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
[ 53, 82, 18, 65 ]
54
[ "82-53=29", "18+65=83", "83-29=54" ]
Current State: 54:[53, 82, 18, 65], Operations: [] Exploring Operation: 82-53=29, Resulting Numbers: [18, 65, 29] Generated Node #2: [18, 65, 29] from Operation: 82-53=29 Current State: 54:[18, 65, 29], Operations: ['82-53=29'] Exploring Operation: 18+65=83, Resulting Numbers: [29, 83] Generated Node #3: [29, 83] from Operation: 18+65=83 Current State: 54:[29, 83], Operations: ['82-53=29', '18+65=83'] Exploring Operation: 83-29=54, Resulting Numbers: [54] 54,54 equal: Goal Reached
4
Current State: 54:[53, 82, 18, 65], Operations: [] Exploring Operation: 82-65=17, Resulting Numbers: [53, 18, 17] Generated Node #0,0: 54:[53, 18, 17] Operation: 82-65=17 Start Sub Search at level 1: Moving to Node #0,0 Current State: 54:[53, 18, 17], Operations: ['82-65=17'] Exploring Operation: 18-17=1, Resulting Numbers: [53, 1] Generated Node #0,0,0: 54:[53, 1] Operation: 18-17=1 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 54:[53, 1], Operations: ['82-65=17', '18-17=1'] Exploring Operation: 53+1=54, Resulting Numbers: [54] 54,54 equal: Goal Reached Moving to Node #0 Current State: 54:[53, 82, 18, 65], Operations: [] Exploring Operation: 82-65=17, Resulting Numbers: [53, 18, 17] Generated Node #0,0: 54:[53, 18, 17] Operation: 82-65=17 Moving to Node #0,0 Current State: 54:[53, 18, 17], Operations: ['82-65=17'] Exploring Operation: 18-17=1, Resulting Numbers: [53, 1] Generated Node #0,0,0: 54:[53, 1] Operation: 18-17=1 Moving to Node #0,0,0 Current State: 54:[53, 1], Operations: ['82-65=17', '18-17=1'] Exploring Operation: 53+1=54, Resulting Numbers: [54] 54,54 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.993924
hs_1
mult_heuristic
[ 85, 26, 37, 88 ]
93
[ "37-26=11", "88/11=8", "85+8=93" ]
Current State: 93:[85, 26, 37, 88], Operations: [] Exploring Operation: 37-26=11, Resulting Numbers: [85, 88, 11] Generated Node #2: [85, 88, 11] from Operation: 37-26=11 Current State: 93:[85, 88, 11], Operations: ['37-26=11'] Exploring Operation: 88/11=8, Resulting Numbers: [85, 8] Generated Node #3: [85, 8] from Operation: 88/11=8 Current State: 93:[85, 8], Operations: ['37-26=11', '88/11=8'] Exploring Operation: 85+8=93, Resulting Numbers: [93] 93,93 equal: Goal Reached
4
Current State: 93:[85, 26, 37, 88], Operations: [] Exploring Operation: 88-85=3, Resulting Numbers: [26, 37, 3] Generated Node #0,0: 93:[26, 37, 3] Operation: 88-85=3 Exploring Operation: 37-26=11, Resulting Numbers: [85, 88, 11] Generated Node #0,1: 93:[85, 88, 11] Operation: 37-26=11 Start Sub Search at level 1: Moving to Node #0,0 Current State: 93:[26, 37, 3], Operations: ['88-85=3'] Exploring Operation: 37-26=11, Resulting Numbers: [3, 11] Generated Node #0,0,0: 93:[3, 11] Operation: 37-26=11 Exploring Operation: 26+3=29, Resulting Numbers: [37, 29] Generated Node #0,0,1: 93:[37, 29] Operation: 26+3=29 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 93:[3, 11], Operations: ['88-85=3', '37-26=11'] Exploring Operation: 3*11=33, Resulting Numbers: [33] 33,93 unequal: No Solution Exploring Operation: 11-3=8, Resulting Numbers: [8] 8,93 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: 93:[37, 29], Operations: ['88-85=3', '26+3=29'] Exploring Operation: 37-29=8, Resulting Numbers: [8] 8,93 unequal: No Solution Exploring Operation: 37+29=66, Resulting Numbers: [66] 66,93 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: 93:[85, 88, 11], Operations: ['37-26=11'] Exploring Operation: 88-85=3, Resulting Numbers: [11, 3] Generated Node #0,1,0: 93:[11, 3] Operation: 88-85=3 Exploring Operation: 85+11=96, Resulting Numbers: [88, 96] Generated Node #0,1,1: 93:[88, 96] Operation: 85+11=96 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 93:[11, 3], Operations: ['37-26=11', '88-85=3'] Exploring Operation: 11*3=33, Resulting Numbers: [33] 33,93 unequal: No Solution Exploring Operation: 11-3=8, Resulting Numbers: [8] 8,93 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: 93:[88, 96], Operations: ['37-26=11', '85+11=96'] Exploring Operation: 96-88=8, Resulting Numbers: [8] 8,93 unequal: No Solution Exploring Operation: 88+96=184, Resulting Numbers: [184] 184,93 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
[ 88, 24, 22, 99 ]
26
[ "99-88=11", "22/11=2", "24+2=26" ]
Current State: 26:[88, 24, 22, 99], Operations: [] Exploring Operation: 99-88=11, Resulting Numbers: [24, 22, 11] Generated Node #2: [24, 22, 11] from Operation: 99-88=11 Current State: 26:[24, 22, 11], Operations: ['99-88=11'] Exploring Operation: 22/11=2, Resulting Numbers: [24, 2] Generated Node #3: [24, 2] from Operation: 22/11=2 Current State: 26:[24, 2], Operations: ['99-88=11', '22/11=2'] Exploring Operation: 24+2=26, Resulting Numbers: [26] 26,26 equal: Goal Reached
4
Current State: 26:[88, 24, 22, 99], Operations: [] Exploring Operation: 88-24=64, Resulting Numbers: [22, 99, 64] Generated Node #0,0: 26:[22, 99, 64] Operation: 88-24=64 Exploring Operation: 99-88=11, Resulting Numbers: [24, 22, 11] Generated Node #0,1: 26:[24, 22, 11] Operation: 99-88=11 Exploring Operation: 88-22=66, Resulting Numbers: [24, 99, 66] Generated Node #0,2: 26:[24, 99, 66] Operation: 88-22=66 Exploring Operation: 88/22=4, Resulting Numbers: [24, 99, 4] Generated Node #0,3: 26:[24, 99, 4] Operation: 88/22=4 Exploring Operation: 99-24=75, Resulting Numbers: [88, 22, 75] Generated Node #0,4: 26:[88, 22, 75] Operation: 99-24=75 Start Sub Search at level 1: Moving to Node #0,1 Current State: 26:[24, 22, 11], Operations: ['99-88=11'] Exploring Operation: 22/11=2, Resulting Numbers: [24, 2] Generated Node #0,1,0: 26:[24, 2] Operation: 22/11=2 Exploring Operation: 22+11=33, Resulting Numbers: [24, 33] Generated Node #0,1,1: 26:[24, 33] Operation: 22+11=33 Exploring Operation: 22-11=11, Resulting Numbers: [24, 11] Generated Node #0,1,2: 26:[24, 11] Operation: 22-11=11 Exploring Operation: 24-11=13, Resulting Numbers: [22, 13] Generated Node #0,1,3: 26:[22, 13] Operation: 24-11=13 Exploring Operation: 24-22=2, Resulting Numbers: [11, 2] Generated Node #0,1,4: 26:[11, 2] Operation: 24-22=2 Moving to Node #0,1,0 Current State: 26:[24, 2], Operations: ['99-88=11', '22/11=2'] Exploring Operation: 24+2=26, Resulting Numbers: [26] 26,26 equal: Goal Reached Moving to Node #0 Current State: 26:[88, 24, 22, 99], Operations: [] Exploring Operation: 99-88=11, Resulting Numbers: [24, 22, 11] Generated Node #0,1: 26:[24, 22, 11] Operation: 99-88=11 Moving to Node #0,1 Current State: 26:[24, 22, 11], Operations: ['99-88=11'] Exploring Operation: 22/11=2, Resulting Numbers: [24, 2] Generated Node #0,1,0: 26:[24, 2] Operation: 22/11=2 Moving to Node #0,1,0 Current State: 26:[24, 2], Operations: ['99-88=11', '22/11=2'] Exploring Operation: 24+2=26, Resulting Numbers: [26] 26,26 equal: Goal Reached Exit Sub Search at level 1
0.986979
hs_5
mult_heuristic
[ 64, 5, 34, 2 ]
44
[ "64+34=98", "98/2=49", "49-5=44" ]
Current State: 44:[64, 5, 34, 2], Operations: [] Exploring Operation: 64+34=98, Resulting Numbers: [5, 2, 98] Generated Node #2: [5, 2, 98] from Operation: 64+34=98 Current State: 44:[5, 2, 98], Operations: ['64+34=98'] Exploring Operation: 98/2=49, Resulting Numbers: [5, 49] Generated Node #3: [5, 49] from Operation: 98/2=49 Current State: 44:[5, 49], Operations: ['64+34=98', '98/2=49'] Exploring Operation: 49-5=44, Resulting Numbers: [44] 44,44 equal: Goal Reached
4
Current State: 44:[64, 5, 34, 2], Operations: [] Exploring Operation: 64/2=32, Resulting Numbers: [5, 34, 32] Generated Node #0,0: 44:[5, 34, 32] Operation: 64/2=32 Exploring Operation: 64-34=30, Resulting Numbers: [5, 2, 30] Generated Node #0,1: 44:[5, 2, 30] Operation: 64-34=30 Moving to Node #0,1 Current State: 44:[5, 2, 30], Operations: ['64-34=30'] Exploring Operation: 30-5=25, Resulting Numbers: [2, 25] Generated Node #0,1,0: 44:[2, 25] Operation: 30-5=25 Exploring Operation: 30/5=6, Resulting Numbers: [2, 6] Generated Node #0,1,1: 44:[2, 6] Operation: 30/5=6 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 44:[2, 6], Operations: ['64-34=30', '30/5=6'] Exploring Operation: 6-2=4, Resulting Numbers: [4] 4,44 unequal: No Solution Exploring Operation: 2*6=12, Resulting Numbers: [12] 12,44 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: 44:[2, 25], Operations: ['64-34=30', '30-5=25'] Exploring Operation: 25-2=23, Resulting Numbers: [23] 23,44 unequal: No Solution Exploring Operation: 2+25=27, Resulting Numbers: [27] 27,44 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: 44:[5, 34, 32], Operations: ['64/2=32'] Exploring Operation: 5+34=39, Resulting Numbers: [32, 39] Generated Node #0,0,0: 44:[32, 39] Operation: 5+34=39 Exploring Operation: 34-32=2, Resulting Numbers: [5, 2] Generated Node #0,0,1: 44:[5, 2] Operation: 34-32=2 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 44:[5, 2], Operations: ['64/2=32', '34-32=2'] Exploring Operation: 5*2=10, Resulting Numbers: [10] 10,44 unequal: No Solution Exploring Operation: 5-2=3, Resulting Numbers: [3] 3,44 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: 44:[32, 39], Operations: ['64/2=32', '5+34=39'] Exploring Operation: 39-32=7, Resulting Numbers: [7] 7,44 unequal: No Solution Exploring Operation: 32+39=71, Resulting Numbers: [71] 71,44 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
[ 9, 6, 13, 46 ]
56
[ "9-6=3", "13+46=59", "59-3=56" ]
