38:[1, 23, 16] Operation: 80/5=16 Start Sub Search at level 1: Moving to Node #0,4 Current State: 38:[1, 23, 16], Operations: ['80/5=16'] Exploring Operation: 1+16=17, Resulting Numbers: [23, 17] Generated Node #0,4,0: 38:[23, 17] Operation: 1+16=17 Exploring Operation: 1*23=23, Resulting Numbers: [16, 23] Generated Node #0,4,1: 38:[16, 23] Operation: 1*23=23 Exploring Operation: 23+16=39, Resulting Numbers: [1, 39] Generated Node #0,4,2: 38:[1, 39] Operation: 23+16=39 Exploring Operation: 23-16=7, Resulting Numbers: [1, 7] Generated Node #0,4,3: 38:[1, 7] Operation: 23-16=7 Exploring Operation: 23-1=22, Resulting Numbers: [16, 22] Generated Node #0,4,4: 38:[16, 22] Operation: 23-1=22 Start Sub Search at level 2: Moving to Node #0,4,2 Current State: 38:[1, 39], Operations: ['80/5=16', '23+16=39'] Exploring Operation: 1+39=40, Resulting Numbers: [40] 40,38 unequal: No Solution Exploring Operation: 39-1=38, Resulting Numbers: [38] 38,38 equal: Goal Reached Moving to Node #0 Current State: 38:[1, 5, 80, 23], Operations: [] Exploring Operation: 80/5=16, Resulting Numbers: [1, 23, 16] Generated Node #0,4: 38:[1, 23, 16] Operation: 80/5=16 Moving to Node #0,4 Current State: 38:[1, 23, 16], Operations: ['80/5=16'] Exploring Operation: 23+16=39, Resulting Numbers: [1, 39] Generated Node #0,4,2: 38:[1, 39] Operation: 23+16=39 Moving to Node #0,4,2 Current State: 38:[1, 39], Operations: ['80/5=16', '23+16=39'] Exploring Operation: 39-1=38, Resulting Numbers: [38] 38,38 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.986111
hs_5
sum_heuristic
[ 20, 69, 5, 25 ]
73
[ "20*5=100", "100/25=4", "69+4=73" ]
Current State: 73:[20, 69, 5, 25], Operations: [] Exploring Operation: 20*5=100, Resulting Numbers: [69, 25, 100] Generated Node #2: [69, 25, 100] from Operation: 20*5=100 Current State: 73:[69, 25, 100], Operations: ['20*5=100'] Exploring Operation: 100/25=4, Resulting Numbers: [69, 4] Generated Node #3: [69, 4] from Operation: 100/25=4 Current State: 73:[69, 4], Operations: ['20*5=100', '100/25=4'] Exploring Operation: 69+4=73, Resulting Numbers: [73] 73,73 equal: Goal Reached
4
Current State: 73:[20, 69, 5, 25], Operations: [] Exploring Operation: 5+25=30, Resulting Numbers: [20, 69, 30] Generated Node #0,0: 73:[20, 69, 30] Operation: 5+25=30 Exploring Operation: 20+5=25, Resulting Numbers: [69, 25, 25] Generated Node #0,1: 73:[69, 25, 25] Operation: 20+5=25 Exploring Operation: 20+25=45, Resulting Numbers: [69, 5, 45] Generated Node #0,2: 73:[69, 5, 45] Operation: 20+25=45 Exploring Operation: 20*5=100, Resulting Numbers: [69, 25, 100] Generated Node #0,3: 73:[69, 25, 100] Operation: 20*5=100 Start Sub Search at level 1: Moving to Node #0,3 Current State: 73:[69, 25, 100], Operations: ['20*5=100'] Exploring Operation: 69+25=94, Resulting Numbers: [100, 94] Generated Node #0,3,0: 73:[100, 94] Operation: 69+25=94 Exploring Operation: 100-25=75, Resulting Numbers: [69, 75] Generated Node #0,3,1: 73:[69, 75] Operation: 100-25=75 Exploring Operation: 25+100=125, Resulting Numbers: [69, 125] Generated Node #0,3,2: 73:[69, 125] Operation: 25+100=125 Exploring Operation: 69-25=44, Resulting Numbers: [100, 44] Generated Node #0,3,3: 73:[100, 44] Operation: 69-25=44 Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 73:[69, 75], Operations: ['20*5=100', '100-25=75'] Exploring Operation: 69*75=5175, Resulting Numbers: [5175] 5175,73 unequal: No Solution Exploring Operation: 75-69=6, Resulting Numbers: [6] 6,73 unequal: No Solution Exploring Operation: 69+75=144, Resulting Numbers: [144] 144,73 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 73:[100, 94], Operations: ['20*5=100', '69+25=94'] Exploring Operation: 100+94=194, Resulting Numbers: [194] 194,73 unequal: No Solution Exploring Operation: 100-94=6, Resulting Numbers: [6] 6,73 unequal: No Solution Exploring Operation: 100*94=9400, Resulting Numbers: [9400] 9400,73 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 73:[69, 125], Operations: ['20*5=100', '25+100=125'] Exploring Operation: 69*125=8625, Resulting Numbers: [8625] 8625,73 unequal: No Solution Exploring Operation: 69+125=194, Resulting Numbers: [194] 194,73 unequal: No Solution Exploring Operation: 125-69=56, Resulting Numbers: [56] 56,73 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 73:[100, 44], Operations: ['20*5=100', '69-25=44'] Exploring Operation: 100-44=56, Resulting Numbers: [56] 56,73 unequal: No Solution Exploring Operation: 100*44=4400, Resulting Numbers: [4400] 4400,73 unequal: No Solution Exploring Operation: 100+44=144, Resulting Numbers: [144] 144,73 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 73:[20, 69, 30], Operations: ['5+25=30'] Exploring Operation: 30-20=10, Resulting Numbers: [69, 10] Generated Node #0,0,0: 73:[69, 10] Operation: 30-20=10 Exploring Operation: 69-20=49, Resulting Numbers: [30, 49] Generated Node #0,0,1: 73:[30, 49] Operation: 69-20=49 Exploring Operation: 20+69=89, Resulting Numbers: [30, 89] Generated Node #0,0,2: 73:[30, 89] Operation: 20+69=89 Exploring Operation: 20+30=50, Resulting Numbers: [69, 50] Generated Node #0,0,3: 73:[69, 50] Operation: 20+30=50 Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 73:[69, 50], Operations: ['5+25=30', '20+30=50'] Exploring Operation: 69+50=119, Resulting Numbers: [119] 119,73 unequal: No Solution Exploring Operation: 69*50=3450, Resulting Numbers: [3450] 3450,73 unequal: No Solution Exploring Operation: 69-50=19, Resulting Numbers: [19] 19,73 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 73:[30, 89], Operations: ['5+25=30', '20+69=89'] Exploring Operation: 89-30=59, Resulting Numbers: [59] 59,73 unequal: No Solution Exploring Operation: 30+89=119, Resulting Numbers: [119] 119,73 unequal: No Solution Exploring Operation: 30*89=2670, Resulting Numbers: [2670] 2670,73 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 73:[69, 10], Operations: ['5+25=30', '30-20=10'] Exploring Operation: 69*10=690, Resulting Numbers: [690] 690,73 unequal: No Solution Exploring Operation: 69-10=59, Resulting Numbers: [59] 59,73 unequal: No Solution Exploring Operation: 69+10=79, Resulting Numbers: [79] 79,73 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 73:[30, 49], Operations: ['5+25=30', '69-20=49'] Exploring Operation: 30+49=79, Resulting Numbers: [79] 79,73 unequal: No Solution Exploring Operation: 49-30=19, Resulting Numbers: [19] 19,73 unequal: No Solution Exploring Operation: 30*49=1470, Resulting Numbers: [1470] 1470,73 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 73:[69, 25, 25], Operations: ['20+5=25'] Exploring Operation: 25+25=50, Resulting Numbers: [69, 50] Generated Node #0,1,0: 73:[69, 50] Operation: 25+25=50 Exploring Operation: 69+25=94, Resulting Numbers: [25, 94] Generated Node #0,1,1: 73:[25, 94] Operation: 69+25=94 Exploring Operation: 69+25=94, Resulting Numbers: [25, 94] Generated Node #0,1,2: 73:[25, 94] Operation: 69+25=94 Exploring Operation: 25/25=1, Resulting Numbers: [69, 1] Generated Node #0,1,3: 73:[69, 1] Operation: 25/25=1 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 73:[69, 50], Operations: ['20+5=25', '25+25=50'] Exploring Operation: 69*50=3450, Resulting Numbers: [3450] 3450,73 unequal: No Solution Exploring Operation: 69+50=119, Resulting Numbers: [119] 119,73 unequal: No Solution Exploring Operation: 69-50=19, Resulting Numbers: [19] 19,73 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 73:[25, 94], Operations: ['20+5=25', '69+25=94'] Exploring Operation: 25*94=2350, Resulting Numbers: [2350] 2350,73 unequal: No Solution Exploring Operation: 25+94=119, Resulting Numbers: [119] 119,73 unequal: No Solution Exploring Operation: 94-25=69, Resulting Numbers: [69] 69,73 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 73:[25, 94], Operations: ['20+5=25', '69+25=94'] Exploring Operation: 25*94=2350, Resulting Numbers: [2350] 2350,73 unequal: No Solution Exploring Operation: 25+94=119, Resulting Numbers: [119] 119,73 unequal: No Solution Exploring Operation: 94-25=69, Resulting Numbers: [69] 69,73 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 73:[69, 1], Operations: ['20+5=25', '25/25=1'] Exploring Operation: 69*1=69, Resulting Numbers: [69] 69,73 unequal: No Solution Exploring Operation: 69+1=70, Resulting Numbers: [70] 70,73 unequal: No Solution Exploring Operation: 69/1=69, Resulting Numbers: [69] 69,73 unequal: No Solution Exploring Operation: 69-1=68, Resulting Numbers: [68] 68,73 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 73:[69, 5, 45], Operations: ['20+25=45'] Exploring Operation: 45-5=40, Resulting Numbers: [69, 40] Generated Node #0,2,0: 73:[69, 40] Operation: 45-5=40 Exploring Operation: 5+45=50, Resulting Numbers: [69, 50] Generated Node #0,2,1: 73:[69, 50] Operation: 5+45=50 Exploring Operation: 69-5=64, Resulting Numbers: [45, 64] Generated Node #0,2,2: 73:[45, 64] Operation: 69-5=64 Exploring Operation: 69+5=74, Resulting Numbers: [45, 74] Generated Node #0,2,3: 73:[45, 74] Operation: 69+5=74 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 73:[69, 50], Operations: ['20+25=45', '5+45=50'] Exploring Operation: 69+50=119, Resulting Numbers: [119] 119,73 unequal: No Solution Exploring Operation: 69-50=19, Resulting Numbers: [19] 19,73 unequal: No Solution Exploring Operation: 69*50=3450, Resulting Numbers: [3450] 3450,73 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 73:[45, 74], Operations: ['20+25=45', '69+5=74'] Exploring Operation: 45*74=3330, Resulting Numbers: [3330] 3330,73 unequal: No Solution Exploring Operation: 45+74=119, Resulting Numbers: [119] 119,73 unequal: No Solution Exploring Operation: 74-45=29, Resulting Numbers: [29] 29,73 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 73:[69, 40], Operations: ['20+25=45', '45-5=40'] Exploring Operation: 69+40=109, Resulting Numbers: [109] 109,73 unequal: No Solution Exploring Operation: 69-40=29, Resulting Numbers: [29] 29,73 unequal: No Solution Exploring Operation: 69*40=2760, Resulting Numbers: [2760] 2760,73 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 73:[45, 64], Operations: ['20+25=45', '69-5=64'] Exploring Operation: 45+64=109, Resulting Numbers: [109] 109,73 unequal: No Solution Exploring Operation: 64-45=19, Resulting Numbers: [19] 19,73 unequal: No Solution Exploring Operation: 45*64=2880, Resulting Numbers: [2880] 2880,73 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_4
mult_heuristic
[ 49, 58, 77, 14 ]
54
[ "58-49=9", "77-14=63", "63-9=54" ]
Current State: 54:[49, 58, 77, 14], Operations: [] Exploring Operation: 58-49=9, Resulting Numbers: [77, 14, 9] Generated Node #2: [77, 14, 9] from Operation: 58-49=9 Current State: 54:[77, 14, 9], Operations: ['58-49=9'] Exploring Operation: 77-14=63, Resulting Numbers: [9, 63] Generated Node #3: [9, 63] from Operation: 77-14=63 Current State: 54:[9, 63], Operations: ['58-49=9', '77-14=63'] Exploring Operation: 63-9=54, Resulting Numbers: [54] 54,54 equal: Goal Reached
4
Current State: 54:[49, 58, 77, 14], Operations: [] Exploring Operation: 77-58=19, Resulting Numbers: [49, 14, 19] Generated Node #0,0: 54:[49, 14, 19] Operation: 77-58=19 Exploring Operation: 58-49=9, Resulting Numbers: [77, 14, 9] Generated Node #0,1: 54:[77, 14, 9] Operation: 58-49=9 Exploring Operation: 49-14=35, Resulting Numbers: [58, 77, 35] Generated Node #0,2: 54:[58, 77, 35] Operation: 49-14=35 Exploring Operation: 77-14=63, Resulting Numbers: [49, 58, 63] Generated Node #0,3: 54:[49, 58, 63] Operation: 77-14=63 Exploring Operation: 77-49=28, Resulting Numbers: [58, 14, 28] Generated Node #0,4: 54:[58, 14, 28] Operation: 77-49=28 Moving to Node #0,4 Current State: 54:[58, 14, 28], Operations: ['77-49=28'] Exploring Operation: 28-14=14, Resulting Numbers: [58, 14] Generated Node #0,4,0: 54:[58, 14] Operation: 28-14=14 Exploring Operation: 58-28=30, Resulting Numbers: [14, 30] Generated Node #0,4,1: 54:[14, 30] Operation: 58-28=30 Exploring Operation: 28/14=2, Resulting Numbers: [58, 2] Generated Node #0,4,2: 54:[58, 2] Operation: 28/14=2 Exploring Operation: 58-14=44, Resulting Numbers: [28, 44] Generated Node #0,4,3: 54:[28, 44] Operation: 58-14=44 Exploring Operation: 14+28=42, Resulting Numbers: [58, 42] Generated Node #0,4,4: 54:[58, 42] Operation: 14+28=42 Start Sub Search at level 1: Moving to Node #0,4,2 Current State: 54:[58, 2], Operations: ['77-49=28', '28/14=2'] Exploring Operation: 58*2=116, Resulting Numbers: [116] 116,54 unequal: No Solution Exploring Operation: 58/2=29, Resulting Numbers: [29] 29,54 unequal: No Solution Exploring Operation: 58-2=56, Resulting Numbers: [56] 56,54 unequal: No Solution Exploring Operation: 58+2=60, Resulting Numbers: [60] 60,54 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,1 Current State: 54:[14, 30], Operations: ['77-49=28', '58-28=30'] Exploring Operation: 30-14=16, Resulting Numbers: [16] 16,54 unequal: No Solution Exploring Operation: 14+30=44, Resulting Numbers: [44] 44,54 unequal: No Solution Exploring Operation: 14*30=420, Resulting Numbers: [420] 420,54 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,0 Current State: 54:[58, 14], Operations: ['77-49=28', '28-14=14'] Exploring Operation: 58+14=72, Resulting Numbers: [72] 72,54 unequal: No Solution Exploring Operation: 58-14=44, Resulting Numbers: [44] 44,54 unequal: No Solution Exploring Operation: 58*14=812, Resulting Numbers: [812] 812,54 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,3 Current State: 54:[28, 44], Operations: ['77-49=28', '58-14=44'] Exploring Operation: 44-28=16, Resulting Numbers: [16] 16,54 unequal: No Solution Exploring Operation: 28*44=1232, Resulting Numbers: [1232] 1232,54 unequal: No Solution Exploring Operation: 28+44=72, Resulting Numbers: [72] 72,54 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,4 Current State: 54:[58, 42], Operations: ['77-49=28', '14+28=42'] Exploring Operation: 58*42=2436, Resulting Numbers: [2436] 2436,54 unequal: No Solution Exploring Operation: 58-42=16, Resulting Numbers: [16] 16,54 unequal: No Solution Exploring Operation: 58+42=100, Resulting Numbers: [100] 100,54 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0 Current State: 54:[49, 14, 19], Operations: ['77-58=19'] Exploring Operation: 19-14=5, Resulting Numbers: [49, 5] Generated Node #0,0,0: 54:[49, 5] Operation: 19-14=5 Exploring Operation: 49-14=35, Resulting Numbers: [19, 35] Generated Node #0,0,1: 54:[19, 35] Operation: 49-14=35 Exploring Operation: 49-19=30, Resulting Numbers: [14, 30] Generated Node #0,0,2: 54:[14, 30] Operation: 49-19=30 Exploring Operation: 14+19=33, Resulting Numbers: [49, 33] Generated Node #0,0,3: 54:[49, 33] Operation: 14+19=33 Exploring Operation: 49+14=63, Resulting Numbers: [19, 63] Generated Node #0,0,4: 54:[19, 63] Operation: 49+14=63 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 54:[49, 5], Operations: ['77-58=19', '19-14=5'] Exploring Operation: 49+5=54, Resulting Numbers: [54] 54,54 equal: Goal Reached Moving to Node #0 Current State: 54:[49, 58, 77, 14], Operations: [] Exploring Operation: 77-58=19, Resulting Numbers: [49, 14, 19] Generated Node #0,0: 54:[49, 14, 19] Operation: 77-58=19 Moving to Node #0,0 Current State: 54:[49, 14, 19], Operations: ['77-58=19'] Exploring Operation: 19-14=5, Resulting Numbers: [49, 5] Generated Node #0,0,0: 54:[49, 5] Operation: 19-14=5 Moving to Node #0,0,0 Current State: 54:[49, 5], Operations: ['77-58=19', '19-14=5'] Exploring Operation: 49+5=54, Resulting Numbers: [54] 54,54 equal: Goal Reached Exit Sub Search at level 1
0.96875
hs_5
mult_heuristic
[ 30, 36, 3, 99 ]
85
[ "3+99=102", "30*102=3060", "3060/36=85" ]
Current State: 85:[30, 36, 3, 99], Operations: [] Exploring Operation: 3+99=102, Resulting Numbers: [30, 36, 102] Generated Node #2: [30, 36, 102] from Operation: 3+99=102 Current State: 85:[30, 36, 102], Operations: ['3+99=102'] Exploring Operation: 30*102=3060, Resulting Numbers: [36, 3060] Generated Node #3: [36, 3060] from Operation: 30*102=3060 Current State: 85:[36, 3060], Operations: ['3+99=102', '30*102=3060'] Exploring Operation: 3060/36=85, Resulting Numbers: [85] 85,85 equal: Goal Reached
4
Current State: 85:[30, 36, 3, 99], Operations: [] Exploring Operation: 36-30=6, Resulting Numbers: [3, 99, 6] Generated Node #0,0: 85:[3, 99, 6] Operation: 36-30=6 Exploring Operation: 36/3=12, Resulting Numbers: [30, 99, 12] Generated Node #0,1: 85:[30, 99, 12] Operation: 36/3=12 Moving to Node #0,0 Current State: 85:[3, 99, 6], Operations: ['36-30=6'] Exploring Operation: 99-3=96, Resulting Numbers: [6, 96] Generated Node #0,0,0: 85:[6, 96] Operation: 99-3=96 Exploring Operation: 99-6=93, Resulting Numbers: [3, 93] Generated Node #0,0,1: 85:[3, 93] Operation: 99-6=93 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 85:[3, 93], Operations: ['36-30=6', '99-6=93'] Exploring Operation: 93-3=90, Resulting Numbers: [90] 90,85 unequal: No Solution Exploring Operation: 3+93=96, Resulting Numbers: [96] 96,85 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 85:[6, 96], Operations: ['36-30=6', '99-3=96'] Exploring Operation: 96-6=90, Resulting Numbers: [90] 90,85 unequal: No Solution Exploring Operation: 96/6=16, Resulting Numbers: [16] 16,85 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 85:[30, 99, 12], Operations: ['36/3=12'] Exploring Operation: 99-12=87, Resulting Numbers: [30, 87] Generated Node #0,1,0: 85:[30, 87] Operation: 99-12=87 Exploring Operation: 30-12=18, Resulting Numbers: [99, 18] Generated Node #0,1,1: 85:[99, 18] Operation: 30-12=18 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 85:[30, 87], Operations: ['36/3=12', '99-12=87'] Exploring Operation: 30+87=117, Resulting Numbers: [117] 117,85 unequal: No Solution Exploring Operation: 87-30=57, Resulting Numbers: [57] 57,85 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 85:[99, 18], Operations: ['36/3=12', '30-12=18'] Exploring Operation: 99+18=117, Resulting Numbers: [117] 117,85 unequal: No Solution Exploring Operation: 99-18=81, Resulting Numbers: [81] 81,85 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
mult_heuristic
[ 6, 6, 14, 51 ]
37
[ "6-6=0", "51-14=37", "0+37=37" ]
Current State: 37:[6, 6, 14, 51], Operations: [] Exploring Operation: 6-6=0, Resulting Numbers: [14, 51, 0] Generated Node #2: [14, 51, 0] from Operation: 6-6=0 Current State: 37:[14, 51, 0], Operations: ['6-6=0'] Exploring Operation: 51-14=37, Resulting Numbers: [0, 37] Generated Node #3: [0, 37] from Operation: 51-14=37 Current State: 37:[0, 37], Operations: ['6-6=0', '51-14=37'] Exploring Operation: 0+37=37, Resulting Numbers: [37] 37,37 equal: Goal Reached
4
Current State: 37:[6, 6, 14, 51], Operations: [] Exploring Operation: 6+14=20, Resulting Numbers: [6, 51, 20] Generated Node #0,0: 37:[6, 51, 20] Operation: 6+14=20 Exploring Operation: 51-6=45, Resulting Numbers: [6, 14, 45] Generated Node #0,1: 37:[6, 14, 45] Operation: 51-6=45 Exploring Operation: 6+6=12, Resulting Numbers: [14, 51, 12] Generated Node #0,2: 37:[14, 51, 12] Operation: 6+6=12 Exploring Operation: 6*6=36, Resulting Numbers: [14, 51, 36] Generated Node #0,3: 37:[14, 51, 36] Operation: 6*6=36 Start Sub Search at level 1: Moving to Node #0,3 Current State: 37:[14, 51, 36], Operations: ['6*6=36'] Exploring Operation: 14+51=65, Resulting Numbers: [36, 65] Generated Node #0,3,0: 37:[36, 65] Operation: 14+51=65 Exploring Operation: 36-14=22, Resulting Numbers: [51, 22] Generated Node #0,3,1: 37:[51, 22] Operation: 36-14=22 Exploring Operation: 14+36=50, Resulting Numbers: [51, 50] Generated Node #0,3,2: 37:[51, 50] Operation: 14+36=50 Exploring Operation: 51-14=37, Resulting Numbers: [36, 37] Generated Node #0,3,3: 37:[36, 37] Operation: 51-14=37 Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 37:[36, 37], Operations: ['6*6=36', '51-14=37'] Exploring Operation: 36+37=73, Resulting Numbers: [73] 73,37 unequal: No Solution Exploring Operation: 37-36=1, Resulting Numbers: [1] 1,37 unequal: No Solution Exploring Operation: 36*37=1332, Resulting Numbers: [1332] 1332,37 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 37:[51, 50], Operations: ['6*6=36', '14+36=50'] Exploring Operation: 51+50=101, Resulting Numbers: [101] 101,37 unequal: No Solution Exploring Operation: 51-50=1, Resulting Numbers: [1] 1,37 unequal: No Solution Exploring Operation: 51*50=2550, Resulting Numbers: [2550] 2550,37 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 37:[36, 65], Operations: ['6*6=36', '14+51=65'] Exploring Operation: 36*65=2340, Resulting Numbers: [2340] 2340,37 unequal: No Solution Exploring Operation: 36+65=101, Resulting Numbers: [101] 101,37 unequal: No Solution Exploring Operation: 65-36=29, Resulting Numbers: [29] 29,37 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 37:[51, 22], Operations: ['6*6=36', '36-14=22'] Exploring Operation: 51-22=29, Resulting Numbers: [29] 29,37 unequal: No Solution Exploring Operation: 51*22=1122, Resulting Numbers: [1122] 1122,37 unequal: No Solution Exploring Operation: 51+22=73, Resulting Numbers: [73] 73,37 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 37:[6, 51, 20], Operations: ['6+14=20'] Exploring Operation: 6+51=57, Resulting Numbers: [20, 57] Generated Node #0,0,0: 37:[20, 57] Operation: 6+51=57 Exploring Operation: 20-6=14, Resulting Numbers: [51, 14] Generated Node #0,0,1: 37:[51, 14] Operation: 20-6=14 Exploring Operation: 6+20=26, Resulting Numbers: [51, 26] Generated Node #0,0,2: 37:[51, 26] Operation: 6+20=26 Exploring Operation: 51-6=45, Resulting Numbers: [20, 45] Generated Node #0,0,3: 37:[20, 45] Operation: 51-6=45 Moving to Node #0,0,2 Current State: 37:[51, 26], Operations: ['6+14=20', '6+20=26'] Exploring Operation: 51+26=77, Resulting Numbers: [77] 77,37 unequal: No Solution Exploring Operation: 51-26=25, Resulting Numbers: [25] 25,37 unequal: No Solution Exploring Operation: 51*26=1326, Resulting Numbers: [1326] 1326,37 unequal: No Solution Moving to Node #0,0,3 Current State: 37:[20, 45], Operations: ['6+14=20', '51-6=45'] Exploring Operation: 45-20=25, Resulting Numbers: [25] 25,37 unequal: No Solution Exploring Operation: 20+45=65, Resulting Numbers: [65] 65,37 unequal: No Solution Exploring Operation: 20*45=900, Resulting Numbers: [900] 900,37 unequal: No Solution Moving to Node #0,0,1 Current State: 37:[51, 14], Operations: ['6+14=20', '20-6=14'] Exploring Operation: 51*14=714, Resulting Numbers: [714] 714,37 unequal: No Solution Exploring Operation: 51-14=37, Resulting Numbers: [37] 37,37 equal: Goal Reached Moving to Node #0 Current State: 37:[6, 6, 14, 51], Operations: [] Exploring Operation: 6+14=20, Resulting Numbers: [6, 51, 20] Generated Node #0,0: 37:[6, 51, 20] Operation: 6+14=20 Moving to Node #0,0 Current State: 37:[6, 51, 20], Operations: ['6+14=20'] Exploring Operation: 20-6=14, Resulting Numbers: [51, 14] Generated Node #0,0,1: 37:[51, 14] Operation: 20-6=14 Moving to Node #0,0,1 Current State: 37:[51, 14], Operations: ['6+14=20', '20-6=14'] Exploring Operation: 51-14=37, Resulting Numbers: [37] 37,37 equal: Goal Reached Exit Sub Search at level 1
0.96875
hs_4
sum_heuristic
[ 58, 56, 57, 11 ]
35
[ "58-56=2", "11*2=22", "57-22=35" ]
Current State: 35:[58, 56, 57, 11], Operations: [] Exploring Operation: 58-56=2, Resulting Numbers: [57, 11, 2] Generated Node #2: [57, 11, 2] from Operation: 58-56=2 Current State: 35:[57, 11, 2], Operations: ['58-56=2'] Exploring Operation: 11*2=22, Resulting Numbers: [57, 22] Generated Node #3: [57, 22] from Operation: 11*2=22 Current State: 35:[57, 22], Operations: ['58-56=2', '11*2=22'] Exploring Operation: 57-22=35, Resulting Numbers: [35] 35,35 equal: Goal Reached
4
Current State: 35:[58, 56, 57, 11], Operations: [] Exploring Operation: 58-56=2, Resulting Numbers: [57, 11, 2] Generated Node #0,0: 35:[57, 11, 2] Operation: 58-56=2 Exploring Operation: 58-57=1, Resulting Numbers: [56, 11, 1] Generated Node #0,1: 35:[56, 11, 1] Operation: 58-57=1 Exploring Operation: 58-11=47, Resulting Numbers: [56, 57, 47] Generated Node #0,2: 35:[56, 57, 47] Operation: 58-11=47 Exploring Operation: 57-56=1, Resulting Numbers: [58, 11, 1] Generated Node #0,3: 35:[58, 11, 1] Operation: 57-56=1 Moving to Node #0,0 Current State: 35:[57, 11, 2], Operations: ['58-56=2'] Exploring Operation: 57-2=55, Resulting Numbers: [11, 55] Generated Node #0,0,0: 35:[11, 55] Operation: 57-2=55 Exploring Operation: 57+2=59, Resulting Numbers: [11, 59] Generated Node #0,0,1: 35:[11, 59] Operation: 57+2=59 Exploring Operation: 57-11=46, Resulting Numbers: [2, 46] Generated Node #0,0,2: 35:[2, 46] Operation: 57-11=46 Exploring Operation: 11-2=9, Resulting Numbers: [57, 9] Generated Node #0,0,3: 35:[57, 9] Operation: 11-2=9 Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 35:[2, 46], Operations: ['58-56=2', '57-11=46'] Exploring Operation: 46/2=23, Resulting Numbers: [23] 23,35 unequal: No Solution Exploring Operation: 2*46=92, Resulting Numbers: [92] 92,35 unequal: No Solution Exploring Operation: 2+46=48, Resulting Numbers: [48] 48,35 unequal: No Solution Exploring Operation: 46-2=44, Resulting Numbers: [44] 44,35 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 35:[11, 55], Operations: ['58-56=2', '57-2=55'] Exploring Operation: 11*55=605, Resulting Numbers: [605] 605,35 unequal: No Solution Exploring Operation: 55/11=5, Resulting Numbers: [5] 5,35 unequal: No Solution Exploring Operation: 11+55=66, Resulting Numbers: [66] 66,35 unequal: No Solution Exploring Operation: 55-11=44, Resulting Numbers: [44] 44,35 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 35:[57, 9], Operations: ['58-56=2', '11-2=9'] Exploring Operation: 57+9=66, Resulting Numbers: [66] 66,35 unequal: No Solution Exploring Operation: 57-9=48, Resulting Numbers: [48] 48,35 unequal: No Solution Exploring Operation: 57*9=513, Resulting Numbers: [513] 513,35 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 35:[11, 59], Operations: ['58-56=2', '57+2=59'] Exploring Operation: 59-11=48, Resulting Numbers: [48] 48,35 unequal: No Solution Exploring Operation: 11*59=649, Resulting Numbers: [649] 649,35 unequal: No Solution Exploring Operation: 11+59=70, Resulting Numbers: [70] 70,35 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 35:[56, 11, 1], Operations: ['58-57=1'] Exploring Operation: 56*1=56, Resulting Numbers: [11, 56] Generated Node #0,1,0: 35:[11, 56] Operation: 56*1=56 Exploring Operation: 56-1=55, Resulting Numbers: [11, 55] Generated Node #0,1,1: 35:[11, 55] Operation: 56-1=55 Exploring Operation: 56-11=45, Resulting Numbers: [1, 45] Generated Node #0,1,2: 35:[1, 45] Operation: 56-11=45 Exploring Operation: 11-1=10, Resulting Numbers: [56, 10] Generated Node #0,1,3: 35:[56, 10] Operation: 11-1=10 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 35:[1, 45], Operations: ['58-57=1', '56-11=45'] Exploring Operation: 1*45=45, Resulting Numbers: [45] 45,35 unequal: No Solution Exploring Operation: 45/1=45, Resulting Numbers: [45] 45,35 unequal: No Solution Exploring Operation: 45-1=44, Resulting Numbers: [44] 44,35 unequal: No Solution Exploring Operation: 1+45=46, Resulting Numbers: [46] 46,35 