Current State: 56:[9, 6, 13, 46], Operations: [] Exploring Operation: 9-6=3, Resulting Numbers: [13, 46, 3] Generated Node #2: [13, 46, 3] from Operation: 9-6=3 Current State: 56:[13, 46, 3], Operations: ['9-6=3'] Exploring Operation: 13+46=59, Resulting Numbers: [3, 59] Generated Node #3: [3, 59] from Operation: 13+46=59 Current State: 56:[3, 59], Operations: ['9-6=3', '13+46=59'] Exploring Operation: 59-3=56, Resulting Numbers: [56] 56,56 equal: Goal Reached
4
Current State: 56:[9, 6, 13, 46], Operations: [] Exploring Operation: 9+46=55, Resulting Numbers: [6, 13, 55] Generated Node #0,0: 56:[6, 13, 55] Operation: 9+46=55 Start Sub Search at level 1: Moving to Node #0,0 Current State: 56:[6, 13, 55], Operations: ['9+46=55'] Exploring Operation: 13-6=7, Resulting Numbers: [55, 7] Generated Node #0,0,0: 56:[55, 7] Operation: 13-6=7 Moving to Node #0,0,0 Current State: 56:[55, 7], Operations: ['9+46=55', '13-6=7'] Exploring Operation: 55+7=62, Resulting Numbers: [62] 62,56 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
[ 45, 36, 84, 59 ]
42
[ "59-45=14", "84/14=6", "36+6=42" ]
Current State: 42:[45, 36, 84, 59], Operations: [] Exploring Operation: 59-45=14, Resulting Numbers: [36, 84, 14] Generated Node #2: [36, 84, 14] from Operation: 59-45=14 Current State: 42:[36, 84, 14], Operations: ['59-45=14'] Exploring Operation: 84/14=6, Resulting Numbers: [36, 6] Generated Node #3: [36, 6] from Operation: 84/14=6 Current State: 42:[36, 6], Operations: ['59-45=14', '84/14=6'] Exploring Operation: 36+6=42, Resulting Numbers: [42] 42,42 equal: Goal Reached
4
Current State: 42:[45, 36, 84, 59], Operations: [] Exploring Operation: 59-36=23, Resulting Numbers: [45, 84, 23] Generated Node #0,0: 42:[45, 84, 23] Operation: 59-36=23 Exploring Operation: 84-45=39, Resulting Numbers: [36, 59, 39] Generated Node #0,1: 42:[36, 59, 39] Operation: 84-45=39 Exploring Operation: 84-36=48, Resulting Numbers: [45, 59, 48] Generated Node #0,2: 42:[45, 59, 48] Operation: 84-36=48 Exploring Operation: 84-59=25, Resulting Numbers: [45, 36, 25] Generated Node #0,3: 42:[45, 36, 25] Operation: 84-59=25 Moving to Node #0,3 Current State: 42:[45, 36, 25], Operations: ['84-59=25'] Exploring Operation: 36-25=11, Resulting Numbers: [45, 11] Generated Node #0,3,0: 42:[45, 11] Operation: 36-25=11 Exploring Operation: 45-25=20, Resulting Numbers: [36, 20] Generated Node #0,3,1: 42:[36, 20] Operation: 45-25=20 Exploring Operation: 36+25=61, Resulting Numbers: [45, 61] Generated Node #0,3,2: 42:[45, 61] Operation: 36+25=61 Exploring Operation: 45-36=9, Resulting Numbers: [25, 9] Generated Node #0,3,3: 42:[25, 9] Operation: 45-36=9 Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 42:[45, 11], Operations: ['84-59=25', '36-25=11'] Exploring Operation: 45*11=495, Resulting Numbers: [495] 495,42 unequal: No Solution Exploring Operation: 45-11=34, Resulting Numbers: [34] 34,42 unequal: No Solution Exploring Operation: 45+11=56, Resulting Numbers: [56] 56,42 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: 42:[25, 9], Operations: ['84-59=25', '45-36=9'] Exploring Operation: 25*9=225, Resulting Numbers: [225] 225,42 unequal: No Solution Exploring Operation: 25+9=34, Resulting Numbers: [34] 34,42 unequal: No Solution Exploring Operation: 25-9=16, Resulting Numbers: [16] 16,42 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: 42:[36, 20], Operations: ['84-59=25', '45-25=20'] Exploring Operation: 36-20=16, Resulting Numbers: [16] 16,42 unequal: No Solution Exploring Operation: 36+20=56, Resulting Numbers: [56] 56,42 unequal: No Solution Exploring Operation: 36*20=720, Resulting Numbers: [720] 720,42 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: 42:[45, 61], Operations: ['84-59=25', '36+25=61'] Exploring Operation: 45*61=2745, Resulting Numbers: [2745] 2745,42 unequal: No Solution Exploring Operation: 45+61=106, Resulting Numbers: [106] 106,42 unequal: No Solution Exploring Operation: 61-45=16, Resulting Numbers: [16] 16,42 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: 42:[45, 59, 48], Operations: ['84-36=48'] Exploring Operation: 48-45=3, Resulting Numbers: [59, 3] Generated Node #0,2,0: 42:[59, 3] Operation: 48-45=3 Exploring Operation: 59-48=11, Resulting Numbers: [45, 11] Generated Node #0,2,1: 42:[45, 11] Operation: 59-48=11 Exploring Operation: 59-45=14, Resulting Numbers: [48, 14] Generated Node #0,2,2: 42:[48, 14] Operation: 59-45=14 Exploring Operation: 45+59=104, Resulting Numbers: [48, 104] Generated Node #0,2,3: 42:[48, 104] Operation: 45+59=104 Moving to Node #0,1 Current State: 42:[36, 59, 39], Operations: ['84-45=39'] Exploring Operation: 59-39=20, Resulting Numbers: [36, 20] Generated Node #0,1,0: 42:[36, 20] Operation: 59-39=20 Exploring Operation: 36+39=75, Resulting Numbers: [59, 75] Generated Node #0,1,1: 42:[59, 75] Operation: 36+39=75 Exploring Operation: 59-36=23, Resulting Numbers: [39, 23] Generated Node #0,1,2: 42:[39, 23] Operation: 59-36=23 Exploring Operation: 39-36=3, Resulting Numbers: [59, 3] Generated Node #0,1,3: 42:[59, 3] Operation: 39-36=3 Moving to Node #0,0 Current State: 42:[45, 84, 23], Operations: ['59-36=23'] Exploring Operation: 84-45=39, Resulting Numbers: [23, 39] Generated Node #0,0,0: 42:[23, 39] Operation: 84-45=39 Exploring Operation: 45-23=22, Resulting Numbers: [84, 22] Generated Node #0,0,1: 42:[84, 22] Operation: 45-23=22 Exploring Operation: 45+23=68, Resulting Numbers: [84, 68] Generated Node #0,0,2: 42:[84, 68] Operation: 45+23=68 Exploring Operation: 84-23=61, Resulting Numbers: [45, 61] Generated Node #0,0,3: 42:[45, 61] Operation: 84-23=61 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 42:[23, 39], Operations: ['59-36=23', '84-45=39'] Exploring Operation: 23*39=897, Resulting Numbers: [897] 897,42 unequal: No Solution Exploring Operation: 23+39=62, Resulting Numbers: [62] 62,42 unequal: No Solution Exploring Operation: 39-23=16, Resulting Numbers: [16] 16,42 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: 42:[45, 61], Operations: ['59-36=23', '84-23=61'] Exploring Operation: 45*61=2745, Resulting Numbers: [2745] 2745,42 unequal: No Solution Exploring Operation: 61-45=16, Resulting Numbers: [16] 16,42 unequal: No Solution Exploring Operation: 45+61=106, Resulting Numbers: [106] 106,42 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: 42:[84, 22], Operations: ['59-36=23', '45-23=22'] Exploring Operation: 84+22=106, Resulting Numbers: [106] 106,42 unequal: No Solution Exploring Operation: 84*22=1848, Resulting Numbers: [1848] 1848,42 unequal: No Solution Exploring Operation: 84-22=62, Resulting Numbers: [62] 62,42 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: 42:[84, 68], Operations: ['59-36=23', '45+23=68'] Exploring Operation: 84+68=152, Resulting Numbers: [152] 152,42 unequal: No Solution Exploring Operation: 84*68=5712, Resulting Numbers: [5712] 5712,42 unequal: No Solution Exploring Operation: 84-68=16, Resulting Numbers: [16] 16,42 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1,2 Current State: 42:[39, 23], Operations: ['84-45=39', '59-36=23'] Exploring Operation: 39*23=897, Resulting Numbers: [897] 897,42 unequal: No Solution Exploring Operation: 39+23=62, Resulting Numbers: [62] 62,42 unequal: No Solution Exploring Operation: 39-23=16, Resulting Numbers: [16] 16,42 unequal: No Solution Moving to Node #0,2,1 Current State: 42:[45, 11], Operations: ['84-36=48', '59-48=11'] Exploring Operation: 45-11=34, Resulting Numbers: [34] 34,42 unequal: No Solution Exploring Operation: 45*11=495, Resulting Numbers: [495] 495,42 unequal: No Solution Exploring Operation: 45+11=56, Resulting Numbers: [56] 56,42 unequal: No Solution Moving to Node #0,2,2 Current State: 42:[48, 14], Operations: ['84-36=48', '59-45=14'] Exploring Operation: 48-14=34, Resulting Numbers: [34] 34,42 unequal: No Solution Exploring Operation: 48+14=62, Resulting Numbers: [62] 62,42 unequal: No Solution Exploring Operation: 48*14=672, Resulting Numbers: [672] 672,42 unequal: No Solution Moving to Node #0,1,0 Current State: 42:[36, 20], Operations: ['84-45=39', '59-39=20'] Exploring Operation: 36+20=56, Resulting Numbers: [56] 56,42 unequal: No Solution Exploring Operation: 36-20=16, Resulting Numbers: [16] 16,42 unequal: No Solution Exploring Operation: 36*20=720, Resulting Numbers: [720] 720,42 unequal: No Solution Moving to Node #0,2,0 Current State: 42:[59, 3], Operations: ['84-36=48', '48-45=3'] Exploring Operation: 59*3=177, Resulting Numbers: [177] 177,42 unequal: No Solution Exploring Operation: 59-3=56, Resulting Numbers: [56] 56,42 unequal: No Solution Exploring Operation: 59+3=62, Resulting Numbers: [62] 62,42 unequal: No Solution Moving to Node #0,1,3 Current State: 42:[59, 3], Operations: ['84-45=39', '39-36=3'] Exploring Operation: 59*3=177, Resulting Numbers: [177] 177,42 unequal: No Solution Exploring Operation: 59-3=56, Resulting Numbers: [56] 56,42 unequal: No Solution Exploring Operation: 59+3=62, Resulting Numbers: [62] 62,42 unequal: No Solution Moving to Node #0,1,1 Current State: 42:[59, 75], Operations: ['84-45=39', '36+39=75'] Exploring Operation: 59*75=4425, Resulting Numbers: [4425] 4425,42 unequal: No Solution Exploring Operation: 59+75=134, Resulting Numbers: [134] 134,42 unequal: No Solution Exploring Operation: 75-59=16, Resulting Numbers: [16] 16,42 unequal: No Solution Moving to Node #0,2,3 Current State: 42:[48, 104], Operations: ['84-36=48', '45+59=104'] Exploring Operation: 104-48=56, Resulting Numbers: [56] 56,42 unequal: No Solution Exploring Operation: 48+104=152, Resulting Numbers: [152] 152,42 unequal: No Solution Exploring Operation: 48*104=4992, Resulting Numbers: [4992] 4992,42 unequal: No Solution No solution found.