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 35:[11, 55], Operations: ['58-57=1', '56-1=55'] Exploring Operation: 11*55=605, Resulting Numbers: [605] 605,35 unequal: No Solution Exploring Operation: 55-11=44, Resulting Numbers: [44] 44,35 unequal: No Solution Exploring Operation: 55/11=5, Resulting Numbers: [5] 5,35 unequal: No Solution Exploring Operation: 11+55=66, Resulting Numbers: [66] 66,35 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 35:[56, 10], Operations: ['58-57=1', '11-1=10'] Exploring Operation: 56*10=560, Resulting Numbers: [560] 560,35 unequal: No Solution Exploring Operation: 56+10=66, Resulting Numbers: [66] 66,35 unequal: No Solution Exploring Operation: 56-10=46, Resulting Numbers: [46] 46,35 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 35:[11, 56], Operations: ['58-57=1', '56*1=56'] Exploring Operation: 11*56=616, Resulting Numbers: [616] 616,35 unequal: No Solution Exploring Operation: 56-11=45, Resulting Numbers: [45] 45,35 unequal: No Solution Exploring Operation: 11+56=67, Resulting Numbers: [67] 67,35 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,3 Current State: 35:[58, 11, 1], Operations: ['57-56=1'] Exploring Operation: 58-1=57, Resulting Numbers: [11, 57] Generated Node #0,3,0: 35:[11, 57] Operation: 58-1=57 Exploring Operation: 58-11=47, Resulting Numbers: [1, 47] Generated Node #0,3,1: 35:[1, 47] Operation: 58-11=47 Exploring Operation: 11-1=10, Resulting Numbers: [58, 10] Generated Node #0,3,2: 35:[58, 10] Operation: 11-1=10 Exploring Operation: 58*1=58, Resulting Numbers: [11, 58] Generated Node #0,3,3: 35:[11, 58] Operation: 58*1=58 Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 35:[1, 47], Operations: ['57-56=1', '58-11=47'] Exploring Operation: 1*47=47, Resulting Numbers: [47] 47,35 unequal: No Solution Exploring Operation: 1+47=48, Resulting Numbers: [48] 48,35 unequal: No Solution Exploring Operation: 47/1=47, Resulting Numbers: [47] 47,35 unequal: No Solution Exploring Operation: 47-1=46, Resulting Numbers: [46] 46,35 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 35:[11, 57], Operations: ['57-56=1', '58-1=57'] Exploring Operation: 11+57=68, Resulting Numbers: [68] 68,35 unequal: No Solution Exploring Operation: 11*57=627, Resulting Numbers: [627] 627,35 unequal: No Solution Exploring Operation: 57-11=46, Resulting Numbers: [46] 46,35 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 35:[58, 10], Operations: ['57-56=1', '11-1=10'] Exploring Operation: 58*10=580, Resulting Numbers: [580] 580,35 unequal: No Solution Exploring Operation: 58+10=68, Resulting Numbers: [68] 68,35 unequal: No Solution Exploring Operation: 58-10=48, Resulting Numbers: [48] 48,35 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 35:[11, 58], Operations: ['57-56=1', '58*1=58'] Exploring Operation: 58-11=47, Resulting Numbers: [47] 47,35 unequal: No Solution Exploring Operation: 11*58=638, Resulting Numbers: [638] 638,35 unequal: No Solution Exploring Operation: 11+58=69, Resulting Numbers: [69] 69,35 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2 Current State: 35:[56, 57, 47], Operations: ['58-11=47'] Exploring Operation: 57-47=10, Resulting Numbers: [56, 10] Generated Node #0,2,0: 35:[56, 10] Operation: 57-47=10 Exploring Operation: 56+57=113, Resulting Numbers: [47, 113] Generated Node #0,2,1: 35:[47, 113] Operation: 56+57=113 Exploring Operation: 57-56=1, Resulting Numbers: [47, 1] Generated Node #0,2,2: 35:[47, 1] Operation: 57-56=1 Exploring Operation: 56-47=9, Resulting Numbers: [57, 9] Generated Node #0,2,3: 35:[57, 9] Operation: 56-47=9 Moving to Node #0,2,2 Current State: 35:[47, 1], Operations: ['58-11=47', '57-56=1'] Exploring Operation: 47-1=46, Resulting Numbers: [46] 46,35 unequal: No Solution Exploring Operation: 47/1=47, Resulting Numbers: [47] 47,35 unequal: No Solution Exploring Operation: 47*1=47, Resulting Numbers: [47] 47,35 unequal: No Solution Exploring Operation: 47+1=48, Resulting Numbers: [48] 48,35 unequal: No Solution Moving to Node #0,2,3 Current State: 35:[57, 9], Operations: ['58-11=47', '56-47=9'] Exploring Operation: 57-9=48, Resulting Numbers: [48] 48,35 unequal: No Solution Exploring Operation: 57*9=513, Resulting Numbers: [513] 513,35 unequal: No Solution Exploring Operation: 57+9=66, Resulting Numbers: [66] 66,35 unequal: No Solution Moving to Node #0,2,0 Current State: 35:[56, 10], Operations: ['58-11=47', '57-47=10'] Exploring Operation: 56*10=560, Resulting Numbers: [560] 560,35 unequal: No Solution Exploring Operation: 56-10=46, Resulting Numbers: [46] 46,35 unequal: No Solution Exploring Operation: 56+10=66, Resulting Numbers: [66] 66,35 unequal: No Solution Moving to Node #0,2,1 Current State: 35:[47, 113], Operations: ['58-11=47', '56+57=113'] Exploring Operation: 47*113=5311, Resulting Numbers: [5311] 5311,35 unequal: No Solution Exploring Operation: 113-47=66, Resulting Numbers: [66] 66,35 unequal: No Solution Exploring Operation: 47+113=160, Resulting Numbers: [160] 160,35 unequal: No Solution No solution found.
0
hs_4
mult_heuristic
[ 39, 50, 61, 94 ]
47
[ "39+61=100", "50*94=4700", "4700/100=47" ]
Current State: 47:[39, 50, 61, 94], Operations: [] Exploring Operation: 39+61=100, Resulting Numbers: [50, 94, 100] Generated Node #2: [50, 94, 100] from Operation: 39+61=100 Current State: 47:[50, 94, 100], Operations: ['39+61=100'] Exploring Operation: 50*94=4700, Resulting Numbers: [100, 4700] Generated Node #3: [100, 4700] from Operation: 50*94=4700 Current State: 47:[100, 4700], Operations: ['39+61=100', '50*94=4700'] Exploring Operation: 4700/100=47, Resulting Numbers: [47] 47,47 equal: Goal Reached
4
Current State: 47:[39, 50, 61, 94], Operations: [] Exploring Operation: 94-39=55, Resulting Numbers: [50, 61, 55] Generated Node #0,0: 47:[50, 61, 55] Operation: 94-39=55 Moving to Node #0,0 Current State: 47:[50, 61, 55], Operations: ['94-39=55'] Exploring Operation: 61-50=11, Resulting Numbers: [55, 11] Generated Node #0,0,0: 47:[55, 11] Operation: 61-50=11 Moving to Node #0,0,0 Current State: 47:[55, 11], Operations: ['94-39=55', '61-50=11'] Exploring Operation: 55-11=44, Resulting Numbers: [44] 44,47 unequal: No Solution No solution found.
0
hs_1
sum_heuristic
[ 11, 73, 40, 5 ]
72
[ "40-11=29", "5*29=145", "145-73=72" ]
Current State: 72:[11, 73, 40, 5], Operations: [] Exploring Operation: 40-11=29, Resulting Numbers: [73, 5, 29] Generated Node #2: [73, 5, 29] from Operation: 40-11=29 Current State: 72:[73, 5, 29], Operations: ['40-11=29'] Exploring Operation: 5*29=145, Resulting Numbers: [73, 145] Generated Node #3: [73, 145] from Operation: 5*29=145 Current State: 72:[73, 145], Operations: ['40-11=29', '5*29=145'] Exploring Operation: 145-73=72, Resulting Numbers: [72] 72,72 equal: Goal Reached
4
Current State: 72:[11, 73, 40, 5], Operations: [] Exploring Operation: 40-11=29, Resulting Numbers: [73, 5, 29] Generated Node #0,0: 72:[73, 5, 29] Operation: 40-11=29 Exploring Operation: 40-5=35, Resulting Numbers: [11, 73, 35] Generated Node #0,1: 72:[11, 73, 35] Operation: 40-5=35 Exploring Operation: 11-5=6, Resulting Numbers: [73, 40, 6] Generated Node #0,2: 72:[73, 40, 6] Operation: 11-5=6 Exploring Operation: 73-40=33, Resulting Numbers: [11, 5, 33] Generated Node #0,3: 72:[11, 5, 33] Operation: 73-40=33 Exploring Operation: 40/5=8, Resulting Numbers: [11, 73, 8] Generated Node #0,4: 72:[11, 73, 8] Operation: 40/5=8 Start Sub Search at level 1: Moving to Node #0,4 Current State: 72:[11, 73, 8], Operations: ['40/5=8'] Exploring Operation: 11+8=19, Resulting Numbers: [73, 19] Generated Node #0,4,0: 72:[73, 19] Operation: 11+8=19 Exploring Operation: 73-11=62, Resulting Numbers: [8, 62] Generated Node #0,4,1: 72:[8, 62] Operation: 73-11=62 Exploring Operation: 73+8=81, Resulting Numbers: [11, 81] Generated Node #0,4,2: 72:[11, 81] Operation: 73+8=81 Exploring Operation: 73-8=65, Resulting Numbers: [11, 65] Generated Node #0,4,3: 72:[11, 65] Operation: 73-8=65 Exploring Operation: 11-8=3, Resulting Numbers: [73, 3] Generated Node #0,4,4: 72:[73, 3] Operation: 11-8=3 Moving to Node #0,4,4 Current State: 72:[73, 3], Operations: ['40/5=8', '11-8=3'] Exploring Operation: 73*3=219, Resulting Numbers: [219] 219,72 unequal: No Solution Exploring Operation: 73+3=76, Resulting Numbers: [76] 76,72 unequal: No Solution Exploring Operation: 73-3=70, Resulting Numbers: [70] 70,72 unequal: No Solution Moving to Node #0,4,0 Current State: 72:[73, 19], Operations: ['40/5=8', '11+8=19'] Exploring Operation: 73-19=54, Resulting Numbers: [54] 54,72 unequal: No Solution Exploring Operation: 73*19=1387, Resulting Numbers: [1387] 1387,72 unequal: No Solution Exploring Operation: 73+19=92, Resulting Numbers: [92] 92,72 unequal: No Solution Moving to Node #0,4,3 Current State: 72:[11, 65], Operations: ['40/5=8', '73-8=65'] Exploring Operation: 11+65=76, Resulting Numbers: [76] 76,72 unequal: No Solution Exploring Operation: 65-11=54, Resulting Numbers: [54] 54,72 unequal: No Solution Exploring Operation: 11*65=715, Resulting Numbers: [715] 715,72 unequal: No Solution Moving to Node #0,4,1 Current State: 72:[8, 62], Operations: ['40/5=8', '73-11=62'] Exploring Operation: 8+62=70, Resulting Numbers: [70] 70,72 unequal: No Solution Exploring Operation: 8*62=496, Resulting Numbers: [496] 496,72 unequal: No Solution Exploring Operation: 62-8=54, Resulting Numbers: [54] 54,72 unequal: No Solution Moving to Node #0,4,2 Current State: 72:[11, 81], Operations: ['40/5=8', '73+8=81'] Exploring Operation: 81-11=70, Resulting Numbers: [70] 70,72 unequal: No Solution Exploring Operation: 11+81=92, Resulting Numbers: [92] 92,72 unequal: No Solution Exploring Operation: 11*81=891, Resulting Numbers: [891] 891,72 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 72:[11, 73, 35], Operations: ['40-5=35'] Exploring Operation: 11+73=84, Resulting Numbers: [35, 84] Generated Node #0,1,0: 72:[35, 84] Operation: 11+73=84 Exploring Operation: 73-11=62, Resulting Numbers: [35, 62] Generated Node #0,1,1: 72:[35, 62] Operation: 73-11=62 Exploring Operation: 11+35=46, Resulting Numbers: [73, 46] Generated Node #0,1,2: 72:[73, 46] Operation: 11+35=46 Exploring Operation: 35-11=24, Resulting Numbers: [73, 24] Generated Node #0,1,3: 72:[73, 24] Operation: 35-11=24 Exploring Operation: 73-35=38, Resulting Numbers: [11, 38] Generated Node #0,1,4: 72:[11, 38] Operation: 73-35=38 Moving to Node #0,1,3 Current State: 72:[73, 24], Operations: ['40-5=35', '35-11=24'] Exploring Operation: 73*24=1752, Resulting Numbers: [1752] 1752,72 unequal: No Solution Exploring Operation: 73+24=97, Resulting Numbers: [97] 97,72 unequal: No Solution Exploring Operation: 73-24=49, Resulting Numbers: [49] 49,72 unequal: No Solution Moving to Node #0,1,4 Current State: 72:[11, 38], Operations: ['40-5=35', '73-35=38'] Exploring Operation: 11+38=49, Resulting Numbers: [49] 49,72 unequal: No Solution Exploring Operation: 38-11=27, Resulting Numbers: [27] 27,72 unequal: No Solution Exploring Operation: 11*38=418, Resulting Numbers: [418] 418,72 unequal: No Solution Moving to Node #0,1,1 Current State: 72:[35, 62], Operations: ['40-5=35', '73-11=62'] Exploring Operation: 62-35=27, Resulting Numbers: [27] 27,72 unequal: No Solution Exploring Operation: 35+62=97, Resulting Numbers: [97] 97,72 unequal: No Solution Exploring Operation: 35*62=2170, Resulting Numbers: [2170] 2170,72 unequal: No Solution Moving to Node #0,1,2 Current State: 72:[73, 46], Operations: ['40-5=35', '11+35=46'] Exploring Operation: 73*46=3358, Resulting Numbers: [3358] 3358,72 unequal: No Solution Exploring Operation: 73-46=27, Resulting Numbers: [27] 27,72 unequal: No Solution Exploring Operation: 73+46=119, Resulting Numbers: [119] 119,72 unequal: No Solution Moving to Node #0,1,0 Current State: 72:[35, 84], Operations: ['40-5=35', '11+73=84'] Exploring Operation: 35+84=119, Resulting Numbers: [119] 119,72 unequal: No Solution Exploring Operation: 35*84=2940, Resulting Numbers: [2940] 2940,72 unequal: No Solution Exploring Operation: 84-35=49, Resulting Numbers: [49] 49,72 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 72:[73, 40, 6], Operations: ['11-5=6'] Exploring Operation: 73+6=79, Resulting Numbers: [40, 79] Generated Node #0,2,0: 72:[40, 79] Operation: 73+6=79 Exploring Operation: 73-6=67, Resulting Numbers: [40, 67] Generated Node #0,2,1: 72:[40, 67] Operation: 73-6=67 Exploring Operation: 40+6=46, Resulting Numbers: [73, 46] Generated Node #0,2,2: 72:[73, 46] Operation: 40+6=46 Exploring Operation: 73-40=33, Resulting Numbers: [6, 33] Generated Node #0,2,3: 72:[6, 33] Operation: 73-40=33 Exploring Operation: 40-6=34, Resulting Numbers: [73, 34] Generated Node #0,2,4: 72:[73, 34] Operation: 40-6=34 Moving to Node #0,2,3 Current State: 72:[6, 33], Operations: ['11-5=6', '73-40=33'] Exploring Operation: 6*33=198, Resulting Numbers: [198] 198,72 unequal: No Solution Exploring Operation: 6+33=39, Resulting Numbers: [39] 39,72 unequal: No Solution Exploring Operation: 33-6=27, Resulting Numbers: [27] 27,72 unequal: No Solution Moving to Node #0,2,4 Current State: 72:[73, 34], Operations: ['11-5=6', '40-6=34'] Exploring Operation: 73-34=39, Resulting Numbers: [39] 39,72 unequal: No Solution Exploring Operation: 73+34=107, Resulting Numbers: [107] 107,72 unequal: No Solution Exploring Operation: 73*34=2482, Resulting Numbers: [2482] 2482,72 unequal: No Solution Moving to Node #0,2,1 Current State: 72:[40, 67], Operations: ['11-5=6', '73-6=67'] Exploring Operation: 40*67=2680, Resulting Numbers: [2680] 2680,72 unequal: No Solution Exploring Operation: 40+67=107, Resulting Numbers: [107] 107,72 unequal: No Solution Exploring Operation: 67-40=27, Resulting Numbers: [27] 27,72 unequal: No Solution Moving to Node #0,2,0 Current State: 72:[40, 79], Operations: ['11-5=6', '73+6=79'] Exploring Operation: 40*79=3160, Resulting Numbers: [3160] 3160,72 unequal: No Solution Exploring Operation: 40+79=119, Resulting Numbers: [119] 119,72 unequal: No Solution Exploring Operation: 79-40=39, Resulting Numbers: [39] 39,72 unequal: No Solution Moving to Node #0,2,2 Current State: 72:[73, 46], Operations: ['11-5=6', '40+6=46'] Exploring Operation: 73+46=119, Resulting Numbers: [119] 119,72 unequal: No Solution Exploring Operation: 73*46=3358, Resulting Numbers: [3358] 3358,72 unequal: No Solution Exploring Operation: 73-46=27, Resulting Numbers: [27] 27,72 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 72:[11, 5, 33], Operations: ['73-40=33'] Exploring Operation: 33-11=22, Resulting Numbers: [5, 22] Generated Node #0,3,0: 72:[5, 22] Operation: 33-11=22 Exploring Operation: 33/11=3, Resulting Numbers: [5, 3] Generated Node #0,3,1: 72:[5, 3] Operation: 33/11=3 Exploring Operation: 5+33=38, Resulting Numbers: [11, 38] Generated Node #0,3,2: 72:[11, 38] Operation: 5+33=38 Exploring Operation: 11+5=16, Resulting Numbers: [33, 16] Generated Node #0,3,3: 72:[33, 16] Operation: 11+5=16 Exploring Operation: 11-5=6, Resulting Numbers: [33, 6] Generated Node #0,3,4: 72:[33, 6] Operation: 11-5=6 Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 72:[5, 3], Operations: ['73-40=33', '33/11=3'] Exploring Operation: 5+3=8, Resulting Numbers: [8] 8,72 unequal: No Solution Exploring Operation: 5*3=15, Resulting Numbers: [15] 15,72 unequal: No Solution Exploring Operation: 5-3=2, Resulting Numbers: [2] 2,72 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 72:[5, 22], Operations: ['73-40=33', '33-11=22'] Exploring Operation: 5*22=110, Resulting Numbers: [110] 110,72 unequal: No Solution Exploring Operation: 5+22=27, Resulting Numbers: [27] 27,72 unequal: No Solution Exploring Operation: 22-5=17, Resulting Numbers: [17] 17,72 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 72:[11, 38], Operations: ['73-40=33', '5+33=38'] Exploring Operation: 11*38=418, Resulting Numbers: [418] 418,72 unequal: No Solution Exploring Operation: 11+38=49, Resulting Numbers: [49] 49,72 unequal: No Solution Exploring Operation: 38-11=27, Resulting Numbers: [27] 27,72 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,4 Current State: 72:[33, 6], Operations: ['73-40=33', '11-5=6'] Exploring Operation: 33+6=39, Resulting Numbers: [39] 39,72 unequal: No Solution Exploring Operation: 33-6=27, Resulting Numbers: [27] 27,72 unequal: No Solution Exploring Operation: 33*6=198, Resulting Numbers: [198] 198,72 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 72:[33, 16], Operations: ['73-40=33', '11+5=16'] Exploring Operation: 33*16=528, Resulting Numbers: [528] 528,72 unequal: No Solution Exploring Operation: 33+16=49, Resulting Numbers: [49] 49,72 unequal: No Solution Exploring Operation: 33-16=17, Resulting Numbers: [17] 17,72 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 72:[73, 5, 29], Operations: ['40-11=29'] Exploring Operation: 73+5=78, Resulting Numbers: [29, 78] Generated Node #0,0,0: 72:[29, 78] Operation: 73+5=78 Exploring Operation: 5+29=34, Resulting Numbers: [73, 34] Generated Node #0,0,1: 72:[73, 34] Operation: 5+29=34 Exploring Operation: 29-5=24, Resulting Numbers: [73, 24] Generated Node #0,0,2: 72:[73, 24] Operation: 29-5=24 Exploring Operation: 73-5=68, Resulting Numbers: [29, 68] Generated Node #0,0,3: 72:[29, 68] Operation: 73-5=68 Exploring Operation: 73-29=44, Resulting Numbers: [5, 44] Generated Node #0,0,4: 72:[5, 44] Operation: 73-29=44 Moving to Node #0,0,2 Current State: 72:[73, 24], Operations: ['40-11=29', '29-5=24'] Exploring Operation: 73+24=97, Resulting Numbers: [97] 97,72 unequal: No Solution Exploring Operation: 73-24=49, Resulting Numbers: [49] 49,72 unequal: No Solution Exploring Operation: 73*24=1752, Resulting Numbers: [1752] 1752,72 unequal: No Solution Moving to Node #0,0,1 Current State: 72:[73, 34], Operations: ['40-11=29', '5+29=34'] Exploring Operation: 73-34=39, Resulting Numbers: [39] 39,72 unequal: No Solution Exploring Operation: 73+34=107, Resulting Numbers: [107] 107,72 unequal: No Solution Exploring Operation: 73*34=2482, Resulting Numbers: [2482] 2482,72 unequal: No Solution Moving to Node #0,0,3 Current State: 72:[29, 68], Operations: ['40-11=29', '73-5=68'] Exploring Operation: 68-29=39, Resulting Numbers: [39] 39,72 unequal: No Solution Exploring Operation: 29*68=1972, Resulting Numbers: [1972] 1972,72 unequal: No Solution Exploring Operation: 29+68=97, Resulting Numbers: [97] 97,72 unequal: No Solution Moving to Node #0,0,4 Current State: 72:[5, 44], Operations: ['40-11=29', '73-29=44'] Exploring Operation: 5*44=220, Resulting Numbers: [220] 220,72 unequal: No Solution Exploring Operation: 44-5=39, Resulting Numbers: [39] 39,72 unequal: No Solution Exploring Operation: 5+44=49, Resulting Numbers: [49] 49,72 unequal: No Solution Moving to Node #0,0,0 Current State: 72:[29, 78], Operations: ['40-11=29', '73+5=78'] Exploring Operation: 29+78=107, Resulting Numbers: [107] 107,72 unequal: No Solution Exploring Operation: 29*78=2262, Resulting Numbers: [2262] 2262,72 unequal: No Solution Exploring Operation: 78-29=49, Resulting Numbers: [49] 49,72 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_5
mult_heuristic
[ 27, 86, 39, 89 ]
14
[ "89-86=3", "39/3=13", "27-13=14" ]
Current State: 14:[27, 86, 39, 89], Operations: [] Exploring Operation: 89-86=3, Resulting Numbers: [27, 39, 3] Generated Node #2: [27, 39, 3] from Operation: 89-86=3 Current State: 14:[27, 39, 3], Operations: ['89-86=3'] Exploring Operation: 39/3=13, Resulting Numbers: [27, 13] Generated Node #3: [27, 13] from Operation: 39/3=13 Current State: 14:[27, 13], Operations: ['89-86=3', '39/3=13'] Exploring Operation: 27-13=14, Resulting Numbers: [14] 14,14 equal: Goal Reached
4
Current State: 14:[27, 86, 39, 89], Operations: [] Exploring Operation: 86-39=47, Resulting Numbers: [27, 89, 47] Generated Node #0,0: 14:[27, 89, 47] Operation: 86-39=47 Exploring Operation: 89-39=50, Resulting Numbers: [27, 86, 50] Generated Node #0,1: 14:[27, 86, 50] Operation: 89-39=50 Exploring Operation: 89-86=3, Resulting Numbers: [27, 39, 3] Generated Node #0,2: 14:[27, 39, 3] Operation: 89-86=3 Moving to Node #0,2 Current State: 14:[27, 39, 3], Operations: ['89-86=3'] Exploring Operation: 27/3=9, Resulting Numbers: [39, 9] Generated Node #0,2,0: 14:[39, 9] Operation: 27/3=9 Exploring Operation: 39/3=13, Resulting Numbers: [27, 13] Generated Node #0,2,1: 14:[27, 13] Operation: 39/3=13 Exploring Operation: 39-27=12, Resulting Numbers: [3, 12] Generated Node #0,2,2: 14:[3, 12] Operation: 39-27=12 Moving to Node #0,0 Current State: 14:[27, 89, 47], Operations: ['86-39=47'] Exploring Operation: 47-27=20, Resulting Numbers: [89, 20] Generated Node #0,0,0: 14:[89, 20] Operation: 47-27=20 Exploring Operation: 89-27=62, Resulting Numbers: [47, 62] Generated Node #0,0,1: 14:[47, 62] Operation: 89-27=62 Exploring Operation: 89-47=42, Resulting Numbers: [27, 42] Generated Node #0,0,2: 14:[27, 42] Operation: 89-47=42 Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 14:[27, 42], Operations: ['86-39=47', '89-47=42'] Exploring Operation: 42-27=15, Resulting Numbers: [15] 15,14 unequal: No Solution Exploring Operation: 27+42=69, Resulting Numbers: [69] 69,14 unequal: No Solution Exploring Operation: 27*42=1134, Resulting Numbers: [1134] 1134,14 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 14:[89, 20], Operations: ['86-39=47', '47-27=20'] Exploring Operation: 89*20=1780, Resulting Numbers: [1780] 1780,14 unequal: No Solution Exploring Operation: 89+20=109, Resulting Numbers: [109] 109,14 unequal: No Solution Exploring Operation: 89-20=69, Resulting Numbers: [69] 69,14 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 14:[47, 62], Operations: ['86-39=47', '89-27=62'] Exploring Operation: 47*62=2914, Resulting Numbers: [2914] 2914,14 unequal: No Solution Exploring Operation: 62-47=15, Resulting Numbers: [15] 15,14 unequal: No Solution Exploring Operation: 47+62=109, Resulting Numbers: [109] 109,14 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 14:[27, 86, 50], Operations: ['89-39=50'] Exploring Operation: 86-27=59, Resulting Numbers: [50, 59] Generated Node #0,1,0: 14:[50, 59] Operation: 86-27=59 Exploring Operation: 50-27=23, Resulting Numbers: [86, 23] Generated Node #0,1,1: 14:[86, 23] Operation: 50-27=23 Exploring Operation: 86-50=36, Resulting Numbers: [27, 36] Generated Node #0,1,2: 14:[27, 36] Operation: 86-50=36 Moving to Node #0,2,2 Current State: 14:[3, 12], Operations: ['89-86=3', '39-27=12'] Exploring Operation: 12/3=4, Resulting Numbers: [4] 4,14 unequal: No Solution Exploring Operation: 3+12=15, Resulting Numbers: [15] 15,14 unequal: No Solution Exploring Operation: 12-3=9, Resulting Numbers: [9] 9,14 unequal: No Solution Moving to Node #0,2,1 Current State: 14:[27, 13], Operations: ['89-86=3', '39/3=13'] Exploring Operation: 27-13=14, Resulting Numbers: [14] 14,14 equal: Goal Reached Moving to Node #0 Current State: 14:[27, 86, 39, 89], Operations: [] Exploring Operation: 89-86=3, Resulting Numbers: [27, 39, 3] Generated Node #0,2: 14:[27, 39, 3] Operation: 89-86=3 Moving to Node #0,2 Current State: 14:[27, 39, 3], Operations: ['89-86=3'] Exploring Operation: 39/3=13, Resulting Numbers: [27, 13] Generated Node #0,2,1: 14:[27, 13] Operation: 39/3=13 Moving to Node #0,2,1 Current State: 14:[27, 13], Operations: ['89-86=3', '39/3=13'] Exploring Operation: 27-13=14, Resulting Numbers: [14] 14,14 equal: Goal Reached
0.974826
hs_3
sum_heuristic
[ 3, 49, 6, 69 ]
74
[ "6+69=75", "75/3=25", "49+25=74" ]
Current State: 74:[3, 49, 6, 69], Operations: [] Exploring Operation: 6+69=75, Resulting Numbers: [3, 49, 75] Generated Node #2: [3, 49, 75] from Operation: 6+69=75 Current State: 74:[3, 49, 75], Operations: ['6+69=75'] Exploring Operation: 75/3=25, Resulting Numbers: [49, 25] Generated Node #3: [49, 25] from Operation: 75/3=25 Current State: 74:[49, 25], Operations: ['6+69=75', '75/3=25'] Exploring Operation: 49+25=74, Resulting Numbers: [74] 74,74 equal: Goal Reached
4
Current State: 74:[3, 49, 6, 69], Operations: [] Exploring Operation: 49-6=43, Resulting Numbers: [3, 69, 43] Generated Node #0,0: 74:[3, 69, 43] Operation: 49-6=43 Start Sub Search at level 1: Moving to Node #0,0 Current State: 74:[3, 69, 43], Operations: ['49-6=43'] Exploring Operation: 3+69=72, Resulting Numbers: [43, 72] Generated Node #0,0,0: 74:[43, 72] Operation: 3+69=72 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 74:[43, 72], Operations: ['49-6=43', '3+69=72'] Exploring Operation: 72-43=29, Resulting Numbers: [29] 29,74 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
mult_heuristic
[ 47, 85, 71, 74 ]
13
[ "47+85=132", "71+74=145", "145-132=13" ]
Current State: 13:[47, 85, 71, 74], Operations: [] Exploring Operation: 47+85=132, Resulting Numbers: [71, 74, 132] Generated Node #2: [71, 74, 132] from Operation: 47+85=132 Current State: 13:[71, 74, 132], Operations: ['47+85=132'] Exploring Operation: 71+74=145, Resulting Numbers: [132, 145] Generated Node #3: [132, 145] from Operation: 71+74=145 Current State: 13:[132, 145], Operations: ['47+85=132', '71+74=145'] Exploring Operation: 145-132=13, Resulting Numbers: [13] 13,13 equal: Goal Reached
4
Current State: 13:[47, 85, 71, 74], Operations: [] Exploring Operation: 74-71=3, Resulting Numbers: [47, 85, 3] Generated Node #0,0: 13:[47, 85, 3] Operation: 74-71=3 Exploring Operation: 85-74=11, Resulting Numbers: [47, 71, 11] Generated Node #0,1: 13:[47, 71, 11] Operation: 85-74=11 Exploring Operation: 85-47=38, Resulting Numbers: [71, 74, 38] Generated Node #0,2: 13:[71, 74, 38] Operation: 85-47=38 Exploring Operation: 85-71=14, Resulting Numbers: [47, 74, 14] Generated Node #0,3: 13:[47, 74, 14] Operation: 85-71=14 Start Sub Search at level 1: Moving to Node #0,1 Current State: 13:[47, 71, 11], Operations: ['85-74=11'] Exploring Operation: 47+11=58, Resulting Numbers: [71, 58] Generated Node #0,1,0: 13:[71, 58] Operation: 47+11=58 Exploring Operation: 71-11=60, Resulting Numbers: [47, 60] Generated Node #0,1,1: 13:[47, 60] Operation: 71-11=60 Exploring Operation: 47-11=36, Resulting Numbers: [71, 36] Generated Node #0,1,2: 13:[71, 36] Operation: 47-11=36 Exploring Operation: 71-47=24, Resulting Numbers: [11, 24] Generated Node #0,1,3: 13:[11, 24] Operation: 71-47=24 Moving to Node #0,1,3 Current State: 13:[11, 24], Operations: ['85-74=11', '71-47=24'] Exploring Operation: 24-11=13, Resulting Numbers: [13] 13,13 equal: Goal Reached Moving to Node #0 Current State: 13:[47, 85, 71, 74], Operations: [] Exploring Operation: 85-74=11, Resulting Numbers: [47, 71, 11] Generated Node #0,1: 13:[47, 71, 11] Operation: 85-74=11 Moving to Node #0,1 Current State: 13:[47, 71, 11], Operations: ['85-74=11'] Exploring Operation: 71-47=24, Resulting Numbers: [11, 24] Generated Node #0,1,3: 13:[11, 24] Operation: 71-47=24 Moving to Node #0,1,3 Current State: 13:[11, 24], Operations: ['85-74=11', '71-47=24'] Exploring Operation: 24-11=13, Resulting Numbers: [13] 13,13 equal: Goal Reached Exit Sub Search at level 1
0.988715
hs_4
mult_heuristic
[ 11, 4, 8, 54 ]
80
[ "11*4=44", "54-44=10", "8*10=80" ]