0
hs_4
mult_heuristic
[ 9, 41, 35, 85 ]
82
[ "41-9=32", "85-35=50", "32+50=82" ]
Current State: 82:[9, 41, 35, 85], Operations: [] Exploring Operation: 41-9=32, Resulting Numbers: [35, 85, 32] Generated Node #2: [35, 85, 32] from Operation: 41-9=32 Current State: 82:[35, 85, 32], Operations: ['41-9=32'] Exploring Operation: 85-35=50, Resulting Numbers: [32, 50] Generated Node #3: [32, 50] from Operation: 85-35=50 Current State: 82:[32, 50], Operations: ['41-9=32', '85-35=50'] Exploring Operation: 32+50=82, Resulting Numbers: [82] 82,82 equal: Goal Reached
4
Current State: 82:[9, 41, 35, 85], Operations: [] Exploring Operation: 85-9=76, Resulting Numbers: [41, 35, 76] Generated Node #0,0: 82:[41, 35, 76] Operation: 85-9=76 Exploring Operation: 9+35=44, Resulting Numbers: [41, 85, 44] Generated Node #0,1: 82:[41, 85, 44] Operation: 9+35=44 Moving to Node #0,1 Current State: 82:[41, 85, 44], Operations: ['9+35=44'] Exploring Operation: 44-41=3, Resulting Numbers: [85, 3] Generated Node #0,1,0: 82:[85, 3] Operation: 44-41=3 Exploring Operation: 85-44=41, Resulting Numbers: [41, 41] Generated Node #0,1,1: 82:[41, 41] Operation: 85-44=41 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 82:[41, 41], Operations: ['9+35=44', '85-44=41'] Exploring Operation: 41+41=82, Resulting Numbers: [82] 82,82 equal: Goal Reached Moving to Node #0 Current State: 82:[9, 41, 35, 85], Operations: [] Exploring Operation: 9+35=44, Resulting Numbers: [41, 85, 44] Generated Node #0,1: 82:[41, 85, 44] Operation: 9+35=44 Moving to Node #0,1 Current State: 82:[41, 85, 44], Operations: ['9+35=44'] Exploring Operation: 85-44=41, Resulting Numbers: [41, 41] Generated Node #0,1,1: 82:[41, 41] Operation: 85-44=41 Moving to Node #0,1,1 Current State: 82:[41, 41], Operations: ['9+35=44', '85-44=41'] Exploring Operation: 41+41=82, Resulting Numbers: [82] 82,82 equal: Goal Reached Exit Sub Search at level 1
0.992188
hs_2
sum_heuristic
[ 3, 56, 19, 60 ]
31
[ "60-56=4", "3*4=12", "19+12=31" ]
Current State: 31:[3, 56, 19, 60], Operations: [] Exploring Operation: 60-56=4, Resulting Numbers: [3, 19, 4] Generated Node #2: [3, 19, 4] from Operation: 60-56=4 Current State: 31:[3, 19, 4], Operations: ['60-56=4'] Exploring Operation: 3*4=12, Resulting Numbers: [19, 12] Generated Node #3: [19, 12] from Operation: 3*4=12 Current State: 31:[19, 12], Operations: ['60-56=4', '3*4=12'] Exploring Operation: 19+12=31, Resulting Numbers: [31] 31,31 equal: Goal Reached
4
Current State: 31:[3, 56, 19, 60], Operations: [] Exploring Operation: 3+19=22, Resulting Numbers: [56, 60, 22] Generated Node #0,0: 31:[56, 60, 22] Operation: 3+19=22 Exploring Operation: 60-3=57, Resulting Numbers: [56, 19, 57] Generated Node #0,1: 31:[56, 19, 57] Operation: 60-3=57 Exploring Operation: 56-3=53, Resulting Numbers: [19, 60, 53] Generated Node #0,2: 31:[19, 60, 53] Operation: 56-3=53 Exploring Operation: 60/3=20, Resulting Numbers: [56, 19, 20] Generated Node #0,3: 31:[56, 19, 20] Operation: 60/3=20 Start Sub Search at level 1: Moving to Node #0,3 Current State: 31:[56, 19, 20], Operations: ['60/3=20'] Exploring Operation: 56-19=37, Resulting Numbers: [20, 37] Generated Node #0,3,0: 31:[20, 37] Operation: 56-19=37 Exploring Operation: 56-20=36, Resulting Numbers: [19, 36] Generated Node #0,3,1: 31:[19, 36] Operation: 56-20=36 Exploring Operation: 56+19=75, Resulting Numbers: [20, 75] Generated Node #0,3,2: 31:[20, 75] Operation: 56+19=75 Exploring Operation: 19+20=39, Resulting Numbers: [56, 39] Generated Node #0,3,3: 31:[56, 39] Operation: 19+20=39 Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 31:[20, 37], Operations: ['60/3=20', '56-19=37'] Exploring Operation: 20*37=740, Resulting Numbers: [740] 740,31 unequal: No Solution Exploring Operation: 20+37=57, Resulting Numbers: [57] 57,31 unequal: No Solution Exploring Operation: 37-20=17, Resulting Numbers: [17] 17,31 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: 31:[19, 36], Operations: ['60/3=20', '56-20=36'] Exploring Operation: 19+36=55, Resulting Numbers: [55] 55,31 unequal: No Solution Exploring Operation: 36-19=17, Resulting Numbers: [17] 17,31 unequal: No Solution Exploring Operation: 19*36=684, Resulting Numbers: [684] 684,31 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: 31:[56, 39], Operations: ['60/3=20', '19+20=39'] Exploring Operation: 56-39=17, Resulting Numbers: [17] 17,31 unequal: No Solution Exploring Operation: 56+39=95, Resulting Numbers: [95] 95,31 unequal: No Solution Exploring Operation: 56*39=2184, Resulting Numbers: [2184] 2184,31 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: 31:[20, 75], Operations: ['60/3=20', '56+19=75'] Exploring Operation: 20*75=1500, Resulting Numbers: [1500] 1500,31 unequal: No Solution Exploring Operation: 20+75=95, Resulting Numbers: [95] 95,31 unequal: No Solution Exploring Operation: 75-20=55, Resulting Numbers: [55] 55,31 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: 31:[56, 60, 22], Operations: ['3+19=22'] Exploring Operation: 60-56=4, Resulting Numbers: [22, 4] Generated Node #0,0,0: 31:[22, 4] Operation: 60-56=4 Exploring Operation: 56+22=78, Resulting Numbers: [60, 78] Generated Node #0,0,1: 31:[60, 78] Operation: 56+22=78 Exploring Operation: 56-22=34, Resulting Numbers: [60, 34] Generated Node #0,0,2: 31:[60, 34] Operation: 56-22=34 Exploring Operation: 60-22=38, Resulting Numbers: [56, 38] Generated Node #0,0,3: 31:[56, 38] Operation: 60-22=38 Moving to Node #0,0,2 Current State: 31:[60, 34], Operations: ['3+19=22', '56-22=34'] Exploring Operation: 60-34=26, Resulting Numbers: [26] 26,31 unequal: No Solution Exploring Operation: 60+34=94, Resulting Numbers: [94] 94,31 unequal: No Solution Exploring Operation: 60*34=2040, Resulting Numbers: [2040] 2040,31 unequal: No Solution Moving to Node #0,0,3 Current State: 31:[56, 38], Operations: ['3+19=22', '60-22=38'] Exploring Operation: 56-38=18, Resulting Numbers: [18] 18,31 unequal: No Solution Exploring Operation: 56*38=2128, Resulting Numbers: [2128] 2128,31 unequal: No Solution Exploring Operation: 56+38=94, Resulting Numbers: [94] 94,31 unequal: No Solution Moving to Node #0,0,0 Current State: 31:[22, 4], Operations: ['3+19=22', '60-56=4'] Exploring Operation: 22*4=88, Resulting Numbers: [88] 88,31 unequal: No Solution Exploring Operation: 22-4=18, Resulting Numbers: [18] 18,31 unequal: No Solution Exploring Operation: 22+4=26, Resulting Numbers: [26] 26,31 unequal: No Solution Moving to Node #0,0,1 Current State: 31:[60, 78], Operations: ['3+19=22', '56+22=78'] Exploring Operation: 60*78=4680, Resulting Numbers: [4680] 4680,31 unequal: No Solution Exploring Operation: 78-60=18, Resulting Numbers: [18] 18,31 unequal: No Solution Exploring Operation: 60+78=138, Resulting Numbers: [138] 138,31 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: 31:[56, 19, 57], Operations: ['60-3=57'] Exploring Operation: 57-19=38, Resulting Numbers: [56, 38] Generated Node #0,1,0: 31:[56, 38] Operation: 57-19=38 Exploring Operation: 57/19=3, Resulting Numbers: [56, 3] Generated Node #0,1,1: 31:[56, 3] Operation: 57/19=3 Exploring Operation: 56-19=37, Resulting Numbers: [57, 37] Generated Node #0,1,2: 31:[57, 37] Operation: 56-19=37 Exploring Operation: 57-56=1, Resulting Numbers: [19, 1] Generated Node #0,1,3: 31:[19, 1] Operation: 57-56=1 Moving to Node #0,1,0 Current State: 31:[56, 38], Operations: ['60-3=57', '57-19=38'] Exploring Operation: 56*38=2128, Resulting Numbers: [2128] 2128,31 unequal: No Solution Exploring Operation: 56+38=94, Resulting Numbers: [94] 94,31 unequal: No Solution Exploring Operation: 56-38=18, Resulting Numbers: [18] 18,31 unequal: No Solution Moving to Node #0,1,2 Current State: 31:[57, 37], Operations: ['60-3=57', '56-19=37'] Exploring Operation: 57*37=2109, Resulting Numbers: [2109] 2109,31 unequal: No Solution Exploring Operation: 57+37=94, Resulting Numbers: [94] 94,31 unequal: No Solution Exploring Operation: 57-37=20, Resulting Numbers: [20] 20,31 unequal: No Solution Moving to Node #0,1,3 Current State: 31:[19, 1], Operations: ['60-3=57', '57-56=1'] Exploring Operation: 19*1=19, Resulting Numbers: [19] 19,31 unequal: No Solution Exploring Operation: 19-1=18, Resulting Numbers: [18] 18,31 unequal: No Solution Exploring Operation: 19+1=20, Resulting Numbers: [20] 20,31 unequal: No Solution Exploring Operation: 19/1=19, Resulting Numbers: [19] 19,31 unequal: No Solution Moving to Node #0,1,1 Current State: 31:[56, 3], Operations: ['60-3=57', '57/19=3'] Exploring Operation: 56-3=53, Resulting Numbers: [53] 53,31 unequal: No Solution Exploring Operation: 56*3=168, Resulting Numbers: [168] 168,31 unequal: No Solution Exploring Operation: 56+3=59, Resulting Numbers: [59] 59,31 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: 31:[19, 60, 53], Operations: ['56-3=53'] Exploring Operation: 60-53=7, Resulting Numbers: [19, 7] Generated Node #0,2,0: 31:[19, 7] Operation: 60-53=7 Exploring Operation: 19+60=79, Resulting Numbers: [53, 79] Generated Node #0,2,1: 31:[53, 79] Operation: 19+60=79 Exploring Operation: 53-19=34, Resulting Numbers: [60, 34] Generated Node #0,2,2: 31:[60, 34] Operation: 53-19=34 Exploring Operation: 60-19=41, Resulting Numbers: [53, 41] Generated Node #0,2,3: 31:[53, 41] Operation: 60-19=41 Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 31:[60, 34], Operations: ['56-3=53', '53-19=34'] Exploring Operation: 60-34=26, Resulting Numbers: [26] 26,31 unequal: No Solution Exploring Operation: 60+34=94, Resulting Numbers: [94] 94,31 unequal: No Solution Exploring Operation: 60*34=2040, Resulting Numbers: [2040] 2040,31 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: 31:[53, 41], Operations: ['56-3=53', '60-19=41'] Exploring Operation: 53-41=12, Resulting Numbers: [12] 12,31 unequal: No Solution Exploring Operation: 53*41=2173, Resulting Numbers: [2173] 2173,31 unequal: No Solution Exploring Operation: 53+41=94, Resulting Numbers: [94] 94,31 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: 31:[19, 7], Operations: ['56-3=53', '60-53=7'] Exploring Operation: 19*7=133, Resulting Numbers: [133] 133,31 unequal: No Solution Exploring Operation: 19-7=12, Resulting Numbers: [12] 12,31 unequal: No Solution Exploring Operation: 19+7=26, Resulting Numbers: [26] 26,31 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: 31:[53, 79], Operations: ['56-3=53', '19+60=79'] Exploring Operation: 53+79=132, Resulting Numbers: [132] 132,31 unequal: No Solution Exploring Operation: 79-53=26, Resulting Numbers: [26] 26,31 unequal: No Solution Exploring Operation: 53*79=4187, Resulting Numbers: [4187] 4187,31 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
[ 87, 4, 64, 52 ]
57
[ "87+64=151", "4*52=208", "208-151=57" ]
Current State: 57:[87, 4, 64, 52], Operations: [] Exploring Operation: 87+64=151, Resulting Numbers: [4, 52, 151] Generated Node #2: [4, 52, 151] from Operation: 87+64=151 Current State: 57:[4, 52, 151], Operations: ['87+64=151'] Exploring Operation: 4*52=208, Resulting Numbers: [151, 208] Generated Node #3: [151, 208] from Operation: 4*52=208 Current State: 57:[151, 208], Operations: ['87+64=151', '4*52=208'] Exploring Operation: 208-151=57, Resulting Numbers: [57] 57,57 equal: Goal Reached
4