Current State: 80:[11, 4, 8, 54], Operations: [] Exploring Operation: 11*4=44, Resulting Numbers: [8, 54, 44] Generated Node #2: [8, 54, 44] from Operation: 11*4=44 Current State: 80:[8, 54, 44], Operations: ['11*4=44'] Exploring Operation: 54-44=10, Resulting Numbers: [8, 10] Generated Node #3: [8, 10] from Operation: 54-44=10 Current State: 80:[8, 10], Operations: ['11*4=44', '54-44=10'] Exploring Operation: 8*10=80, Resulting Numbers: [80] 80,80 equal: Goal Reached
4
Current State: 80:[11, 4, 8, 54], Operations: [] Exploring Operation: 54-11=43, Resulting Numbers: [4, 8, 43] Generated Node #0,0: 80:[4, 8, 43] Operation: 54-11=43 Start Sub Search at level 1: Moving to Node #0,0 Current State: 80:[4, 8, 43], Operations: ['54-11=43'] Exploring Operation: 43-4=39, Resulting Numbers: [8, 39] Generated Node #0,0,0: 80:[8, 39] Operation: 43-4=39 Moving to Node #0,0,0 Current State: 80:[8, 39], Operations: ['54-11=43', '43-4=39'] Exploring Operation: 8+39=47, Resulting Numbers: [47] 47,80 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
mult_heuristic
[ 32, 91, 87, 35 ]
63
[ "91-32=59", "87+35=122", "122-59=63" ]
Current State: 63:[32, 91, 87, 35], Operations: [] Exploring Operation: 91-32=59, Resulting Numbers: [87, 35, 59] Generated Node #2: [87, 35, 59] from Operation: 91-32=59 Current State: 63:[87, 35, 59], Operations: ['91-32=59'] Exploring Operation: 87+35=122, Resulting Numbers: [59, 122] Generated Node #3: [59, 122] from Operation: 87+35=122 Current State: 63:[59, 122], Operations: ['91-32=59', '87+35=122'] Exploring Operation: 122-59=63, Resulting Numbers: [63] 63,63 equal: Goal Reached
4
Current State: 63:[32, 91, 87, 35], Operations: [] Exploring Operation: 91-87=4, Resulting Numbers: [32, 35, 4] Generated Node #0,0: 63:[32, 35, 4] Operation: 91-87=4 Exploring Operation: 91-32=59, Resulting Numbers: [87, 35, 59] Generated Node #0,1: 63:[87, 35, 59] Operation: 91-32=59 Moving to Node #0,0 Current State: 63:[32, 35, 4], Operations: ['91-87=4'] Exploring Operation: 35-32=3, Resulting Numbers: [4, 3] Generated Node #0,0,0: 63:[4, 3] Operation: 35-32=3 Exploring Operation: 32+35=67, Resulting Numbers: [4, 67] Generated Node #0,0,1: 63:[4, 67] Operation: 32+35=67 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 63:[4, 3], Operations: ['91-87=4', '35-32=3'] Exploring Operation: 4-3=1, Resulting Numbers: [1] 1,63 unequal: No Solution Exploring Operation: 4+3=7, Resulting Numbers: [7] 7,63 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 63:[4, 67], Operations: ['91-87=4', '32+35=67'] Exploring Operation: 67-4=63, Resulting Numbers: [63] 63,63 equal: Goal Reached Moving to Node #0 Current State: 63:[32, 91, 87, 35], Operations: [] Exploring Operation: 91-87=4, Resulting Numbers: [32, 35, 4] Generated Node #0,0: 63:[32, 35, 4] Operation: 91-87=4 Moving to Node #0,0 Current State: 63:[32, 35, 4], Operations: ['91-87=4'] Exploring Operation: 32+35=67, Resulting Numbers: [4, 67] Generated Node #0,0,1: 63:[4, 67] Operation: 32+35=67 Moving to Node #0,0,1 Current State: 63:[4, 67], Operations: ['91-87=4', '32+35=67'] Exploring Operation: 67-4=63, Resulting Numbers: [63] 63,63 equal: Goal Reached Exit Sub Search at level 1
0.990451
hs_2
sum_heuristic
[ 36, 31, 77, 27 ]
32
[ "31+77=108", "108/27=4", "36-4=32" ]
Current State: 32:[36, 31, 77, 27], Operations: [] Exploring Operation: 31+77=108, Resulting Numbers: [36, 27, 108] Generated Node #2: [36, 27, 108] from Operation: 31+77=108 Current State: 32:[36, 27, 108], Operations: ['31+77=108'] Exploring Operation: 108/27=4, Resulting Numbers: [36, 4] Generated Node #3: [36, 4] from Operation: 108/27=4 Current State: 32:[36, 4], Operations: ['31+77=108', '108/27=4'] Exploring Operation: 36-4=32, Resulting Numbers: [32] 32,32 equal: Goal Reached
4
Current State: 32:[36, 31, 77, 27], Operations: [] Exploring Operation: 77-31=46, Resulting Numbers: [36, 27, 46] Generated Node #0,0: 32:[36, 27, 46] Operation: 77-31=46 Exploring Operation: 77-36=41, Resulting Numbers: [31, 27, 41] Generated Node #0,1: 32:[31, 27, 41] Operation: 77-36=41 Moving to Node #0,1 Current State: 32:[31, 27, 41], Operations: ['77-36=41'] Exploring Operation: 41-27=14, Resulting Numbers: [31, 14] Generated Node #0,1,0: 32:[31, 14] Operation: 41-27=14 Exploring Operation: 41-31=10, Resulting Numbers: [27, 10] Generated Node #0,1,1: 32:[27, 10] Operation: 41-31=10 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 32:[31, 14], Operations: ['77-36=41', '41-27=14'] Exploring Operation: 31+14=45, Resulting Numbers: [45] 45,32 unequal: No Solution Exploring Operation: 31-14=17, Resulting Numbers: [17] 17,32 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 32:[27, 10], Operations: ['77-36=41', '41-31=10'] Exploring Operation: 27-10=17, Resulting Numbers: [17] 17,32 unequal: No Solution Exploring Operation: 27+10=37, Resulting Numbers: [37] 37,32 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0 Current State: 32:[36, 27, 46], Operations: ['77-31=46'] Exploring Operation: 46-27=19, Resulting Numbers: [36, 19] Generated Node #0,0,0: 32:[36, 19] Operation: 46-27=19 Exploring Operation: 46-36=10, Resulting Numbers: [27, 10] Generated Node #0,0,1: 32:[27, 10] Operation: 46-36=10 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 32:[36, 19], Operations: ['77-31=46', '46-27=19'] Exploring Operation: 36-19=17, Resulting Numbers: [17] 17,32 unequal: No Solution Exploring Operation: 36+19=55, Resulting Numbers: [55] 55,32 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 32:[27, 10], Operations: ['77-31=46', '46-36=10'] Exploring Operation: 27+10=37, Resulting Numbers: [37] 37,32 unequal: No Solution Exploring Operation: 27-10=17, Resulting Numbers: [17] 17,32 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
sum_heuristic
[ 56, 47, 17, 51 ]
100
[ "56+47=103", "51/17=3", "103-3=100" ]
Current State: 100:[56, 47, 17, 51], Operations: [] Exploring Operation: 56+47=103, Resulting Numbers: [17, 51, 103] Generated Node #2: [17, 51, 103] from Operation: 56+47=103 Current State: 100:[17, 51, 103], Operations: ['56+47=103'] Exploring Operation: 51/17=3, Resulting Numbers: [103, 3] Generated Node #3: [103, 3] from Operation: 51/17=3 Current State: 100:[103, 3], Operations: ['56+47=103', '51/17=3'] Exploring Operation: 103-3=100, Resulting Numbers: [100] 100,100 equal: Goal Reached
4
Current State: 100:[56, 47, 17, 51], Operations: [] Exploring Operation: 56-47=9, Resulting Numbers: [17, 51, 9] Generated Node #0,0: 100:[17, 51, 9] Operation: 56-47=9 Exploring Operation: 56-51=5, Resulting Numbers: [47, 17, 5] Generated Node #0,1: 100:[47, 17, 5] Operation: 56-51=5 Exploring Operation: 56+47=103, Resulting Numbers: [17, 51, 103] Generated Node #0,2: 100:[17, 51, 103] Operation: 56+47=103 Start Sub Search at level 1: Moving to Node #0,0 Current State: 100:[17, 51, 9], Operations: ['56-47=9'] Exploring Operation: 17+9=26, Resulting Numbers: [51, 26] Generated Node #0,0,0: 100:[51, 26] Operation: 17+9=26 Exploring Operation: 17-9=8, Resulting Numbers: [51, 8] Generated Node #0,0,1: 100:[51, 8] Operation: 17-9=8 Exploring Operation: 51/17=3, Resulting Numbers: [9, 3] Generated Node #0,0,2: 100:[9, 3] Operation: 51/17=3 Moving to Node #0,0,0 Current State: 100:[51, 26], Operations: ['56-47=9', '17+9=26'] Exploring Operation: 51*26=1326, Resulting Numbers: [1326] 1326,100 unequal: No Solution Exploring Operation: 51-26=25, Resulting Numbers: [25] 25,100 unequal: No Solution Exploring Operation: 51+26=77, Resulting Numbers: [77] 77,100 unequal: No Solution Moving to Node #0,0,2 Current State: 100:[9, 3], Operations: ['56-47=9', '51/17=3'] Exploring Operation: 9/3=3, Resulting Numbers: [3] 3,100 unequal: No Solution Exploring Operation: 9+3=12, Resulting Numbers: [12] 12,100 unequal: No Solution Exploring Operation: 9-3=6, Resulting Numbers: [6] 6,100 unequal: No Solution Moving to Node #0,0,1 Current State: 100:[51, 8], Operations: ['56-47=9', '17-9=8'] Exploring Operation: 51*8=408, Resulting Numbers: [408] 408,100 unequal: No Solution Exploring Operation: 51-8=43, Resulting Numbers: [43] 43,100 unequal: No Solution Exploring Operation: 51+8=59, Resulting Numbers: [59] 59,100 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 100:[47, 17, 5], Operations: ['56-51=5'] Exploring Operation: 17+5=22, Resulting Numbers: [47, 22] Generated Node #0,1,0: 100:[47, 22] Operation: 17+5=22 Exploring Operation: 47-17=30, Resulting Numbers: [5, 30] Generated Node #0,1,1: 100:[5, 30] Operation: 47-17=30 Exploring Operation: 47+5=52, Resulting Numbers: [17, 52] Generated Node #0,1,2: 100:[17, 52] Operation: 47+5=52 Moving to Node #0,1,0 Current State: 100:[47, 22], Operations: ['56-51=5', '17+5=22'] Exploring Operation: 47*22=1034, Resulting Numbers: [1034] 1034,100 unequal: No Solution Exploring Operation: 47+22=69, Resulting Numbers: [69] 69,100 unequal: No Solution Exploring Operation: 47-22=25, Resulting Numbers: [25] 25,100 unequal: No Solution Moving to Node #0,1,1 Current State: 100:[5, 30], Operations: ['56-51=5', '47-17=30'] Exploring Operation: 5+30=35, Resulting Numbers: [35] 35,100 unequal: No Solution Exploring Operation: 30-5=25, Resulting Numbers: [25] 25,100 unequal: No Solution Exploring Operation: 30/5=6, Resulting Numbers: [6] 6,100 unequal: No Solution Moving to Node #0,1,2 Current State: 100:[17, 52], Operations: ['56-51=5', '47+5=52'] Exploring Operation: 52-17=35, Resulting Numbers: [35] 35,100 unequal: No Solution Exploring Operation: 17*52=884, Resulting Numbers: [884] 884,100 unequal: No Solution Exploring Operation: 17+52=69, Resulting Numbers: [69] 69,100 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 100:[17, 51, 103], Operations: ['56+47=103'] Exploring Operation: 51-17=34, Resulting Numbers: [103, 34] Generated Node #0,2,0: 100:[103, 34] Operation: 51-17=34 Exploring Operation: 103-51=52, Resulting Numbers: [17, 52] Generated Node #0,2,1: 100:[17, 52] Operation: 103-51=52 Exploring Operation: 51/17=3, Resulting Numbers: [103, 3] Generated Node #0,2,2: 100:[103, 3] Operation: 51/17=3 Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 100:[103, 3], Operations: ['56+47=103', '51/17=3'] Exploring Operation: 103+3=106, Resulting Numbers: [106] 106,100 unequal: No Solution Exploring Operation: 103*3=309, Resulting Numbers: [309] 309,100 unequal: No Solution Exploring Operation: 103-3=100, Resulting Numbers: [100] 100,100 equal: Goal Reached Moving to Node #0 Current State: 100:[56, 47, 17, 51], Operations: [] Exploring Operation: 56+47=103, Resulting Numbers: [17, 51, 103] Generated Node #0,2: 100:[17, 51, 103] Operation: 56+47=103 Moving to Node #0,2 Current State: 100:[17, 51, 103], Operations: ['56+47=103'] Exploring Operation: 51/17=3, Resulting Numbers: [103, 3] Generated Node #0,2,2: 100:[103, 3] Operation: 51/17=3 Moving to Node #0,2,2 Current State: 100:[103, 3], Operations: ['56+47=103', '51/17=3'] Exploring Operation: 103-3=100, Resulting Numbers: [100] 100,100 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.967882
hs_3
sum_heuristic
[ 42, 82, 50, 68 ]
79
[ "50*68=3400", "3400-82=3318", "3318/42=79" ]
Current State: 79:[42, 82, 50, 68], Operations: [] Exploring Operation: 50*68=3400, Resulting Numbers: [42, 82, 3400] Generated Node #2: [42, 82, 3400] from Operation: 50*68=3400 Current State: 79:[42, 82, 3400], Operations: ['50*68=3400'] Exploring Operation: 3400-82=3318, Resulting Numbers: [42, 3318] Generated Node #3: [42, 3318] from Operation: 3400-82=3318 Current State: 79:[42, 3318], Operations: ['50*68=3400', '3400-82=3318'] Exploring Operation: 3318/42=79, Resulting Numbers: [79] 79,79 equal: Goal Reached
4
Current State: 79:[42, 82, 50, 68], Operations: [] Exploring Operation: 42+68=110, Resulting Numbers: [82, 50, 110] Generated Node #0,0: 79:[82, 50, 110] Operation: 42+68=110 Exploring Operation: 42+50=92, Resulting Numbers: [82, 68, 92] Generated Node #0,1: 79:[82, 68, 92] Operation: 42+50=92 Moving to Node #0,1 Current State: 79:[82, 68, 92], Operations: ['42+50=92'] Exploring Operation: 92-68=24, Resulting Numbers: [82, 24] Generated Node #0,1,0: 79:[82, 24] Operation: 92-68=24 Exploring Operation: 82-68=14, Resulting Numbers: [92, 14] Generated Node #0,1,1: 79:[92, 14] Operation: 82-68=14 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 79:[82, 24], Operations: ['42+50=92', '92-68=24'] Exploring Operation: 82+24=106, Resulting Numbers: [106] 106,79 unequal: No Solution Exploring Operation: 82-24=58, Resulting Numbers: [58] 58,79 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 79:[92, 14], Operations: ['42+50=92', '82-68=14'] Exploring Operation: 92-14=78, Resulting Numbers: [78] 78,79 unequal: No Solution Exploring Operation: 92+14=106, Resulting Numbers: [106] 106,79 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0 Current State: 79:[82, 50, 110], Operations: ['42+68=110'] Exploring Operation: 110-50=60, Resulting Numbers: [82, 60] Generated Node #0,0,0: 79:[82, 60] Operation: 110-50=60 Exploring Operation: 82-50=32, Resulting Numbers: [110, 32] Generated Node #0,0,1: 79:[110, 32] Operation: 82-50=32 Moving to Node #0,0,0 Current State: 79:[82, 60], Operations: ['42+68=110', '110-50=60'] Exploring Operation: 82+60=142, Resulting Numbers: [142] 142,79 unequal: No Solution Exploring Operation: 82-60=22, Resulting Numbers: [22] 22,79 unequal: No Solution Moving to Node #0,0,1 Current State: 79:[110, 32], Operations: ['42+68=110', '82-50=32'] Exploring Operation: 110+32=142, Resulting Numbers: [142] 142,79 unequal: No Solution Exploring Operation: 110-32=78, Resulting Numbers: [78] 78,79 unequal: No Solution No solution found.
0
hs_2
mult_heuristic
[ 15, 2, 23, 82 ]
88
[ "15+2=17", "23+82=105", "105-17=88" ]
Current State: 88:[15, 2, 23, 82], Operations: [] Exploring Operation: 15+2=17, Resulting Numbers: [23, 82, 17] Generated Node #2: [23, 82, 17] from Operation: 15+2=17 Current State: 88:[23, 82, 17], Operations: ['15+2=17'] Exploring Operation: 23+82=105, Resulting Numbers: [17, 105] Generated Node #3: [17, 105] from Operation: 23+82=105 Current State: 88:[17, 105], Operations: ['15+2=17', '23+82=105'] Exploring Operation: 105-17=88, Resulting Numbers: [88] 88,88 equal: Goal Reached
4
Current State: 88:[15, 2, 23, 82], Operations: [] Exploring Operation: 82/2=41, Resulting Numbers: [15, 23, 41] Generated Node #0,0: 88:[15, 23, 41] Operation: 82/2=41 Exploring Operation: 15-2=13, Resulting Numbers: [23, 82, 13] Generated Node #0,1: 88:[23, 82, 13] Operation: 15-2=13 Exploring Operation: 23-15=8, Resulting Numbers: [2, 82, 8] Generated Node #0,2: 88:[2, 82, 8] Operation: 23-15=8 Exploring Operation: 2+82=84, Resulting Numbers: [15, 23, 84] Generated Node #0,3: 88:[15, 23, 84] Operation: 2+82=84 Start Sub Search at level 1: Moving to Node #0,2 Current State: 88:[2, 82, 8], Operations: ['23-15=8'] Exploring Operation: 82+8=90, Resulting Numbers: [2, 90] Generated Node #0,2,0: 88:[2, 90] Operation: 82+8=90 Exploring Operation: 82/2=41, Resulting Numbers: [8, 41] Generated Node #0,2,1: 88:[8, 41] Operation: 82/2=41 Exploring Operation: 8/2=4, Resulting Numbers: [82, 4] Generated Node #0,2,2: 88:[82, 4] Operation: 8/2=4 Exploring Operation: 2+82=84, Resulting Numbers: [8, 84] Generated Node #0,2,3: 88:[8, 84] Operation: 2+82=84 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 88:[2, 90], Operations: ['23-15=8', '82+8=90'] Exploring Operation: 2+90=92, Resulting Numbers: [92] 92,88 unequal: No Solution Exploring Operation: 2*90=180, Resulting Numbers: [180] 180,88 unequal: No Solution Exploring Operation: 90/2=45, Resulting Numbers: [45] 45,88 unequal: No Solution Exploring Operation: 90-2=88, Resulting Numbers: [88] 88,88 equal: Goal Reached Moving to Node #0 Current State: 88:[15, 2, 23, 82], Operations: [] Exploring Operation: 23-15=8, Resulting Numbers: [2, 82, 8] Generated Node #0,2: 88:[2, 82, 8] Operation: 23-15=8 Moving to Node #0,2 Current State: 88:[2, 82, 8], Operations: ['23-15=8'] Exploring Operation: 82+8=90, Resulting Numbers: [2, 90] Generated Node #0,2,0: 88:[2, 90] Operation: 82+8=90 Moving to Node #0,2,0 Current State: 88:[2, 90], Operations: ['23-15=8', '82+8=90'] Exploring Operation: 90-2=88, Resulting Numbers: [88] 88,88 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.986111
hs_4
sum_heuristic
[ 53, 68, 78, 17 ]
46
[ "68-53=15", "78-17=61", "61-15=46" ]
Current State: 46:[53, 68, 78, 17], Operations: [] Exploring Operation: 68-53=15, Resulting Numbers: [78, 17, 15] Generated Node #2: [78, 17, 15] from Operation: 68-53=15 Current State: 46:[78, 17, 15], Operations: ['68-53=15'] Exploring Operation: 78-17=61, Resulting Numbers: [15, 61] Generated Node #3: [15, 61] from Operation: 78-17=61 Current State: 46:[15, 61], Operations: ['68-53=15', '78-17=61'] Exploring Operation: 61-15=46, Resulting Numbers: [46] 46,46 equal: Goal Reached
4
Current State: 46:[53, 68, 78, 17], Operations: [] Exploring Operation: 78-68=10, Resulting Numbers: [53, 17, 10] Generated Node #0,0: 46:[53, 17, 10] Operation: 78-68=10 Exploring Operation: 78-53=25, Resulting Numbers: [68, 17, 25] Generated Node #0,1: 46:[68, 17, 25] Operation: 78-53=25 Start Sub Search at level 1: Moving to Node #0,0 Current State: 46:[53, 17, 10], Operations: ['78-68=10'] Exploring Operation: 53-10=43, Resulting Numbers: [17, 43] Generated Node #0,0,0: 46:[17, 43] Operation: 53-10=43 Exploring Operation: 17+10=27, Resulting Numbers: [53, 27] Generated Node #0,0,1: 46:[53, 27] Operation: 17+10=27 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 46:[17, 43], Operations: ['78-68=10', '53-10=43'] Exploring Operation: 17+43=60, Resulting Numbers: [60] 60,46 unequal: No Solution Exploring Operation: 43-17=26, Resulting Numbers: [26] 26,46 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 46:[53, 27], Operations: ['78-68=10', '17+10=27'] Exploring Operation: 53+27=80, Resulting Numbers: [80] 80,46 unequal: No Solution Exploring Operation: 53-27=26, Resulting Numbers: [26] 26,46 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 46:[68, 17, 25], Operations: ['78-53=25'] Exploring Operation: 68-17=51, Resulting Numbers: [25, 51] Generated Node #0,1,0: 46:[25, 51] Operation: 68-17=51 Exploring Operation: 68/17=4, Resulting Numbers: [25, 4] Generated Node #0,1,1: 46:[25, 4] Operation: 68/17=4 Moving to Node #0,1,1 Current State: 46:[25, 4], Operations: ['78-53=25', '68/17=4'] Exploring Operation: 25-4=21, Resulting Numbers: [21] 21,46 unequal: No Solution Exploring Operation: 25+4=29, Resulting Numbers: [29] 29,46 unequal: No Solution Moving to Node #0,1,0 Current State: 46:[25, 51], Operations: ['78-53=25', '68-17=51'] Exploring Operation: 51-25=26, Resulting Numbers: [26] 26,46 unequal: No Solution Exploring Operation: 25+51=76, Resulting Numbers: [76] 76,46 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
mult_heuristic
[ 82, 50, 36, 5 ]
36
[ "82-36=46", "50/5=10", "46-10=36" ]
Current State: 36:[82, 50, 36, 5], Operations: [] Exploring Operation: 82-36=46, Resulting Numbers: [50, 5, 46] Generated Node #2: [50, 5, 46] from Operation: 82-36=46 Current State: 36:[50, 5, 46], Operations: ['82-36=46'] Exploring Operation: 50/5=10, Resulting Numbers: [46, 10] Generated Node #3: [46, 10] from Operation: 50/5=10 Current State: 36:[46, 10], Operations: ['82-36=46', '50/5=10'] Exploring Operation: 46-10=36, Resulting Numbers: [36] 36,36 equal: Goal Reached
4
Current State: 36:[82, 50, 36, 5], Operations: [] Exploring Operation: 82-36=46, Resulting Numbers: [50, 5, 46] Generated Node #0,0: 36:[50, 5, 46] Operation: 82-36=46 Exploring Operation: 50/5=10, Resulting Numbers: [82, 36, 10] Generated Node #0,1: 36:[82, 36, 10] Operation: 50/5=10 Exploring Operation: 82-50=32, Resulting Numbers: [36, 5, 32] Generated Node #0,2: 36:[36, 5, 32] Operation: 82-50=32 Start Sub Search at level 1: Moving to Node #0,2 Current State: 36:[36, 5, 32], Operations: ['82-50=32'] Exploring Operation: 36+5=41, Resulting Numbers: [32, 41] Generated Node #0,2,0: 36:[32, 41] Operation: 36+5=41 Exploring Operation: 36-32=4, Resulting Numbers: [5, 4] Generated Node #0,2,1: 36:[5, 4] Operation: 36-32=4 Exploring Operation: 5+32=37, Resulting Numbers: [36, 37] Generated Node #0,2,2: 36:[36, 37] Operation: 5+32=37 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 36:[5, 4], Operations: ['82-50=32', '36-32=4'] Exploring Operation: 5+4=9, Resulting Numbers: [9] 9,36 unequal: No Solution Exploring Operation: 5*4=20, Resulting Numbers: [20] 20,36 unequal: No Solution Exploring Operation: 5-4=1, Resulting Numbers: [1] 1,36 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 36:[36, 37], Operations: ['82-50=32', '5+32=37'] Exploring Operation: 37-36=1, Resulting Numbers: [1] 1,36 unequal: No Solution Exploring Operation: 36+37=73, Resulting Numbers: [73] 73,36 unequal: No Solution Exploring Operation: 36*37=1332, Resulting Numbers: [1332] 1332,36 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 36:[32, 41], Operations: ['82-50=32', '36+5=41'] Exploring Operation: 41-32=9, Resulting Numbers: [9] 9,36 unequal: No Solution Exploring Operation: 32+41=73, Resulting Numbers: [73] 73,36 unequal: No Solution Exploring Operation: 32*41=1312, Resulting Numbers: [1312] 1312,36 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 36:[50, 5, 46], Operations: ['82-36=46'] Exploring Operation: 50-46=4, Resulting Numbers: [5, 4] Generated Node #0,0,0: 36:[5, 4] Operation: 50-46=4 Exploring Operation: 50/5=10, Resulting Numbers: [46, 10] Generated Node #0,0,1: 36:[46, 10] Operation: 50/5=10 Exploring Operation: 50-5=45, Resulting Numbers: [46, 45] Generated Node #0,0,2: 36:[46, 45] Operation: 50-5=45 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 36:[5, 4], Operations: ['82-36=46', '50-46=4'] Exploring Operation: 5*4=20, Resulting Numbers: [20] 20,36 unequal: No Solution Exploring Operation: 5+4=9, Resulting Numbers: [9] 9,36 unequal: No Solution Exploring Operation: 5-4=1, Resulting Numbers: [1] 1,36 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 36:[46, 10], Operations: ['82-36=46', '50/5=10'] Exploring Operation: 46-10=36, Resulting Numbers: [36] 36,36 equal: Goal Reached Moving to Node #0 Current State: 36:[82, 50, 36, 5], Operations: [] Exploring Operation: 82-36=46, Resulting Numbers: [50, 5, 46] Generated Node #0,0: 36:[50, 5, 46] Operation: 82-36=46 Moving to Node #0,0 Current State: 36:[50, 5, 46], Operations: ['82-36=46'] Exploring Operation: 50/5=10, Resulting Numbers: [46, 10] Generated Node #0,0,1: 36:[46, 10] Operation: 50/5=10 Moving to Node #0,0,1 Current State: 36:[46, 10], Operations: ['82-36=46', '50/5=10'] Exploring Operation: 46-10=36, Resulting Numbers: [36] 36,36 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.977431
hs_3
mult_heuristic
[ 28, 84, 58, 89 ]
85
[ "84/28=3", "58*3=174", "174-89=85" ]
Current State: 85:[28, 84, 58, 89], Operations: [] Exploring Operation: 84/28=3, Resulting Numbers: [58, 89, 3] Generated Node #2: [58, 89, 3] from Operation: 84/28=3 Current State: 85:[58, 89, 3], Operations: ['84/28=3'] Exploring Operation: 58*3=174, Resulting Numbers: [89, 174] Generated Node #3: [89, 174] from Operation: 58*3=174 Current State: 85:[89, 174], Operations: ['84/28=3', '58*3=174'] Exploring Operation: 174-89=85, Resulting Numbers: [85] 85,85 equal: Goal Reached
4
Current State: 85:[28, 84, 58, 89], Operations: [] Exploring Operation: 84-58=26, Resulting Numbers: [28, 89, 26] Generated Node #0,0: 85:[28, 89, 26] Operation: 84-58=26 Exploring Operation: 84/28=3, Resulting Numbers: [58, 89, 3] Generated Node #0,1: 85:[58, 89, 3] Operation: 84/28=3 Exploring Operation: 28+58=86, Resulting Numbers: [84, 89, 86] Generated Node #0,2: 85:[84, 89, 86] Operation: 28+58=86 Exploring Operation: 89-58=31, Resulting Numbers: [28, 84, 31] Generated Node #0,3: 85:[28, 84, 31] Operation: 89-58=31 Exploring Operation: 58-28=30, Resulting Numbers: [84, 89, 30] Generated Node #0,4: 85:[84, 89, 30] Operation: 58-28=30 Start Sub Search at level 1: Moving to Node #0,2 Current State: 85:[84, 89, 86], Operations: ['28+58=86'] Exploring Operation: 86-84=2, Resulting Numbers: [89, 2] Generated Node #0,2,0: 85:[89, 2] Operation: 86-84=2 Exploring Operation: 84+89=173, Resulting Numbers: [86, 173] Generated Node #0,2,1: 85:[86, 173] Operation: 84+89=173 Exploring Operation: 89-84=5, Resulting Numbers: [86, 5] Generated Node #0,2,2: 85:[86, 5] Operation: 89-84=5 Exploring Operation: 84+86=170, Resulting Numbers: [89, 170] Generated Node #0,2,3: 85:[89, 170] Operation: 84+86=170 Exploring Operation: 89-86=3, Resulting Numbers: [84, 3] Generated Node #0,2,4: 85:[84, 3] Operation: 89-86=3 Moving to Node #0,2,2 Current State: 85:[86, 5], Operations: ['28+58=86', '89-84=5'] Exploring Operation: 86-5=81, Resulting Numbers: [81] 81,85 unequal: No Solution Exploring Operation: 86*5=430, Resulting Numbers: [430] 430,85 unequal: No Solution Exploring Operation: 86+5=91, Resulting Numbers: [91] 91,85 unequal: No Solution Moving to Node #0,2,4 Current State: 85:[84, 3], Operations: ['28+58=86', '89-86=3'] Exploring Operation: 84-3=81, Resulting Numbers: [81] 81,85 unequal: No Solution Exploring Operation: 84/3=28, Resulting Numbers: [28] 28,85 unequal: No Solution Exploring Operation: 84*3=252, Resulting Numbers: [252] 252,85 unequal: No Solution Exploring Operation: 84+3=87, Resulting Numbers: [87] 87,85 unequal: No Solution Moving to Node #0,2,0 Current State: 85:[89, 2], Operations: ['28+58=86', '86-84=2'] Exploring Operation: 89-2=87, Resulting Numbers: [87] 87,85 unequal: No Solution Exploring Operation: 89+2=91, Resulting Numbers: [91] 91,85 unequal: No Solution Exploring Operation: 89*2=178, Resulting Numbers: [178] 178,85 unequal: No Solution Moving to Node #0,2,1 Current State: 85:[86, 173], Operations: ['28+58=86', '84+89=173'] Exploring Operation: 86*173=14878, Resulting Numbers: [14878] 14878,85 unequal: No Solution Exploring Operation: 86+173=259, Resulting