Current State: 57:[87, 4, 64, 52], Operations: [] Exploring Operation: 87-52=35, Resulting Numbers: [4, 64, 35] Generated Node #0,0: 57:[4, 64, 35] Operation: 87-52=35 Exploring Operation: 87-64=23, Resulting Numbers: [4, 52, 23] Generated Node #0,1: 57:[4, 52, 23] Operation: 87-64=23 Exploring Operation: 64/4=16, Resulting Numbers: [87, 52, 16] Generated Node #0,2: 57:[87, 52, 16] Operation: 64/4=16 Exploring Operation: 64-4=60, Resulting Numbers: [87, 52, 60] Generated Node #0,3: 57:[87, 52, 60] Operation: 64-4=60 Exploring Operation: 87-4=83, Resulting Numbers: [64, 52, 83] Generated Node #0,4: 57:[64, 52, 83] Operation: 87-4=83 Moving to Node #0,1 Current State: 57:[4, 52, 23], Operations: ['87-64=23'] Exploring Operation: 4+52=56, Resulting Numbers: [23, 56] Generated Node #0,1,0: 57:[23, 56] Operation: 4+52=56 Exploring Operation: 52/4=13, Resulting Numbers: [23, 13] Generated Node #0,1,1: 57:[23, 13] Operation: 52/4=13 Exploring Operation: 23-4=19, Resulting Numbers: [52, 19] Generated Node #0,1,2: 57:[52, 19] Operation: 23-4=19 Exploring Operation: 52-23=29, Resulting Numbers: [4, 29] Generated Node #0,1,3: 57:[4, 29] Operation: 52-23=29 Exploring Operation: 52-4=48, Resulting Numbers: [23, 48] Generated Node #0,1,4: 57:[23, 48] Operation: 52-4=48 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 57:[23, 56], Operations: ['87-64=23', '4+52=56'] Exploring Operation: 56-23=33, Resulting Numbers: [33] 33,57 unequal: No Solution Exploring Operation: 23+56=79, Resulting Numbers: [79] 79,57 unequal: No Solution Exploring Operation: 23*56=1288, Resulting Numbers: [1288] 1288,57 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: 57:[52, 19], Operations: ['87-64=23', '23-4=19'] Exploring Operation: 52-19=33, Resulting Numbers: [33] 33,57 unequal: No Solution Exploring Operation: 52*19=988, Resulting Numbers: [988] 988,57 unequal: No Solution Exploring Operation: 52+19=71, Resulting Numbers: [71] 71,57 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: 57:[23, 13], Operations: ['87-64=23', '52/4=13'] Exploring Operation: 23-13=10, Resulting Numbers: [10] 10,57 unequal: No Solution Exploring Operation: 23*13=299, Resulting Numbers: [299] 299,57 unequal: No Solution Exploring Operation: 23+13=36, Resulting Numbers: [36] 36,57 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: 57:[4, 29], Operations: ['87-64=23', '52-23=29'] Exploring Operation: 29-4=25, Resulting Numbers: [25] 25,57 unequal: No Solution Exploring Operation: 4+29=33, Resulting Numbers: [33] 33,57 unequal: No Solution Exploring Operation: 4*29=116, Resulting Numbers: [116] 116,57 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: 57:[23, 48], Operations: ['87-64=23', '52-4=48'] Exploring Operation: 23*48=1104, Resulting Numbers: [1104] 1104,57 unequal: No Solution Exploring Operation: 23+48=71, Resulting Numbers: [71] 71,57 unequal: No Solution Exploring Operation: 48-23=25, Resulting Numbers: [25] 25,57 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: 57:[4, 64, 35], Operations: ['87-52=35'] Exploring Operation: 64-35=29, Resulting Numbers: [4, 29] Generated Node #0,0,0: 57:[4, 29] Operation: 64-35=29 Exploring Operation: 64/4=16, Resulting Numbers: [35, 16] Generated Node #0,0,1: 57:[35, 16] Operation: 64/4=16 Exploring Operation: 4+35=39, Resulting Numbers: [64, 39] Generated Node #0,0,2: 57:[64, 39] Operation: 4+35=39 Exploring Operation: 35-4=31, Resulting Numbers: [64, 31] Generated Node #0,0,3: 57:[64, 31] Operation: 35-4=31 Exploring Operation: 64-4=60, Resulting Numbers: [35, 60] Generated Node #0,0,4: 57:[35, 60] Operation: 64-4=60 Moving to Node #0,2 Current State: 57:[87, 52, 16], Operations: ['64/4=16'] Exploring Operation: 87-16=71, Resulting Numbers: [52, 71] Generated Node #0,2,0: 57:[52, 71] Operation: 87-16=71 Exploring Operation: 52-16=36, Resulting Numbers: [87, 36] Generated Node #0,2,1: 57:[87, 36] Operation: 52-16=36 Exploring Operation: 52+16=68, Resulting Numbers: [87, 68] Generated Node #0,2,2: 57:[87, 68] Operation: 52+16=68 Exploring Operation: 87-52=35, Resulting Numbers: [16, 35] Generated Node #0,2,3: 57:[16, 35] Operation: 87-52=35 Exploring Operation: 87+16=103, Resulting Numbers: [52, 103] Generated Node #0,2,4: 57:[52, 103] Operation: 87+16=103 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 57:[52, 71], Operations: ['64/4=16', '87-16=71'] Exploring Operation: 52+71=123, Resulting Numbers: [123] 123,57 unequal: No Solution Exploring Operation: 52*71=3692, Resulting Numbers: [3692] 3692,57 unequal: No Solution Exploring Operation: 71-52=19, Resulting Numbers: [19] 19,57 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: 57:[16, 35], Operations: ['64/4=16', '87-52=35'] Exploring Operation: 35-16=19, Resulting Numbers: [19] 19,57 unequal: No Solution Exploring Operation: 16+35=51, Resulting Numbers: [51] 51,57 unequal: No Solution Exploring Operation: 16*35=560, Resulting Numbers: [560] 560,57 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: 57:[87, 68], Operations: ['64/4=16', '52+16=68'] Exploring Operation: 87+68=155, Resulting Numbers: [155] 155,57 unequal: No Solution Exploring Operation: 87*68=5916, Resulting Numbers: [5916] 5916,57 unequal: No Solution Exploring Operation: 87-68=19, Resulting Numbers: [19] 19,57 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: 57:[87, 36], Operations: ['64/4=16', '52-16=36'] Exploring Operation: 87*36=3132, Resulting Numbers: [3132] 3132,57 unequal: No Solution Exploring Operation: 87+36=123, Resulting Numbers: [123] 123,57 unequal: No Solution Exploring Operation: 87-36=51, Resulting Numbers: [51] 51,57 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: 57:[52, 103], Operations: ['64/4=16', '87+16=103'] Exploring Operation: 103-52=51, Resulting Numbers: [51] 51,57 unequal: No Solution Exploring Operation: 52*103=5356, Resulting Numbers: [5356] 5356,57 unequal: No Solution Exploring Operation: 52+103=155, Resulting Numbers: [155] 155,57 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: 57:[87, 52, 60], Operations: ['64-4=60'] Exploring Operation: 60-52=8, Resulting Numbers: [87, 8] Generated Node #0,3,0: 57:[87, 8] Operation: 60-52=8 Exploring Operation: 87+52=139, Resulting Numbers: [60, 139] Generated Node #0,3,1: 57:[60, 139] Operation: 87+52=139 Exploring Operation: 87-52=35, Resulting Numbers: [60, 35] Generated Node #0,3,2: 57:[60, 35] Operation: 87-52=35 Exploring Operation: 87-60=27, Resulting Numbers: [52, 27] Generated Node #0,3,3: 57:[52, 27] Operation: 87-60=27 Exploring Operation: 52+60=112, Resulting Numbers: [87, 112] Generated Node #0,3,4: 57:[87, 112] Operation: 52+60=112 Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 57:[52, 27], Operations: ['64-4=60', '87-60=27'] Exploring Operation: 52-27=25, Resulting Numbers: [25] 25,57 unequal: No Solution Exploring Operation: 52+27=79, Resulting Numbers: [79] 79,57 unequal: No Solution Exploring Operation: 52*27=1404, Resulting Numbers: [1404] 1404,57 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: 57:[60, 35], Operations: ['64-4=60', '87-52=35'] Exploring Operation: 60+35=95, Resulting Numbers: [95] 95,57 unequal: No Solution Exploring Operation: 60-35=25, Resulting Numbers: [25] 25,57 unequal: No Solution Exploring Operation: 60*35=2100, Resulting Numbers: [2100] 2100,57 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: 57:[87, 8], Operations: ['64-4=60', '60-52=8'] Exploring Operation: 87+8=95, Resulting Numbers: [95] 95,57 unequal: No Solution Exploring Operation: 87-8=79, Resulting Numbers: [79] 79,57 unequal: No Solution Exploring Operation: 87*8=696, Resulting Numbers: [696] 696,57 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: 57:[60, 139], Operations: ['64-4=60', '87+52=139'] Exploring Operation: 60+139=199, Resulting Numbers: [199] 199,57 unequal: No Solution Exploring Operation: 60*139=8340, Resulting Numbers: [8340] 8340,57 unequal: No Solution Exploring Operation: 139-60=79, Resulting Numbers: [79] 79,57 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: 57:[87, 112], Operations: ['64-4=60', '52+60=112'] Exploring Operation: 112-87=25, Resulting Numbers: [25] 25,57 unequal: No Solution Exploring Operation: 87*112=9744, Resulting Numbers: [9744] 9744,57 unequal: No Solution Exploring Operation: 87+112=199, Resulting Numbers: [199] 199,57 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: 57:[64, 52, 83], Operations: ['87-4=83'] Exploring Operation: 83-52=31, Resulting Numbers: [64, 31] Generated Node #0,4,0: 57:[64, 31] Operation: 83-52=31 Exploring Operation: 64+52=116, Resulting Numbers: [83, 116] Generated Node #0,4,1: 57:[83, 116] Operation: 64+52=116 Exploring Operation: 83-64=19, Resulting Numbers: [52, 19] Generated Node #0,4,2: 57:[52, 19] Operation: 83-64=19 Exploring Operation: 64-52=12, Resulting Numbers: [83, 12] Generated Node #0,4,3: 57:[83, 12] Operation: 64-52=12 Exploring Operation: 52+83=135, Resulting Numbers: [64, 135] Generated Node #0,4,4: 57:[64, 135] Operation: 52+83=135 Moving to Node #0,4,2 Current State: 57:[52, 19], Operations: ['87-4=83', '83-64=19'] Exploring Operation: 52*19=988, Resulting Numbers: [988] 988,57 unequal: No Solution Exploring Operation: 52-19=33, Resulting Numbers: [33] 33,57 unequal: No Solution Exploring Operation: 52+19=71, Resulting Numbers: [71] 71,57 unequal: No Solution Moving to Node #0,0,0 Current State: 57:[4, 29], Operations: ['87-52=35', '64-35=29'] Exploring Operation: 4*29=116, Resulting Numbers: [116] 116,57 unequal: No Solution Exploring Operation: 4+29=33, Resulting Numbers: [33] 33,57 unequal: No Solution Exploring Operation: 29-4=25, Resulting Numbers: [25] 25,57 unequal: No Solution Moving to Node #0,4,0 Current State: 57:[64, 31], Operations: ['87-4=83', '83-52=31'] Exploring Operation: 64+31=95, Resulting Numbers: [95] 95,57 unequal: No Solution Exploring Operation: 64*31=1984, Resulting Numbers: [1984] 1984,57 unequal: No Solution Exploring Operation: 64-31=33, Resulting Numbers: [33] 33,57 unequal: No Solution Moving to Node #0,0,3 Current State: 57:[64, 31], Operations: ['87-52=35', '35-4=31'] Exploring Operation: 64-31=33, Resulting Numbers: [33] 33,57 unequal: No Solution Exploring Operation: 64+31=95, Resulting Numbers: [95] 95,57 unequal: No Solution Exploring Operation: 64*31=1984, Resulting Numbers: [1984] 1984,57 unequal: No Solution Moving to Node #0,0,1 Current State: 57:[35, 16], Operations: ['87-52=35', '64/4=16'] Exploring Operation: 35+16=51, Resulting Numbers: [51] 51,57 unequal: No Solution Exploring Operation: 35*16=560, Resulting Numbers: [560] 560,57 unequal: No Solution Exploring Operation: 35-16=19, Resulting Numbers: [19] 19,57 unequal: No Solution Moving to Node #0,0,4 Current State: 57:[35, 60], Operations: ['87-52=35', '64-4=60'] Exploring Operation: 35*60=2100, Resulting Numbers: [2100] 2100,57 unequal: No Solution Exploring Operation: 35+60=95, Resulting Numbers: [95] 95,57 unequal: No Solution Exploring Operation: 60-35=25, Resulting Numbers: [25] 25,57 unequal: No Solution Moving to Node #0,0,2 Current State: 57:[64, 39], Operations: ['87-52=35', '4+35=39'] Exploring Operation: 64-39=25, Resulting Numbers: [25] 25,57 unequal: No Solution Exploring Operation: 64+39=103, Resulting Numbers: [103] 103,57 unequal: No Solution Exploring Operation: 64*39=2496, Resulting Numbers: [2496] 2496,57 unequal: No Solution Moving to Node #0,4,3 Current State: 57:[83, 12], Operations: ['87-4=83', '64-52=12'] Exploring Operation: 83+12=95, Resulting Numbers: [95] 95,57 unequal: No Solution Exploring Operation: 83*12=996, Resulting Numbers: [996] 996,57 unequal: No Solution Exploring Operation: 83-12=71, Resulting Numbers: [71] 71,57 unequal: No Solution Moving to Node #0,4,4 Current State: 57:[64, 135], Operations: ['87-4=83', '52+83=135'] Exploring Operation: 64*135=8640, Resulting Numbers: [8640] 8640,57 unequal: No Solution Exploring Operation: 64+135=199, Resulting Numbers: [199] 199,57 unequal: No Solution Exploring Operation: 135-64=71, Resulting Numbers: [71] 71,57 unequal: No Solution Moving to Node #0,4,1 Current State: 57:[83, 116], Operations: ['87-4=83', '64+52=116'] Exploring Operation: 83*116=9628, Resulting Numbers: [9628] 9628,57 unequal: No Solution Exploring Operation: 116-83=33, Resulting Numbers: [33] 33,57 unequal: No Solution Exploring Operation: 83+116=199, Resulting Numbers: [199] 199,57 unequal: No Solution No solution found.