Numbers: [259] 259,85 unequal: No Solution Exploring Operation: 173-86=87, Resulting Numbers: [87] 87,85 unequal: No Solution Moving to Node #0,2,3 Current State: 85:[89, 170], Operations: ['28+58=86', '84+86=170'] Exploring Operation: 89*170=15130, Resulting Numbers: [15130] 15130,85 unequal: No Solution Exploring Operation: 89+170=259, Resulting Numbers: [259] 259,85 unequal: No Solution Exploring Operation: 170-89=81, Resulting Numbers: [81] 81,85 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4 Current State: 85:[84, 89, 30], Operations: ['58-28=30'] Exploring Operation: 84+30=114, Resulting Numbers: [89, 114] Generated Node #0,4,0: 85:[89, 114] Operation: 84+30=114 Exploring Operation: 84-30=54, Resulting Numbers: [89, 54] Generated Node #0,4,1: 85:[89, 54] Operation: 84-30=54 Exploring Operation: 89-84=5, Resulting Numbers: [30, 5] Generated Node #0,4,2: 85:[30, 5] Operation: 89-84=5 Exploring Operation: 89+30=119, Resulting Numbers: [84, 119] Generated Node #0,4,3: 85:[84, 119] Operation: 89+30=119 Exploring Operation: 89-30=59, Resulting Numbers: [84, 59] Generated Node #0,4,4: 85:[84, 59] Operation: 89-30=59 Moving to Node #0,4,2 Current State: 85:[30, 5], Operations: ['58-28=30', '89-84=5'] Exploring Operation: 30/5=6, Resulting Numbers: [6] 6,85 unequal: No Solution Exploring Operation: 30-5=25, Resulting Numbers: [25] 25,85 unequal: No Solution Exploring Operation: 30+5=35, Resulting Numbers: [35] 35,85 unequal: No Solution Exploring Operation: 30*5=150, Resulting Numbers: [150] 150,85 unequal: No Solution Moving to Node #0,4,4 Current State: 85:[84, 59], Operations: ['58-28=30', '89-30=59'] Exploring Operation: 84+59=143, Resulting Numbers: [143] 143,85 unequal: No Solution Exploring Operation: 84*59=4956, Resulting Numbers: [4956] 4956,85 unequal: No Solution Exploring Operation: 84-59=25, Resulting Numbers: [25] 25,85 unequal: No Solution Moving to Node #0,4,0 Current State: 85:[89, 114], Operations: ['58-28=30', '84+30=114'] Exploring Operation: 89*114=10146, Resulting Numbers: [10146] 10146,85 unequal: No Solution Exploring Operation: 89+114=203, Resulting Numbers: [203] 203,85 unequal: No Solution Exploring Operation: 114-89=25, Resulting Numbers: [25] 25,85 unequal: No Solution Moving to Node #0,4,1 Current State: 85:[89, 54], Operations: ['58-28=30', '84-30=54'] Exploring Operation: 89*54=4806, Resulting Numbers: [4806] 4806,85 unequal: No Solution Exploring Operation: 89-54=35, Resulting Numbers: [35] 35,85 unequal: No Solution Exploring Operation: 89+54=143, Resulting Numbers: [143] 143,85 unequal: No Solution Moving to Node #0,4,3 Current State: 85:[84, 119], Operations: ['58-28=30', '89+30=119'] Exploring Operation: 119-84=35, Resulting Numbers: [35] 35,85 unequal: No Solution Exploring Operation: 84+119=203, Resulting Numbers: [203] 203,85 unequal: No Solution Exploring Operation: 84*119=9996, Resulting Numbers: [9996] 9996,85 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 85:[28, 89, 26], Operations: ['84-58=26'] Exploring Operation: 89-26=63, Resulting Numbers: [28, 63] Generated Node #0,0,0: 85:[28, 63] Operation: 89-26=63 Exploring Operation: 28+89=117, Resulting Numbers: [26, 117] Generated Node #0,0,1: 85:[26, 117] Operation: 28+89=117 Exploring Operation: 28-26=2, Resulting Numbers: [89, 2] Generated Node #0,0,2: 85:[89, 2] Operation: 28-26=2 Exploring Operation: 89-28=61, Resulting Numbers: [26, 61] Generated Node #0,0,3: 85:[26, 61] Operation: 89-28=61 Exploring Operation: 28+26=54, Resulting Numbers: [89, 54] Generated Node #0,0,4: 85:[89, 54] Operation: 28+26=54 Moving to Node #0,0,2 Current State: 85:[89, 2], Operations: ['84-58=26', '28-26=2'] Exploring Operation: 89*2=178, Resulting Numbers: [178] 178,85 unequal: No Solution Exploring Operation: 89-2=87, Resulting Numbers: [87] 87,85 unequal: No Solution Exploring Operation: 89+2=91, Resulting Numbers: [91] 91,85 unequal: No Solution Moving to Node #0,0,3 Current State: 85:[26, 61], Operations: ['84-58=26', '89-28=61'] Exploring Operation: 26*61=1586, Resulting Numbers: [1586] 1586,85 unequal: No Solution Exploring Operation: 61-26=35, Resulting Numbers: [35] 35,85 unequal: No Solution Exploring Operation: 26+61=87, Resulting Numbers: [87] 87,85 unequal: No Solution Moving to Node #0,0,0 Current State: 85:[28, 63], Operations: ['84-58=26', '89-26=63'] Exploring Operation: 63-28=35, Resulting Numbers: [35] 35,85 unequal: No Solution Exploring Operation: 28+63=91, Resulting Numbers: [91] 91,85 unequal: No Solution Exploring Operation: 28*63=1764, Resulting Numbers: [1764] 1764,85 unequal: No Solution Moving to Node #0,0,4 Current State: 85:[89, 54], Operations: ['84-58=26', '28+26=54'] Exploring Operation: 89+54=143, Resulting Numbers: [143] 143,85 unequal: No Solution Exploring Operation: 89*54=4806, Resulting Numbers: [4806] 4806,85 unequal: No Solution Exploring Operation: 89-54=35, Resulting Numbers: [35] 35,85 unequal: No Solution Moving to Node #0,0,1 Current State: 85:[26, 117], Operations: ['84-58=26', '28+89=117'] Exploring Operation: 26+117=143, Resulting Numbers: [143] 143,85 unequal: No Solution Exploring Operation: 26*117=3042, Resulting Numbers: [3042] 3042,85 unequal: No Solution Exploring Operation: 117-26=91, Resulting Numbers: [91] 91,85 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 85:[28, 84, 31], Operations: ['89-58=31'] Exploring Operation: 28+31=59, Resulting Numbers: [84, 59] Generated Node #0,3,0: 85:[84, 59] Operation: 28+31=59 Exploring Operation: 28+84=112, Resulting Numbers: [31, 112] Generated Node #0,3,1: 85:[31, 112] Operation: 28+84=112 Exploring Operation: 31-28=3, Resulting Numbers: [84, 3] Generated Node #0,3,2: 85:[84, 3] Operation: 31-28=3 Exploring Operation: 84/28=3, Resulting Numbers: [31, 3] Generated Node #0,3,3: 85:[31, 3] Operation: 84/28=3 Exploring Operation: 84+31=115, Resulting Numbers: [28, 115] Generated Node #0,3,4: 85:[28, 115] Operation: 84+31=115 Moving to Node #0,3,2 Current State: 85:[84, 3], Operations: ['89-58=31', '31-28=3'] Exploring Operation: 84-3=81, Resulting Numbers: [81] 81,85 unequal: No Solution Exploring Operation: 84/3=28, Resulting Numbers: [28] 28,85 unequal: No Solution Exploring Operation: 84*3=252, Resulting Numbers: [252] 252,85 unequal: No Solution Exploring Operation: 84+3=87, Resulting Numbers: [87] 87,85 unequal: No Solution Moving to Node #0,3,3 Current State: 85:[31, 3], Operations: ['89-58=31', '84/28=3'] Exploring Operation: 31+3=34, Resulting Numbers: [34] 34,85 unequal: No Solution Exploring Operation: 31-3=28, Resulting Numbers: [28] 28,85 unequal: No Solution Exploring Operation: 31*3=93, Resulting Numbers: [93] 93,85 unequal: No Solution Moving to Node #0,3,0 Current State: 85:[84, 59], Operations: ['89-58=31', '28+31=59'] Exploring Operation: 84*59=4956, Resulting Numbers: [4956] 4956,85 unequal: No Solution Exploring Operation: 84+59=143, Resulting Numbers: [143] 143,85 unequal: No Solution Exploring Operation: 84-59=25, Resulting Numbers: [25] 25,85 unequal: No Solution Moving to Node #0,3,1 Current State: 85:[31, 112], Operations: ['89-58=31', '28+84=112'] Exploring Operation: 112-31=81, Resulting Numbers: [81] 81,85 unequal: No Solution Exploring Operation: 31*112=3472, Resulting Numbers: [3472] 3472,85 unequal: No Solution Exploring Operation: 31+112=143, Resulting Numbers: [143] 143,85 unequal: No Solution Moving to Node #0,3,4 Current State: 85:[28, 115], Operations: ['89-58=31', '84+31=115'] Exploring Operation: 28*115=3220, Resulting Numbers: [3220] 3220,85 unequal: No Solution Exploring Operation: 28+115=143, Resulting Numbers: [143] 143,85 unequal: No Solution Exploring Operation: 115-28=87, Resulting Numbers: [87] 87,85 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 85:[58, 89, 3], Operations: ['84/28=3'] Exploring Operation: 89-3=86, Resulting Numbers: [58, 86] Generated Node #0,1,0: 85:[58, 86] Operation: 89-3=86 Exploring Operation: 58-3=55, Resulting Numbers: [89, 55] Generated Node #0,1,1: 85:[89, 55] Operation: 58-3=55 Exploring Operation: 58+3=61, Resulting Numbers: [89, 61] Generated Node #0,1,2: 85:[89, 61] Operation: 58+3=61 Exploring Operation: 89-58=31, Resulting Numbers: [3, 31] Generated Node #0,1,3: 85:[3, 31] Operation: 89-58=31 Exploring Operation: 89+3=92, Resulting Numbers: [58, 92] Generated Node #0,1,4: 85:[58, 92] Operation: 89+3=92 Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 85:[3, 31], Operations: ['84/28=3', '89-58=31'] Exploring Operation: 3+31=34, Resulting Numbers: [34] 34,85 unequal: No Solution Exploring Operation: 31-3=28, Resulting Numbers: [28] 28,85 unequal: No Solution Exploring Operation: 3*31=93, Resulting Numbers: [93] 93,85 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 85:[58, 86], Operations: ['84/28=3', '89-3=86'] Exploring Operation: 58*86=4988, Resulting Numbers: [4988] 4988,85 unequal: No Solution Exploring Operation: 86-58=28, Resulting Numbers: [28] 28,85 unequal: No Solution Exploring Operation: 58+86=144, Resulting Numbers: [144] 144,85 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 85:[89, 61], Operations: ['84/28=3', '58+3=61'] Exploring Operation: 89+61=150, Resulting Numbers: [150] 150,85 unequal: No Solution Exploring Operation: 89*61=5429, Resulting Numbers: [5429] 5429,85 unequal: No Solution Exploring Operation: 89-61=28, Resulting Numbers: [28] 28,85 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 85:[89, 55], Operations: ['84/28=3', '58-3=55'] Exploring Operation: 89*55=4895, Resulting Numbers: [4895] 4895,85 unequal: No Solution Exploring Operation: 89+55=144, Resulting Numbers: [144] 144,85 unequal: No Solution Exploring Operation: 89-55=34, Resulting Numbers: [34] 34,85 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,4 Current State: 85:[58, 92], Operations: ['84/28=3', '89+3=92'] Exploring Operation: 92-58=34, Resulting Numbers: [34] 34,85 unequal: No Solution Exploring Operation: 58+92=150, Resulting Numbers: [150] 150,85 unequal: No Solution Exploring Operation: 58*92=5336, Resulting Numbers: [5336] 5336,85 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_5
sum_heuristic
[ 2, 67, 31, 19 ]
34
[ "67-31=36", "36-19=17", "2*17=34" ]
Current State: 34:[2, 67, 31, 19], Operations: [] Exploring Operation: 67-31=36, Resulting Numbers: [2, 19, 36] Generated Node #2: [2, 19, 36] from Operation: 67-31=36 Current State: 34:[2, 19, 36], Operations: ['67-31=36'] Exploring Operation: 36-19=17, Resulting Numbers: [2, 17] Generated Node #3: [2, 17] from Operation: 36-19=17 Current State: 34:[2, 17], Operations: ['67-31=36', '36-19=17'] Exploring Operation: 2*17=34, Resulting Numbers: [34] 34,34 equal: Goal Reached
4
Current State: 34:[2, 67, 31, 19], Operations: [] Exploring Operation: 67-31=36, Resulting Numbers: [2, 19, 36] Generated Node #0,0: 34:[2, 19, 36] Operation: 67-31=36 Exploring Operation: 67-2=65, Resulting Numbers: [31, 19, 65] Generated Node #0,1: 34:[31, 19, 65] Operation: 67-2=65 Exploring Operation: 67-19=48, Resulting Numbers: [2, 31, 48] Generated Node #0,2: 34:[2, 31, 48] Operation: 67-19=48 Moving to Node #0,0 Current State: 34:[2, 19, 36], Operations: ['67-31=36'] Exploring Operation: 19-2=17, Resulting Numbers: [36, 17] Generated Node #0,0,0: 34:[36, 17] Operation: 19-2=17 Exploring Operation: 36-19=17, Resulting Numbers: [2, 17] Generated Node #0,0,1: 34:[2, 17] Operation: 36-19=17 Exploring Operation: 36-2=34, Resulting Numbers: [19, 34] Generated Node #0,0,2: 34:[19, 34] Operation: 36-2=34 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 34:[2, 17], Operations: ['67-31=36', '36-19=17'] Exploring Operation: 2+17=19, Resulting Numbers: [19] 19,34 unequal: No Solution Exploring Operation: 17-2=15, Resulting Numbers: [15] 15,34 unequal: No Solution Exploring Operation: 2*17=34, Resulting Numbers: [34] 34,34 equal: Goal Reached Moving to Node #0 Current State: 34:[2, 67, 31, 19], Operations: [] Exploring Operation: 67-31=36, Resulting Numbers: [2, 19, 36] Generated Node #0,0: 34:[2, 19, 36] Operation: 67-31=36 Moving to Node #0,0 Current State: 34:[2, 19, 36], Operations: ['67-31=36'] Exploring Operation: 36-19=17, Resulting Numbers: [2, 17] Generated Node #0,0,1: 34:[2, 17] Operation: 36-19=17 Moving to Node #0,0,1 Current State: 34:[2, 17], Operations: ['67-31=36', '36-19=17'] Exploring Operation: 2*17=34, Resulting Numbers: [34] 34,34 equal: Goal Reached Exit Sub Search at level 1
0.988715
hs_3
sum_heuristic
[ 16, 20, 34, 31 ]
76
[ "16*34=544", "20*31=620", "620-544=76" ]
Current State: 76:[16, 20, 34, 31], Operations: [] Exploring Operation: 16*34=544, Resulting Numbers: [20, 31, 544] Generated Node #2: [20, 31, 544] from Operation: 16*34=544 Current State: 76:[20, 31, 544], Operations: ['16*34=544'] Exploring Operation: 20*31=620, Resulting Numbers: [544, 620] Generated Node #3: [544, 620] from Operation: 20*31=620 Current State: 76:[544, 620], Operations: ['16*34=544', '20*31=620'] Exploring Operation: 620-544=76, Resulting Numbers: [76] 76,76 equal: Goal Reached
4
Current State: 76:[16, 20, 34, 31], Operations: [] Exploring Operation: 31-16=15, Resulting Numbers: [20, 34, 15] Generated Node #0,0: 76:[20, 34, 15] Operation: 31-16=15 Exploring Operation: 34-16=18, Resulting Numbers: [20, 31, 18] Generated Node #0,1: 76:[20, 31, 18] Operation: 34-16=18 Exploring Operation: 20-16=4, Resulting Numbers: [34, 31, 4] Generated Node #0,2: 76:[34, 31, 4] Operation: 20-16=4 Exploring Operation: 34-31=3, Resulting Numbers: [16, 20, 3] Generated Node #0,3: 76:[16, 20, 3] Operation: 34-31=3 Start Sub Search at level 1: Moving to Node #0,3 Current State: 76:[16, 20, 3], Operations: ['34-31=3'] Exploring Operation: 16+20=36, Resulting Numbers: [3, 36] Generated Node #0,3,0: 76:[3, 36] Operation: 16+20=36 Exploring Operation: 16+3=19, Resulting Numbers: [20, 19] Generated Node #0,3,1: 76:[20, 19] Operation: 16+3=19 Exploring Operation: 20-16=4, Resulting Numbers: [3, 4] Generated Node #0,3,2: 76:[3, 4] Operation: 20-16=4 Exploring Operation: 20-3=17, Resulting Numbers: [16, 17] Generated Node #0,3,3: 76:[16, 17] Operation: 20-3=17 Moving to Node #0,3,1 Current State: 76:[20, 19], Operations: ['34-31=3', '16+3=19'] Exploring Operation: 20*19=380, Resulting Numbers: [380] 380,76 unequal: No Solution Exploring Operation: 20-19=1, Resulting Numbers: [1] 1,76 unequal: No Solution Exploring Operation: 20+19=39, Resulting Numbers: [39] 39,76 unequal: No Solution Moving to Node #0,3,2 Current State: 76:[3, 4], Operations: ['34-31=3', '20-16=4'] Exploring Operation: 3*4=12, Resulting Numbers: [12] 12,76 unequal: No Solution Exploring Operation: 4-3=1, Resulting Numbers: [1] 1,76 unequal: No Solution Exploring Operation: 3+4=7, Resulting Numbers: [7] 7,76 unequal: No Solution Moving to Node #0,3,0 Current State: 76:[3, 36], Operations: ['34-31=3', '16+20=36'] Exploring Operation: 36/3=12, Resulting Numbers: [12] 12,76 unequal: No Solution Exploring Operation: 3+36=39, Resulting Numbers: [39] 39,76 unequal: No Solution Exploring Operation: 3*36=108, Resulting Numbers: [108] 108,76 unequal: No Solution Exploring Operation: 36-3=33, Resulting Numbers: [33] 33,76 unequal: No Solution Moving to Node #0,3,3 Current State: 76:[16, 17], Operations: ['34-31=3', '20-3=17'] Exploring Operation: 16+17=33, Resulting Numbers: [33] 33,76 unequal: No Solution Exploring Operation: 17-16=1, Resulting Numbers: [1] 1,76 unequal: No Solution Exploring Operation: 16*17=272, Resulting Numbers: [272] 272,76 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 76:[20, 34, 15], Operations: ['31-16=15'] Exploring Operation: 34-20=14, Resulting Numbers: [15, 14] Generated Node #0,0,0: 76:[15, 14] Operation: 34-20=14 Exploring Operation: 34-15=19, Resulting Numbers: [20, 19] Generated Node #0,0,1: 76:[20, 19] Operation: 34-15=19 Exploring Operation: 20+15=35, Resulting Numbers: [34, 35] Generated Node #0,0,2: 76:[34, 35] Operation: 20+15=35 Exploring Operation: 20-15=5, Resulting Numbers: [34, 5] Generated Node #0,0,3: 76:[34, 5] Operation: 20-15=5 Moving to Node #0,0,1 Current State: 76:[20, 19], Operations: ['31-16=15', '34-15=19'] Exploring Operation: 20*19=380, Resulting Numbers: [380] 380,76 unequal: No Solution Exploring Operation: 20-19=1, Resulting Numbers: [1] 1,76 unequal: No Solution Exploring Operation: 20+19=39, Resulting Numbers: [39] 39,76 unequal: No Solution Moving to Node #0,0,3 Current State: 76:[34, 5], Operations: ['31-16=15', '20-15=5'] Exploring Operation: 34*5=170, Resulting Numbers: [170] 170,76 unequal: No Solution Exploring Operation: 34+5=39, Resulting Numbers: [39] 39,76 unequal: No Solution Exploring Operation: 34-5=29, Resulting Numbers: [29] 29,76 unequal: No Solution Moving to Node #0,0,2 Current State: 76:[34, 35], Operations: ['31-16=15', '20+15=35'] Exploring Operation: 34*35=1190, Resulting Numbers: [1190] 1190,76 unequal: No Solution Exploring Operation: 34+35=69, Resulting Numbers: [69] 69,76 unequal: No Solution Exploring Operation: 35-34=1, Resulting Numbers: [1] 1,76 unequal: No Solution Moving to Node #0,0,0 Current State: 76:[15, 14], Operations: ['31-16=15', '34-20=14'] Exploring Operation: 15-14=1, Resulting Numbers: [1] 1,76 unequal: No Solution Exploring Operation: 15*14=210, Resulting Numbers: [210] 210,76 unequal: No Solution Exploring Operation: 15+14=29, Resulting Numbers: [29] 29,76 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 76:[20, 31, 18], Operations: ['34-16=18'] Exploring Operation: 31-18=13, Resulting Numbers: [20, 13] Generated Node #0,1,0: 76:[20, 13] Operation: 31-18=13 Exploring Operation: 31-20=11, Resulting Numbers: [18, 11] Generated Node #0,1,1: 76:[18, 11] Operation: 31-20=11 Exploring Operation: 20-18=2, Resulting Numbers: [31, 2] Generated Node #0,1,2: 76:[31, 2] Operation: 20-18=2 Exploring Operation: 20+18=38, Resulting Numbers: [31, 38] Generated Node #0,1,3: 76:[31, 38] Operation: 20+18=38 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 76:[20, 13], Operations: ['34-16=18', '31-18=13'] Exploring Operation: 20-13=7, Resulting Numbers: [7] 7,76 unequal: No Solution Exploring Operation: 20+13=33, Resulting Numbers: [33] 33,76 unequal: No Solution Exploring Operation: 20*13=260, Resulting Numbers: [260] 260,76 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 76:[31, 2], Operations: ['34-16=18', '20-18=2'] Exploring Operation: 31+2=33, Resulting Numbers: [33] 33,76 unequal: No Solution Exploring Operation: 31*2=62, Resulting Numbers: [62] 62,76 unequal: No Solution Exploring Operation: 31-2=29, Resulting Numbers: [29] 29,76 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 76:[31, 38], Operations: ['34-16=18', '20+18=38'] Exploring Operation: 31*38=1178, Resulting Numbers: [1178] 1178,76 unequal: No Solution Exploring Operation: 38-31=7, Resulting Numbers: [7] 7,76 unequal: No Solution Exploring Operation: 31+38=69, Resulting Numbers: [69] 69,76 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 76:[18, 11], Operations: ['34-16=18', '31-20=11'] Exploring Operation: 18-11=7, Resulting Numbers: [7] 7,76 unequal: No Solution Exploring Operation: 18+11=29, Resulting Numbers: [29] 29,76 unequal: No Solution Exploring Operation: 18*11=198, Resulting Numbers: [198] 198,76 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 76:[34, 31, 4], Operations: ['20-16=4'] Exploring Operation: 31+4=35, Resulting Numbers: [34, 35] Generated Node #0,2,0: 76:[34, 35] Operation: 31+4=35 Exploring Operation: 34-31=3, Resulting Numbers: [4, 3] Generated Node #0,2,1: 76:[4, 3] Operation: 34-31=3 Exploring Operation: 34+4=38, Resulting Numbers: [31, 38] Generated Node #0,2,2: 76:[31, 38] Operation: 34+4=38 Exploring Operation: 34+31=65, Resulting Numbers: [4, 65] Generated Node #0,2,3: 76:[4, 65] Operation: 34+31=65 Moving to Node #0,2,1 Current State: 76:[4, 3], Operations: ['20-16=4', '34-31=3'] Exploring Operation: 4*3=12, Resulting Numbers: [12] 12,76 unequal: No Solution Exploring Operation: 4-3=1, Resulting Numbers: [1] 1,76 unequal: No Solution Exploring Operation: 4+3=7, Resulting Numbers: [7] 7,76 unequal: No Solution Moving to Node #0,2,2 Current State: 76:[31, 38], Operations: ['20-16=4', '34+4=38'] Exploring Operation: 31+38=69, Resulting Numbers: [69] 69,76 unequal: No Solution Exploring Operation: 31*38=1178, Resulting Numbers: [1178] 1178,76 unequal: No Solution Exploring Operation: 38-31=7, Resulting Numbers: [7] 7,76 unequal: No Solution Moving to Node #0,2,0 Current State: 76:[34, 35], Operations: ['20-16=4', '31+4=35'] Exploring Operation: 34+35=69, Resulting Numbers: [69] 69,76 unequal: No Solution Exploring Operation: 34*35=1190, Resulting Numbers: [1190] 1190,76 unequal: No Solution Exploring Operation: 35-34=1, Resulting Numbers: [1] 1,76 unequal: No Solution Moving to Node #0,2,3 Current State: 76:[4, 65], Operations: ['20-16=4', '34+31=65'] Exploring Operation: 65-4=61, Resulting Numbers: [61] 61,76 unequal: No Solution Exploring Operation: 4*65=260, Resulting Numbers: [260] 260,76 unequal: No Solution Exploring Operation: 4+65=69, Resulting Numbers: [69] 69,76 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_4
mult_heuristic
[ 68, 22, 75, 15 ]
41
[ "68-22=46", "75/15=5", "46-5=41" ]
Current State: 41:[68, 22, 75, 15], Operations: [] Exploring Operation: 68-22=46, Resulting Numbers: [75, 15, 46] Generated Node #2: [75, 15, 46] from Operation: 68-22=46 Current State: 41:[75, 15, 46], Operations: ['68-22=46'] Exploring Operation: 75/15=5, Resulting Numbers: [46, 5] Generated Node #3: [46, 5] from Operation: 75/15=5 Current State: 41:[46, 5], Operations: ['68-22=46', '75/15=5'] Exploring Operation: 46-5=41, Resulting Numbers: [41] 41,41 equal: Goal Reached
4
Current State: 41:[68, 22, 75, 15], Operations: [] Exploring Operation: 68-22=46, Resulting Numbers: [75, 15, 46] Generated Node #0,0: 41:[75, 15, 46] Operation: 68-22=46 Exploring Operation: 68-15=53, Resulting Numbers: [22, 75, 53] Generated Node #0,1: 41:[22, 75, 53] Operation: 68-15=53 Exploring Operation: 75-22=53, Resulting Numbers: [68, 15, 53] Generated Node #0,2: 41:[68, 15, 53] Operation: 75-22=53 Exploring Operation: 75-15=60, Resulting Numbers: [68, 22, 60] Generated Node #0,3: 41:[68, 22, 60] Operation: 75-15=60 Exploring Operation: 22+15=37, Resulting Numbers: [68, 75, 37] Generated Node #0,4: 41:[68, 75, 37] Operation: 22+15=37 Start Sub Search at level 1: Moving to Node #0,0 Current State: 41:[75, 15, 46], Operations: ['68-22=46'] Exploring Operation: 75-15=60, Resulting Numbers: [46, 60] Generated Node #0,0,0: 41:[46, 60] Operation: 75-15=60 Exploring Operation: 75+15=90, Resulting Numbers: [46, 90] Generated Node #0,0,1: 41:[46, 90] Operation: 75+15=90 Exploring Operation: 75/15=5, Resulting Numbers: [46, 5] Generated Node #0,0,2: 41:[46, 5] Operation: 75/15=5 Exploring Operation: 46-15=31, Resulting Numbers: [75, 31] Generated Node #0,0,3: 41:[75, 31] Operation: 46-15=31 Exploring Operation: 75-46=29, Resulting Numbers: [15, 29] Generated Node #0,0,4: 41:[15, 29] Operation: 75-46=29 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 41:[46, 60], Operations: ['68-22=46', '75-15=60'] Exploring Operation: 46*60=2760, Resulting Numbers: [2760] 2760,41 unequal: No Solution Exploring Operation: 46+60=106, Resulting Numbers: [106] 106,41 unequal: No Solution Exploring Operation: 60-46=14, Resulting Numbers: [14] 14,41 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,4 Current State: 41:[15, 29], Operations: ['68-22=46', '75-46=29'] Exploring Operation: 15+29=44, Resulting Numbers: [44] 44,41 unequal: No Solution Exploring Operation: 15*29=435, Resulting Numbers: [435] 435,41 unequal: No Solution Exploring Operation: 29-15=14, Resulting Numbers: [14] 14,41 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 41:[46, 5], Operations: ['68-22=46', '75/15=5'] Exploring Operation: 46*5=230, Resulting Numbers: [230] 230,41 unequal: No Solution Exploring Operation: 46-5=41, Resulting Numbers: [41] 41,41 equal: Goal Reached Moving to Node #0 Current State: 41:[68, 22, 75, 15], Operations: [] Exploring Operation: 68-22=46, Resulting Numbers: [75, 15, 46] Generated Node #0,0: 41:[75, 15, 46] Operation: 68-22=46 Moving to Node #0,0 Current State: 41:[75, 15, 46], Operations: ['68-22=46'] Exploring Operation: 75/15=5, Resulting Numbers: [46, 5] Generated Node #0,0,2: 41:[46, 5] Operation: 75/15=5 Moving to Node #0,0,2 Current State: 41:[46, 5], Operations: ['68-22=46', '75/15=5'] Exploring Operation: 46-5=41, Resulting Numbers: [41] 41,41 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.980903
hs_5
mult_heuristic