0
hs_5
mult_heuristic
[ 31, 1, 62, 86 ]
55
[ "31*1=31", "86-62=24", "31+24=55" ]
Current State: 55:[31, 1, 62, 86], Operations: [] Exploring Operation: 31*1=31, Resulting Numbers: [62, 86, 31] Generated Node #2: [62, 86, 31] from Operation: 31*1=31 Current State: 55:[62, 86, 31], Operations: ['31*1=31'] Exploring Operation: 86-62=24, Resulting Numbers: [31, 24] Generated Node #3: [31, 24] from Operation: 86-62=24 Current State: 55:[31, 24], Operations: ['31*1=31', '86-62=24'] Exploring Operation: 31+24=55, Resulting Numbers: [55] 55,55 equal: Goal Reached
4
Current State: 55:[31, 1, 62, 86], Operations: [] Exploring Operation: 86-31=55, Resulting Numbers: [1, 62, 55] Generated Node #0,0: 55:[1, 62, 55] Operation: 86-31=55 Exploring Operation: 62-31=31, Resulting Numbers: [1, 86, 31] Generated Node #0,1: 55:[1, 86, 31] Operation: 62-31=31 Exploring Operation: 86-62=24, Resulting Numbers: [31, 1, 24] Generated Node #0,2: 55:[31, 1, 24] Operation: 86-62=24 Exploring Operation: 62/31=2, Resulting Numbers: [1, 86, 2] Generated Node #0,3: 55:[1, 86, 2] Operation: 62/31=2 Moving to Node #0,0 Current State: 55:[1, 62, 55], Operations: ['86-31=55'] Exploring Operation: 1*62=62, Resulting Numbers: [55, 62] Generated Node #0,0,0: 55:[55, 62] Operation: 1*62=62 Exploring Operation: 62-55=7, Resulting Numbers: [1, 7] Generated Node #0,0,1: 55:[1, 7] Operation: 62-55=7 Exploring Operation: 62-1=61, Resulting Numbers: [55, 61] Generated Node #0,0,2: 55:[55, 61] Operation: 62-1=61 Exploring Operation: 62/1=62, Resulting Numbers: [55, 62] Generated Node #0,0,3: 55:[55, 62] Operation: 62/1=62 Moving to Node #0,2 Current State: 55:[31, 1, 24], Operations: ['86-62=24'] Exploring Operation: 24-1=23, Resulting Numbers: [31, 23] Generated Node #0,2,0: 55:[31, 23] Operation: 24-1=23 Exploring Operation: 31-24=7, Resulting Numbers: [1, 7] Generated Node #0,2,1: 55:[1, 7] Operation: 31-24=7 Exploring Operation: 31+24=55, Resulting Numbers: [1, 55] Generated Node #0,2,2: 55:[1, 55] Operation: 31+24=55 Exploring Operation: 31-1=30, Resulting Numbers: [24, 30] Generated Node #0,2,3: 55:[24, 30] Operation: 31-1=30 Moving to Node #0,3 Current State: 55:[1, 86, 2], Operations: ['62/31=2'] Exploring Operation: 86-1=85, Resulting Numbers: [2, 85] Generated Node #0,3,0: 55:[2, 85] Operation: 86-1=85 Exploring Operation: 1+2=3, Resulting Numbers: [86, 3] Generated Node #0,3,1: 55:[86, 3] Operation: 1+2=3 Exploring Operation: 86/2=43, Resulting Numbers: [1, 43] Generated Node #0,3,2: 55:[1, 43] Operation: 86/2=43 Exploring Operation: 86-2=84, Resulting Numbers: [1, 84] Generated Node #0,3,3: 55:[1, 84] Operation: 86-2=84 Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 55:[1, 43], Operations: ['62/31=2', '86/2=43'] Exploring Operation: 43-1=42, Resulting Numbers: [42] 42,55 unequal: No Solution Exploring Operation: 1+43=44, Resulting Numbers: [44] 44,55 unequal: No Solution Exploring Operation: 1*43=43, Resulting Numbers: [43] 43,55 unequal: No Solution Exploring Operation: 43/1=43, Resulting Numbers: [43] 43,55 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: 55:[2, 85], Operations: ['62/31=2', '86-1=85'] Exploring Operation: 2*85=170, Resulting Numbers: [170] 170,55 unequal: No Solution Exploring Operation: 2+85=87, Resulting Numbers: [87] 87,55 unequal: No Solution Exploring Operation: 85-2=83, Resulting Numbers: [83] 83,55 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: 55:[86, 3], Operations: ['62/31=2', '1+2=3'] Exploring Operation: 86*3=258, Resulting Numbers: [258] 258,55 unequal: No Solution Exploring Operation: 86-3=83, Resulting Numbers: [83] 83,55 unequal: No Solution Exploring Operation: 86+3=89, Resulting Numbers: [89] 89,55 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: 55:[1, 84], Operations: ['62/31=2', '86-2=84'] Exploring Operation: 1+84=85, Resulting Numbers: [85] 85,55 unequal: No Solution Exploring Operation: 1*84=84, Resulting Numbers: [84] 84,55 unequal: No Solution Exploring Operation: 84/1=84, Resulting Numbers: [84] 84,55 unequal: No Solution Exploring Operation: 84-1=83, Resulting Numbers: [83] 83,55 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: 55:[1, 86, 31], Operations: ['62-31=31'] Exploring Operation: 86-1=85, Resulting Numbers: [31, 85] Generated Node #0,1,0: 55:[31, 85] Operation: 86-1=85 Exploring Operation: 1*86=86, Resulting Numbers: [31, 86] Generated Node #0,1,1: 55:[31, 86] Operation: 1*86=86 Exploring Operation: 86-31=55, Resulting Numbers: [1, 55] Generated Node #0,1,2: 55:[1, 55] Operation: 86-31=55 Exploring Operation: 31-1=30, Resulting Numbers: [86, 30] Generated Node #0,1,3: 55:[86, 30] Operation: 31-1=30 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 55:[1, 55], Operations: ['62-31=31', '86-31=55'] Exploring Operation: 55/1=55, Resulting Numbers: [55] 55,55 equal: Goal Reached Moving to Node #0 Current State: 55:[31, 1, 62, 86], Operations: [] Exploring Operation: 62-31=31, Resulting Numbers: [1, 86, 31] Generated Node #0,1: 55:[1, 86, 31] Operation: 62-31=31 Moving to Node #0,1 Current State: 55:[1, 86, 31], Operations: ['62-31=31'] Exploring Operation: 86-31=55, Resulting Numbers: [1, 55] Generated Node #0,1,2: 55:[1, 55] Operation: 86-31=55 Moving to Node #0,1,2 Current State: 55:[1, 55], Operations: ['62-31=31', '86-31=55'] Exploring Operation: 55/1=55, Resulting Numbers: [55] 55,55 equal: Goal Reached Exit Sub Search at level 1
0.966146
hs_4
mult_heuristic
[ 47, 15, 3, 91 ]
61
[ "47+91=138", "138/3=46", "15+46=61" ]
Current State: 61:[47, 15, 3, 91], Operations: [] Exploring Operation: 47+91=138, Resulting Numbers: [15, 3, 138] Generated Node #2: [15, 3, 138] from Operation: 47+91=138 Current State: 61:[15, 3, 138], Operations: ['47+91=138'] Exploring Operation: 138/3=46, Resulting Numbers: [15, 46] Generated Node #3: [15, 46] from Operation: 138/3=46 Current State: 61:[15, 46], Operations: ['47+91=138', '138/3=46'] Exploring Operation: 15+46=61, Resulting Numbers: [61] 61,61 equal: Goal Reached
4
Current State: 61:[47, 15, 3, 91], Operations: [] Exploring Operation: 47+3=50, Resulting Numbers: [15, 91, 50] Generated Node #0,0: 61:[15, 91, 50] Operation: 47+3=50 Exploring Operation: 15*3=45, Resulting Numbers: [47, 91, 45] Generated Node #0,1: 61:[47, 91, 45] Operation: 15*3=45 Moving to Node #0,1 Current State: 61:[47, 91, 45], Operations: ['15*3=45'] Exploring Operation: 91-47=44, Resulting Numbers: [45, 44] Generated Node #0,1,0: 61:[45, 44] Operation: 91-47=44 Exploring Operation: 91-45=46, Resulting Numbers: [47, 46] Generated Node #0,1,1: 61:[47, 46] Operation: 91-45=46 Moving to Node #0,0 Current State: 61:[15, 91, 50], Operations: ['47+3=50'] Exploring Operation: 91-15=76, Resulting Numbers: [50, 76] Generated Node #0,0,0: 61:[50, 76] Operation: 91-15=76 Exploring Operation: 15+50=65, Resulting Numbers: [91, 65] Generated Node #0,0,1: 61:[91, 65] Operation: 15+50=65 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 61:[50, 76], Operations: ['47+3=50', '91-15=76'] Exploring Operation: 50+76=126, Resulting Numbers: [126] 126,61 unequal: No Solution Exploring Operation: 76-50=26, Resulting Numbers: [26] 26,61 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: 61:[91, 65], Operations: ['47+3=50', '15+50=65'] Exploring Operation: 91+65=156, Resulting Numbers: [156] 156,61 unequal: No Solution Exploring Operation: 91-65=26, Resulting Numbers: [26] 26,61 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: 61:[47, 46], Operations: ['15*3=45', '91-45=46'] Exploring Operation: 47+46=93, Resulting Numbers: [93] 93,61 unequal: No Solution Exploring Operation: 47-46=1, Resulting Numbers: [1] 1,61 unequal: No Solution Moving to Node #0,1,0 Current State: 61:[45, 44], Operations: ['15*3=45', '91-47=44'] Exploring Operation: 45-44=1, Resulting Numbers: [1] 1,61 unequal: No Solution Exploring Operation: 45+44=89, Resulting Numbers: [89] 89,61 unequal: No Solution No solution found.
0
hs_2
sum_heuristic
[ 20, 15, 33, 20 ]
29
[ "20-15=5", "20/5=4", "33-4=29" ]
Current State: 29:[20, 15, 33, 20], Operations: [] Exploring Operation: 20-15=5, Resulting Numbers: [33, 5] Generated Node #2: [33, 5] from Operation: 20-15=5 Current State: 29:[33, 5], Operations: ['20-15=5'] Exploring Operation: 20/5=4, Resulting Numbers: [33, 4] Generated Node #3: [33, 4] from Operation: 20/5=4 Current State: 29:[33, 4], Operations: ['20-15=5', '20/5=4'] Exploring Operation: 33-4=29, Resulting Numbers: [29] 29,29 equal: Goal Reached
4
Current State: 29:[20, 15, 33, 20], Operations: [] Exploring Operation: 20+15=35, Resulting Numbers: [33, 20, 35] Generated Node #0,0: 29:[33, 20, 35] Operation: 20+15=35 Exploring Operation: 15+20=35, Resulting Numbers: [20, 33, 35] Generated Node #0,1: 29:[20, 33, 35] Operation: 15+20=35 Start Sub Search at level 1: Moving to Node #0,0 Current State: 29:[33, 20, 35], Operations: ['20+15=35'] Exploring Operation: 35-20=15, Resulting Numbers: [33, 15] Generated Node #0,0,0: 29:[33, 15] Operation: 35-20=15 Exploring Operation: 33-20=13, Resulting Numbers: [35, 13] Generated Node #0,0,1: 29:[35, 13] Operation: 33-20=13 Moving to Node #0,0,0 Current State: 29:[33, 15], Operations: ['20+15=35', '35-20=15'] Exploring Operation: 33+15=48, Resulting Numbers: [48] 48,29 unequal: No Solution Exploring Operation: 33-15=18, Resulting Numbers: [18] 18,29 unequal: No Solution Moving to Node #0,0,1 Current State: 29:[35, 13], Operations: ['20+15=35', '33-20=13'] Exploring Operation: 35+13=48, Resulting Numbers: [48] 48,29 unequal: No Solution Exploring Operation: 35-13=22, Resulting Numbers: [22] 22,29 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 Current State: 29:[20, 33, 35], Operations: ['15+20=35'] Exploring Operation: 35-20=15, Resulting Numbers: [33, 15] Generated Node #0,1,0: 29:[33, 15] Operation: 35-20=15 Exploring Operation: 33-20=13, Resulting Numbers: [35, 13] Generated Node #0,1,1: 29:[35, 13] Operation: 33-20=13 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 29:[33, 15], Operations: ['15+20=35', '35-20=15'] Exploring Operation: 33+15=48, Resulting Numbers: [48] 48,29 unequal: No Solution Exploring Operation: 33-15=18, Resulting Numbers: [18] 18,29 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: 29:[35, 13], Operations: ['15+20=35', '33-20=13'] Exploring Operation: 35+13=48, Resulting Numbers: [48] 48,29 unequal: No Solution Exploring Operation: 35-13=22, Resulting Numbers: [22] 22,29 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
[ 70, 32, 22, 2 ]
98
[ "70-32=38", "2*38=76", "22+76=98" ]
Current State: 98:[70, 32, 22, 2], Operations: [] Exploring Operation: 70-32=38, Resulting Numbers: [22, 2, 38] Generated Node #2: [22, 2, 38] from Operation: 70-32=38 Current State: 98:[22, 2, 38], Operations: ['70-32=38'] Exploring Operation: 2*38=76, Resulting Numbers: [22, 76] Generated Node #3: [22, 76] from Operation: 2*38=76 Current State: 98:[22, 76], Operations: ['70-32=38', '2*38=76'] Exploring Operation: 22+76=98, Resulting Numbers: [98] 98,98 equal: Goal Reached
4
Current State: 98:[70, 32, 22, 2], Operations: [] Exploring Operation: 70+32=102, Resulting Numbers: [22, 2, 102] Generated Node #0,0: 98:[22, 2, 102] Operation: 70+32=102 Start Sub Search at level 1: Moving to Node #0,0 Current State: 98:[22, 2, 102], Operations: ['70+32=102'] Exploring Operation: 22/2=11, Resulting Numbers: [102, 11] Generated Node #0,0,0: 98:[102, 11] Operation: 22/2=11 Moving to Node #0,0,0 Current State: 98:[102, 11], Operations: ['70+32=102', '22/2=11'] Exploring Operation: 102-11=91, Resulting Numbers: [91] 91,98 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
[ 2, 10, 83, 68 ]
44
[ "10+68=78", "78/2=39", "83-39=44" ]
Current State: 44:[2, 10, 83, 68], Operations: [] Exploring Operation: 10+68=78, Resulting Numbers: [2, 83, 78] Generated Node #2: [2, 83, 78] from Operation: 10+68=78 Current State: 44:[2, 83, 78], Operations: ['10+68=78'] Exploring Operation: 78/2=39, Resulting Numbers: [83, 39] Generated Node #3: [83, 39] from Operation: 78/2=39 Current State: 44:[83, 39], Operations: ['10+68=78', '78/2=39'] Exploring Operation: 83-39=44, Resulting Numbers: [44] 44,44 equal: Goal Reached
4
Current State: 44:[2, 10, 83, 68], Operations: [] Exploring Operation: 68-10=58, Resulting Numbers: [2, 83, 58] Generated Node #0,0: 44:[2, 83, 58] Operation: 68-10=58 Exploring Operation: 83-10=73, Resulting Numbers: [2, 68, 73] Generated Node #0,1: 44:[2, 68, 73] Operation: 83-10=73 Exploring Operation: 83-68=15, Resulting Numbers: [2, 10, 15] Generated Node #0,2: 44:[2, 10, 15] Operation: 83-68=15 Exploring Operation: 68/2=34, Resulting Numbers: [10, 83, 34] Generated Node #0,3: 44:[10, 83, 34] Operation: 68/2=34 Start Sub Search at level 1: Moving to Node #0,2 Current State: 44:[2, 10, 15], Operations: ['83-68=15'] Exploring Operation: 15-10=5, Resulting Numbers: [2, 5] Generated Node #0,2,0: 44:[2, 5] Operation: 15-10=5 Exploring Operation: 10+15=25, Resulting Numbers: [2, 25] Generated Node #0,2,1: 44:[2, 25] Operation: 10+15=25 Exploring Operation: 15-2=13, Resulting Numbers: [10, 13] Generated Node #0,2,2: 44:[10, 13] Operation: 15-2=13 Exploring Operation: 2+10=12, Resulting Numbers: [15, 12] Generated Node #0,2,3: 44:[15, 12] Operation: 2+10=12 Moving to Node #0,2,0 Current State: 44:[2, 5], Operations: ['83-68=15', '15-10=5'] Exploring Operation: 5-2=3, Resulting Numbers: [3] 3,44 unequal: No Solution Exploring Operation: 2+5=7, Resulting Numbers: [7] 7,44 unequal: No Solution Exploring Operation: 2*5=10, Resulting Numbers: [10] 10,44 unequal: No Solution Moving to Node #0,2,2 Current State: 44:[10, 13], Operations: ['83-68=15', '15-2=13'] Exploring Operation: 10*13=130, Resulting Numbers: [130] 130,44 unequal: No Solution Exploring Operation: 13-10=3, Resulting Numbers: [3] 3,44 unequal: No Solution Exploring Operation: 10+13=23, Resulting Numbers: [23] 23,44 unequal: No Solution Moving to Node #0,2,1 Current State: 44:[2, 25], Operations: ['83-68=15', '10+15=25'] Exploring Operation: 2*25=50, Resulting Numbers: [50] 50,44 unequal: No Solution Exploring Operation: 25-2=23, Resulting Numbers: [23] 23,44 unequal: No Solution Exploring Operation: 2+25=27, Resulting Numbers: [27] 27,44 unequal: No Solution Moving to Node #0,2,3 Current State: 44:[15, 12], Operations: ['83-68=15', '2+10=12'] Exploring Operation: 15*12=180, Resulting Numbers: [180] 180,44 unequal: No Solution Exploring Operation: 15+12=27, Resulting Numbers: [27] 27,44 unequal: No Solution Exploring Operation: 15-12=3, Resulting Numbers: [3] 3,44 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: 44:[10, 83, 34], Operations: ['68/2=34'] Exploring Operation: 83-34=49, Resulting Numbers: [10, 49] Generated Node #0,3,0: 44:[10, 49] Operation: 83-34=49 Exploring Operation: 34-10=24, Resulting Numbers: [83, 24] Generated Node #0,3,1: 44:[83, 24] Operation: 34-10=24 Exploring Operation: 10+34=44, Resulting Numbers: [83, 44] Generated Node #0,3,2: 44:[83, 44] Operation: 10+34=44 Exploring Operation: 83-10=73, Resulting Numbers: [34, 73] Generated Node #0,3,3: 44:[34, 73] Operation: 83-10=73 Moving to Node #0,3,0 Current State: 44:[10, 49], Operations: ['68/2=34', '83-34=49'] Exploring Operation: 49-10=39, Resulting Numbers: [39] 39,44 unequal: No Solution Exploring Operation: 10*49=490, Resulting Numbers: [490] 490,44 unequal: No Solution Exploring Operation: 10+49=59, Resulting Numbers: [59] 59,44 unequal: No Solution Moving to Node #0,3,3 Current State: 44:[34, 73], Operations: ['68/2=34', '83-10=73'] Exploring Operation: 73-34=39, Resulting Numbers: [39] 39,44 unequal: No Solution Exploring Operation: 34+73=107, Resulting Numbers: [107] 107,44 unequal: No Solution Exploring Operation: 34*73=2482, Resulting Numbers: [2482] 2482,44 unequal: No Solution Moving to Node #0,3,2 Current State: 44:[83, 44], Operations: ['68/2=34', '10+34=44'] Exploring Operation: 83+44=127, Resulting Numbers: [127] 127,44 unequal: No Solution Exploring Operation: 83*44=3652, Resulting Numbers: [3652] 3652,44 unequal: No Solution Exploring Operation: 83-44=39, Resulting Numbers: [39] 39,44 unequal: No Solution Moving to Node #0,3,1 Current State: 44:[83, 24], Operations: ['68/2=34', '34-10=24'] Exploring Operation: 83-24=59, Resulting Numbers: [59] 59,44 unequal: No Solution Exploring Operation: 83+24=107, Resulting Numbers: [107] 107,44 unequal: No Solution Exploring Operation: 83*24=1992, Resulting Numbers: [1992] 1992,44 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: 44:[2, 83, 58], Operations: ['68-10=58'] Exploring Operation: 83-2=81, Resulting Numbers: [58, 81] Generated Node #0,0,0: 44:[58, 81] Operation: 83-2=81 Exploring Operation: 58-2=56, Resulting Numbers: [83, 56] Generated Node #0,0,1: 44:[83, 56] Operation: 58-2=56 Exploring Operation: 58/2=29, Resulting Numbers: [83, 29] Generated Node #0,0,2: 44:[83, 29] Operation: 58/2=29 Exploring Operation: 83-58=25, Resulting Numbers: [2, 25] Generated Node #0,0,3: 44:[2, 25] Operation: 83-58=25 Moving to Node #0,0,3 Current State: 44:[2, 25], Operations: ['68-10=58', '83-58=25'] Exploring Operation: 2*25=50, Resulting Numbers: [50] 50,44 unequal: No Solution Exploring Operation: 2+25=27, Resulting Numbers: [27] 27,44 unequal: No Solution Exploring Operation: 25-2=23, Resulting Numbers: [23] 23,44 unequal: No Solution Moving to Node #0,0,2 Current State: 44:[83, 29], Operations: ['68-10=58', '58/2=29'] Exploring Operation: 83-29=54, Resulting Numbers: [54] 54,44 unequal: No Solution Exploring Operation: 83*29=2407, Resulting Numbers: [2407] 2407,44 unequal: No Solution Exploring Operation: 83+29=112, Resulting Numbers: [112] 112,44 unequal: No Solution Moving to Node #0,0,1 Current State: 44:[83, 56], Operations: ['68-10=58', '58-2=56'] Exploring Operation: 83-56=27, Resulting Numbers: [27] 27,44 unequal: No Solution Exploring Operation: 83*56=4648, Resulting Numbers: [4648] 4648,44 unequal: No Solution Exploring Operation: 83+56=139, Resulting Numbers: [139] 139,44 unequal: No Solution Moving to Node #0,0,0 Current State: 44:[58, 81], Operations: ['68-10=58', '83-2=81'] Exploring Operation: 58+81=139, Resulting Numbers: [139] 139,44 unequal: No Solution Exploring Operation: 81-58=23, Resulting Numbers: [23] 23,44 unequal: No Solution Exploring Operation: 58*81=4698, Resulting Numbers: [4698] 4698,44 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: 44:[2, 68, 73], Operations: ['83-10=73'] Exploring Operation: 68-2=66, Resulting Numbers: [73, 66] Generated Node #0,1,0: 44:[73, 66] Operation: 68-2=66 Exploring Operation: 73-68=5, Resulting Numbers: [2, 5] Generated Node #0,1,1: 44:[2, 5] Operation: 73-68=5 Exploring Operation: 68/2=34, Resulting Numbers: [73, 34] Generated Node #0,1,2: 44:[73, 34] Operation: 68/2=34 Exploring Operation: 73-2=71, Resulting Numbers: [68, 71] Generated Node #0,1,3: 44:[68, 71] Operation: 73-2=71 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 44:[2, 5], Operations: ['83-10=73', '73-68=5'] Exploring Operation: 2+5=7, Resulting Numbers: [7] 7,44 unequal: No Solution Exploring Operation: 5-2=3, Resulting Numbers: [3] 3,44 unequal: No Solution Exploring Operation: 2*5=10, Resulting Numbers: [10] 10,44 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: 44:[73, 34], Operations: ['83-10=73', '68/2=34'] Exploring Operation: 73-34=39, Resulting Numbers: [39] 39,44 unequal: No Solution Exploring Operation: 73+34=107, Resulting Numbers: [107] 107,44 unequal: No Solution Exploring Operation: 73*34=2482, Resulting Numbers: [2482] 2482,44 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: 44:[73, 66], Operations: ['83-10=73', '68-2=66'] Exploring Operation: 73+66=139, Resulting Numbers: [139] 139,44 unequal: No Solution Exploring Operation: 73*66=4818, Resulting Numbers: [4818] 4818,44 unequal: No Solution Exploring Operation: 73-66=7, Resulting Numbers: [7] 7,44 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: 44:[68, 71], Operations: ['83-10=73', '73-2=71'] Exploring Operation: 71-68=3, Resulting Numbers: [3] 3,44 unequal: No Solution Exploring Operation: 68+71=139, Resulting Numbers: [139] 139,44 unequal: No Solution Exploring Operation: 68*71=4828, Resulting Numbers: [4828] 4828,44 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
sum_heuristic
[ 3, 49, 84, 9 ]
78
[ "84-49=35", "35-9=26", "3*26=78" ]
Current State: 78:[3, 49, 84, 9], Operations: [] Exploring Operation: 84-49=35, Resulting Numbers: [3, 9, 35] Generated Node #2: [3, 9, 35] from Operation: 84-49=35 Current State: 78:[3, 9, 35], Operations: ['84-49=35'] Exploring Operation: 35-9=26, Resulting Numbers: [3, 26] Generated Node #3: [3, 26] from Operation: 35-9=26 Current State: 78:[3, 26], Operations: ['84-49=35', '35-9=26'] Exploring Operation: 3*26=78, Resulting Numbers: [78] 78,78 equal: Goal Reached
4
Current State: 78:[3, 49, 84, 9], Operations: [] Exploring Operation: 84/3=28, Resulting Numbers: [49, 9, 28] Generated Node #0,0: 78:[49, 9, 28] Operation: 84/3=28 Exploring Operation: 84-49=35, Resulting Numbers: [3, 9, 35] Generated Node #0,1: 78:[3, 9, 35] Operation: 84-49=35 Exploring Operation: 49-3=46, Resulting Numbers: [84, 9, 46] Generated Node #0,2: 78:[84, 9, 46] Operation: 49-3=46 Exploring Operation: 49-9=40, Resulting Numbers: [3, 84, 40] Generated Node #0,3: 78:[3, 84, 40] Operation: 49-9=40 Exploring Operation: 84-9=75, Resulting Numbers: [3, 49, 75] Generated Node #0,4: 78:[3, 49, 75] Operation: 84-9=75 Start Sub Search at level 1: Moving to Node #0,1 Current State: 78:[3, 9, 35], Operations: ['84-49=35'] Exploring Operation: 9-3=6, Resulting Numbers: [35, 6] Generated Node #0,1,0: 78:[35, 6] Operation: 9-3=6 Exploring Operation: 9/3=3, Resulting Numbers: [35, 3] Generated Node #0,1,1: 78:[35, 3] Operation: 9/3=3 Exploring Operation: 3+35=38, Resulting Numbers: [9, 38] Generated Node #0,1,2: 78:[9, 38] Operation: 3+35=38 Exploring Operation: 35-9=26, Resulting Numbers: [3, 26] Generated Node #0,1,3: 78:[3, 26] Operation: 35-9=26 Exploring Operation: 3+9=12, Resulting Numbers: [35, 12] Generated Node #0,1,4: 78:[35, 12] Operation: 3+9=12 Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 78:[3, 26], Operations: ['84-49=35', '35-9=26'] Exploring Operation: 3*26=78, Resulting Numbers: [78] 78,78 equal: Goal Reached Moving to Node #0 Current State: 78:[3, 49, 84, 9], Operations: [] Exploring Operation: 84-49=35, Resulting Numbers: [3, 9, 35] Generated Node #0,1: 78:[3, 9, 35] Operation: 84-49=35 Moving to Node #0,1 Current State: 78:[3, 9, 35], Operations: ['84-49=35'] Exploring Operation: 35-9=26, Resulting Numbers: [3, 26] Generated Node #0,1,3: 78:[3, 26] Operation: 35-9=26 Moving to Node #0,1,3 Current State: 78:[3, 26], Operations: ['84-49=35', '35-9=26'] Exploring Operation: 3*26=78, Resulting Numbers: [78] 78,78 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.986979
hs_5
mult_heuristic
[ 55, 15, 39, 2 ]
46
[ "55-39=16", "15*2=30", "16+30=46" ]
Current State: 46:[55, 15, 39, 2], Operations: [] Exploring Operation: 55-39=16, Resulting Numbers: [15, 2, 16] Generated Node #2: [15, 2, 16] from Operation: 55-39=16 Current State: 46:[15, 2, 16], Operations: ['55-39=16'] Exploring Operation: 15*2=30, Resulting Numbers: [16, 30] Generated Node #3: [16, 30] from Operation: 15*2=30 Current State: 46:[16, 30], Operations: ['55-39=16', '15*2=30'] Exploring Operation: 16+30=46, Resulting Numbers: [46] 46,46 equal: Goal Reached
4
Current State: 46:[55, 15, 39, 2], Operations: [] Exploring Operation: 39-15=24, Resulting Numbers: [55, 2, 24] Generated Node #0,0: 46:[55, 2, 24] Operation: 39-15=24 Exploring Operation: 55-39=16, Resulting Numbers: [15, 2, 16] Generated Node #0,1: 46:[15, 2, 16] Operation: 55-39=16 Exploring Operation: 55-15=40, Resulting Numbers: [39, 2, 40] Generated Node #0,2: 46:[39, 2, 40] Operation: 55-15=40 Start Sub Search at level 1: Moving to Node #0,0 Current State: 46:[55, 2, 24], Operations: ['39-15=24'] Exploring Operation: 24-2=22, Resulting Numbers: [55, 22] Generated Node #0,0,0: 46:[55, 22] Operation: 24-2=22 Exploring Operation: 55-24=31, Resulting Numbers: [2, 31] Generated Node #0,0,1: 46:[2, 31] Operation: 55-24=31 Exploring Operation: 55-2=53, Resulting Numbers: [24, 53] Generated Node #0,0,2: 46:[24, 53] Operation: 55-2=53 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 46:[2, 31], Operations: ['39-15=24', '55-24=31'] Exploring Operation: 31-2=29, Resulting Numbers: [29] 29,46 unequal: No Solution Exploring Operation: 2+31=33, Resulting Numbers: [33] 33,46 unequal: No Solution Exploring Operation: 2*31=62, Resulting Numbers: [62] 62,46 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 #0,0,2 Current State: 46:[24, 53], Operations: ['39-15=24', '55-2=53'] Exploring Operation: 24+53=77, Resulting Numbers: [77] 77,46 unequal: No Solution Exploring Operation: 53-24=29, Resulting Numbers: [29] 29,46 unequal: No Solution Exploring Operation: 24*53=1272, Resulting Numbers: [1272] 1272,46 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 #0,0,0 Current State: 46:[55, 22], Operations: ['39-15=24', '24-2=22'] Exploring Operation: 55+22=77, Resulting Numbers: [77] 77,46 unequal: No Solution Exploring Operation: 55-22=33, Resulting Numbers: [33] 33,46 unequal: No Solution Exploring Operation: 55*22=1210, Resulting Numbers: [1210] 1210,46 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 #0,2 Current State: 46:[39, 2, 40], Operations: ['55-15=40'] Exploring Operation: 40-39=1, Resulting Numbers: [2, 1] Generated Node #0,2,0: 46:[2, 1] Operation: 40-39=1 Exploring Operation: 39+2=41, Resulting Numbers: [40, 41] Generated Node #0,2,1: 46:[40, 41] Operation: 39+2=41 Exploring Operation: 40/2=20, Resulting Numbers: [39, 20] Generated Node #0,2,2: 46:[39, 20] Operation: 40/2=20 Moving to Node #0,2,0 Current State: 46:[2, 1], Operations: ['55-15=40', '40-39=1'] Exploring Operation: 2/1=2, Resulting Numbers: [2] 2,46 unequal: No Solution Exploring Operation: 2*1=2, Resulting Numbers: [2] 2,46 unequal: No Solution Exploring Operation: 2+1=3, Resulting Numbers: [3] 3,46 unequal: No Solution Moving to Node #0,2,2 Current State: 46:[39, 20], Operations: ['55-15=40', '40/2=20'] Exploring Operation: 39+20=59, Resulting Numbers: [59] 59,46 unequal: No Solution Exploring Operation: 39*20=780, Resulting Numbers: [780] 780,46 unequal: No Solution Exploring Operation: 39-20=19, Resulting Numbers: [19] 19,46 unequal: No Solution Moving to Node #0,2,1 Current State: 46:[40, 41], Operations: ['55-15=40', '39+2=41'] Exploring Operation: 40+41=81, Resulting Numbers: [81] 81,46 unequal: No Solution Exploring Operation: 40*41=1640, Resulting Numbers: [1640] 1640,46 unequal: No Solution Exploring Operation: 41-40=1, Resulting Numbers: [1] 1,46 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:[15, 2, 16], Operations: ['55-39=16'] Exploring Operation: 16-15=1, Resulting Numbers: [2, 1] Generated Node #0,1,0: 46:[2, 1] Operation: 16-15=1 Exploring Operation: 15+16=31, Resulting Numbers: [2, 31] Generated Node #0,1,1: 46:[2, 31] Operation: 15+16=31 Exploring Operation: 15+2=17, Resulting Numbers: [16, 17] Generated Node #0,1,2: 46:[16, 17] Operation: 15+2=17 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 46:[2, 1], Operations: ['55-39=16', '16-15=1'] Exploring Operation: 2*1=2, Resulting Numbers: [2] 2,46 unequal: No Solution Exploring Operation: 2/1=2, Resulting Numbers: [2] 2,46 unequal: No Solution Exploring Operation: 2+1=3, Resulting Numbers: [3] 3,46 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 #0,1,1 Current State: 46:[2, 31], Operations: ['55-39=16', '15+16=31'] Exploring Operation: 31-2=29, Resulting Numbers: [29] 29,46 unequal: No Solution Exploring Operation: 2*31=62, Resulting Numbers: [62] 62,46 unequal: No Solution Exploring Operation: 2+31=33, Resulting Numbers: [33] 33,46 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 #0,1,2 Current State: 46:[16, 17], Operations: ['55-39=16', '15+2=17'] Exploring Operation: 16*17=272, Resulting Numbers: [272] 272,46 unequal: No Solution Exploring Operation: 16+17=33, Resulting Numbers: [33] 33,46 unequal: No Solution Exploring Operation: 17-16=1, Resulting Numbers: [1] 1,46 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 No solution found.
0
hs_3
sum_heuristic
[ 64, 16, 68, 99 ]
95
[ "68-64=4", "16/4=4", "99-4=95" ]
Current State: 95:[64, 16, 68, 99], Operations: [] Exploring Operation: 68-64=4, Resulting Numbers: [16, 99, 4] Generated Node #2: [16, 99, 4] from Operation: 68-64=4 Current State: 95:[16, 99, 4], Operations: ['68-64=4'] Exploring Operation: 16/4=4, Resulting Numbers: [99, 4] Generated Node #3: [99, 4] from Operation: 16/4=4 Current State: 95:[99, 4], Operations: ['68-64=4', '16/4=4'] Exploring Operation: 99-4=95, Resulting Numbers: [95] 95,95 equal: Goal Reached
4
Current State: 95:[64, 16, 68, 99], Operations: [] Exploring Operation: 64/16=4, Resulting Numbers: [68, 99, 4] Generated Node #0,0: 95:[68, 99, 4] Operation: 64/16=4 Exploring Operation: 64+68=132, Resulting Numbers: [16, 99, 132] Generated Node #0,1: 95:[16, 99, 132] Operation: 64+68=132 Exploring Operation: 68-64=4, Resulting Numbers: [16, 99, 4] Generated Node #0,2: 95:[16, 99, 4] Operation: 68-64=4 Moving to Node #0,2 Current State: 95:[16, 99, 4], Operations: ['68-64=4'] Exploring Operation: 16+4=20, Resulting Numbers: [99, 20] Generated Node #0,2,0: 95:[99, 20] Operation: 16+4=20 Exploring Operation: 99-4=95, Resulting Numbers: [16, 95] Generated Node #0,2,1: 95:[16, 95] Operation: 99-4=95 Exploring Operation: 16/4=4, Resulting Numbers: [99, 4] Generated Node #0,2,2: 95:[99, 4] Operation: 16/4=4 Moving to Node #0,0 Current State: 95:[68, 99, 4], Operations: ['64/16=4'] Exploring Operation: 68+4=72, Resulting Numbers: [99, 72] Generated Node #0,0,0: 95:[99, 72] Operation: 68+4=72 Exploring Operation: 99-68=31, Resulting Numbers: [4, 31] Generated Node #0,0,1: 95:[4, 31] Operation: 99-68=31 Exploring Operation: 68/4=17, Resulting Numbers: [99, 17] Generated Node #0,0,2: 95:[99, 17] Operation: 68/4=17 Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 95:[99, 17], Operations: ['64/16=4', '68/4=17'] Exploring Operation: 99-17=82, Resulting Numbers: [82] 82,95 unequal: No Solution Exploring Operation: 99*17=1683, Resulting Numbers: [1683] 1683,95 unequal: No Solution Exploring Operation: 99+17=116, Resulting Numbers: [116] 116,95 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:[4, 31], Operations: ['64/16=4', '99-68=31'] Exploring Operation: 31-4=27, Resulting Numbers: [27] 27,95 unequal: No Solution Exploring Operation: 4*31=124, Resulting Numbers: [124] 124,95 unequal: No Solution Exploring Operation: 4+31=35, Resulting Numbers: [35] 35,95 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 #0,0,0 Current State: 95:[99, 72], Operations: ['64/16=4', '68+4=72'] Exploring Operation: 99*72=7128, Resulting Numbers: [7128] 7128,95 unequal: No Solution Exploring Operation: 99+72=171, Resulting Numbers: [171] 171,95 unequal: No Solution Exploring Operation: 99-72=27, Resulting Numbers: [27] 27,95 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:[16, 99, 132], Operations: ['64+68=132'] Exploring Operation: 132-16=116, Resulting Numbers: [99, 116] Generated Node #0,1,0: 95:[99, 116] Operation: 132-16=116 Exploring Operation: 99-16=83, Resulting Numbers: [132, 83] Generated Node #0,1,1: 95:[132, 83] Operation: 99-16=83 Exploring Operation: 132-99=33, Resulting Numbers: [16, 33] Generated Node #0,1,2: 95:[16, 33] Operation: 132-99=33 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 95:[16, 33], Operations: ['64+68=132', '132-99=33'] Exploring Operation: 16*33=528, Resulting Numbers: [528] 528,95 unequal: No Solution Exploring Operation: 33-16=17, Resulting Numbers: [17] 17,95 unequal: No Solution Exploring Operation: 16+33=49, Resulting Numbers: [49] 49,95 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:[99, 116], Operations: ['64+68=132', '132-16=116'] Exploring Operation: 99*116=11484, Resulting Numbers: [11484] 11484,95 unequal: No Solution Exploring Operation: 99+116=215, Resulting Numbers: [215] 215,95 unequal: No Solution Exploring Operation: 116-99=17, Resulting Numbers: [17] 17,95 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 #0,1,1 Current State: 95:[132, 83], Operations: ['64+68=132', '99-16=83'] Exploring Operation: 132+83=215, Resulting Numbers: [215] 215,95 unequal: No Solution Exploring Operation: 132*83=10956, Resulting Numbers: [10956] 10956,95 unequal: No Solution Exploring Operation: 132-83=49, Resulting Numbers: [49] 49,95 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: 95:[16, 95], Operations: ['68-64=4', '99-4=95'] Exploring Operation: 16+95=111, Resulting Numbers: [111] 111,95 unequal: No Solution Exploring Operation: 16*95=1520, Resulting Numbers: [1520] 1520,95 unequal: No Solution Exploring Operation: 95-16=79, Resulting Numbers: [79] 79,95 unequal: No Solution Moving to Node #0,2,0 Current State: 95:[99, 20], Operations: ['68-64=4', '16+4=20'] Exploring Operation: 99+20=119, Resulting Numbers: [119] 119,95 unequal: No Solution Exploring Operation: 99-20=79, Resulting Numbers: [79] 79,95 unequal: No Solution Exploring Operation: 99*20=1980, Resulting Numbers: [1980] 1980,95 unequal: No Solution Moving to Node #0,2,2 Current State: 95:[99, 4], Operations: ['68-64=4', '16/4=4'] Exploring Operation: 99-4=95, Resulting Numbers: [95] 95,95 equal: Goal Reached Moving to Node #0 Current State: 95:[64, 16, 68, 99], Operations: [] Exploring Operation: 68-64=4, Resulting Numbers: [16, 99, 4] Generated Node #0,2: 95:[16, 99, 4] Operation: 68-64=4 Moving to Node #0,2 Current State: 95:[16, 99, 4], Operations: ['68-64=4'] Exploring Operation: 16/4=4, Resulting Numbers: [99, 4] Generated Node #0,2,2: 95:[99, 4] Operation: 16/4=4 Moving to Node #0,2,2 Current State: 95:[99, 4], Operations: ['68-64=4', '16/4=4'] Exploring Operation: 99-4=95, Resulting Numbers: [95] 95,95 equal: Goal Reached
0.96441
hs_3
sum_heuristic
[ 34, 73, 26, 69 ]
82
[ "73-34=39", "69-26=43", "39+43=82" ]
Current State: 82:[34, 73, 26, 69], Operations: [] Exploring Operation: 73-34=39, Resulting Numbers: [26, 69, 39] Generated Node #2: [26, 69, 39] from Operation: 73-34=39 Current State: 82:[26, 69, 39], Operations: ['73-34=39'] Exploring Operation: 69-26=43, Resulting Numbers: [39, 43] Generated Node #3: [39, 43] from Operation: 69-26=43 Current State: 82:[39, 43], Operations: ['73-34=39', '69-26=43'] Exploring Operation: 39+43=82, Resulting Numbers: [82] 82,82 equal: Goal Reached
4
Current State: 82:[34, 73, 26, 69], Operations: [] Exploring Operation: 34-26=8, Resulting Numbers: [73, 69, 8] Generated Node #0,0: 82:[73, 69, 8] Operation: 34-26=8 Exploring Operation: 73-69=4, Resulting Numbers: [34, 26, 4] Generated Node #0,1: 82:[34, 26, 4] Operation: 73-69=4 Exploring Operation: 69-26=43, Resulting Numbers: [34, 73, 43] Generated Node #0,2: 82:[34, 73, 43] Operation: 69-26=43 Exploring Operation: 73-26=47, Resulting Numbers: [34, 69, 47] Generated Node #0,3: 82:[34, 69, 47] Operation: 73-26=47 Moving to Node #0,2 Current State: 82:[34, 73, 43], Operations: ['69-26=43'] Exploring Operation: 34+43=77, Resulting Numbers: [73, 77] Generated Node #0,2,0: 82:[73, 77] Operation: 34+43=77 Exploring Operation: 73-43=30, Resulting Numbers: [34, 30] Generated Node #0,2,1: 82:[34, 30] Operation: 73-43=30 Exploring Operation: 73-34=39, Resulting Numbers: [43, 39] Generated Node #0,2,2: 82:[43, 39] Operation: 73-34=39 Exploring Operation: 43-34=9, Resulting Numbers: [73, 9] Generated Node #0,2,3: 82:[73, 9] Operation: 43-34=9 Moving to Node #0,1 Current State: 82:[34, 26, 4], Operations: ['73-69=4'] Exploring Operation: 34-26=8, Resulting Numbers: [4, 8] Generated Node #0,1,0: 82:[4, 8] Operation: 34-26=8 Exploring Operation: 34+26=60, Resulting Numbers: [4, 60] Generated Node #0,1,1: 82:[4, 60] Operation: 34+26=60 Exploring Operation: 34+4=38, Resulting Numbers: [26, 38] Generated Node #0,1,2: 82:[26, 38] Operation: 34+4=38 Exploring Operation: 26+4=30, Resulting Numbers: [34, 30] Generated Node #0,1,3: 82:[34, 30] Operation: 26+4=30 Moving to Node #0,3 Current State: 82:[34, 69, 47], Operations: ['73-26=47'] Exploring Operation: 47-34=13, Resulting Numbers: [69, 13] Generated Node #0,3,0: 82:[69, 13] Operation: 47-34=13 Exploring Operation: 69-34=35, Resulting Numbers: [47, 35] Generated Node #0,3,1: 82:[47, 35] Operation: 69-34=35 Exploring Operation: 34+47=81, Resulting Numbers: [69, 81] Generated Node #0,3,2: 82:[69, 81] Operation: 34+47=81 Exploring Operation: 69-47=22, Resulting Numbers: [34, 22] Generated Node #0,3,3: 82:[34, 22] Operation: 69-47=22 Moving to Node #0,0 Current State: 82:[73, 69, 8], Operations: ['34-26=8'] Exploring Operation: 73-69=4, Resulting Numbers: [8, 4] Generated Node #0,0,0: 82:[8, 4] Operation: 73-69=4 Exploring Operation: 73+8=81, Resulting Numbers: [69, 81] Generated Node #0,0,1: 82:[69, 81] Operation: 73+8=81 Exploring Operation: 69-8=61, Resulting Numbers: [73, 61] Generated Node #0,0,2: 82:[73, 61] Operation: 69-8=61 Exploring Operation: 69+8=77, Resulting Numbers: [73, 77] Generated Node #0,0,3: 82:[73, 77] Operation: 69+8=77 Moving to Node #0,2,2 Current State: 82:[43, 39], Operations: ['69-26=43', '73-34=39'] Exploring Operation: 43*39=1677, Resulting Numbers: [1677] 1677,82 unequal: No Solution Exploring Operation: 43+39=82, Resulting Numbers: [82] 82,82 equal: Goal Reached Moving to Node #0 Current State: 82:[34, 73, 26, 69], Operations: [] Exploring Operation: 69-26=43, Resulting Numbers: [34, 73, 43] Generated Node #0,2: 82:[34, 73, 43] Operation: 69-26=43 Moving to Node #0,2 Current State: 82:[34, 73, 43], Operations: ['69-26=43'] Exploring Operation: 73-34=39, Resulting Numbers: [43, 39] Generated Node #0,2,2: 82:[43, 39] Operation: 73-34=39 Moving to Node #0,2,2 Current State: 82:[43, 39], Operations: ['69-26=43', '73-34=39'] Exploring Operation: 43+39=82, Resulting Numbers: [82] 82,82 equal: Goal Reached
0.977431
hs_4
sum_heuristic
[ 63, 72, 9, 36 ]
51
[ "63+72=135", "135/9=15", "36+15=51" ]
Current State: 51:[63, 72, 9, 36], Operations: [] Exploring Operation: 63+72=135, Resulting Numbers: [9, 36, 135] Generated Node #2: [9, 36, 135] from Operation: 63+72=135 Current State: 51:[9, 36, 135], Operations: ['63+72=135'] Exploring Operation: 135/9=15, Resulting Numbers: [36, 15] Generated Node #3: [36, 15] from Operation: 135/9=15 Current State: 51:[36, 15], Operations: ['63+72=135', '135/9=15'] Exploring Operation: 36+15=51, Resulting Numbers: [51] 51,51 equal: Goal Reached
4
Current State: 51:[63, 72, 9, 36], Operations: [] Exploring Operation: 72/9=8, Resulting Numbers: [63, 36, 8] Generated Node #0,0: 51:[63, 36, 8] Operation: 72/9=8 Exploring Operation: 72/36=2, Resulting Numbers: [63, 9, 2] Generated Node #0,1: 51:[63, 9, 2] Operation: 72/36=2 Exploring Operation: 72-63=9, Resulting Numbers: [9, 36, 9] Generated Node #0,2: 51:[9, 36, 9] Operation: 72-63=9 Exploring Operation: 72-36=36, Resulting Numbers: [63, 9, 36] Generated Node #0,3: 51:[63, 9, 36] Operation: 72-36=36 Moving to Node #0,1 Current State: 51:[63, 9, 2], Operations: ['72/36=2'] Exploring Operation: 63-9=54, Resulting Numbers: [2, 54] Generated Node #0,1,0: 51:[2, 54] Operation: 63-9=54 Exploring Operation: 63/9=7, Resulting Numbers: [2, 7] Generated Node #0,1,1: 51:[2, 7] Operation: 63/9=7 Exploring Operation: 9*2=18, Resulting Numbers: [63, 18] Generated Node #0,1,2: 51:[63, 18] Operation: 9*2=18 Exploring Operation: 63-2=61, Resulting Numbers: [9, 61] Generated Node #0,1,3: 51:[9, 61] Operation: 63-2=61 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 51:[2, 54], Operations: ['72/36=2', '63-9=54'] Exploring Operation: 2*54=108, Resulting Numbers: [108] 108,51 unequal: No Solution Exploring Operation: 2+54=56, Resulting Numbers: [56] 56,51 unequal: No Solution Exploring Operation: 54-2=52, Resulting Numbers: [52] 52,51 unequal: No Solution Exploring Operation: 54/2=27, Resulting Numbers: [27] 27,51 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: 51:[2, 7], Operations: ['72/36=2', '63/9=7'] Exploring Operation: 2*7=14, Resulting Numbers: [14] 14,51 unequal: No Solution Exploring Operation: 7-2=5, Resulting Numbers: [5] 5,51 unequal: No Solution Exploring Operation: 2+7=9, Resulting Numbers: [9] 9,51 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: 51:[63, 18], Operations: ['72/36=2', '9*2=18'] Exploring Operation: 63*18=1134, Resulting Numbers: [1134] 1134,51 unequal: No Solution Exploring Operation: 63-18=45, Resulting Numbers: [45] 45,51 unequal: No Solution Exploring Operation: 63+18=81, Resulting Numbers: [81] 81,51 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: 51:[9, 61], Operations: ['72/36=2', '63-2=61'] Exploring Operation: 9*61=549, Resulting Numbers: [549] 549,51 unequal: No Solution Exploring Operation: 9+61=70, Resulting Numbers: [70] 70,51 unequal: No Solution Exploring Operation: 61-9=52, Resulting Numbers: [52] 52,51 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: 51:[9, 36, 9], Operations: ['72-63=9'] Exploring Operation: 9+36=45, Resulting Numbers: [9, 45] Generated Node #0,2,0: 51:[9, 45] Operation: 9+36=45 Exploring Operation: 36/9=4, Resulting Numbers: [9, 4] Generated Node #0,2,1: 51:[9, 4] Operation: 36/9=4 Exploring Operation: 36/9=4, Resulting Numbers: [9, 4] Generated Node #0,2,2: 51:[9, 4] Operation: 36/9=4 Exploring Operation: 36+9=45, Resulting Numbers: [9, 45] Generated Node #0,2,3: 51:[9, 45] Operation: 36+9=45 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 51:[9, 4], Operations: ['72-63=9', '36/9=4'] Exploring Operation: 9+4=13, Resulting Numbers: [13] 13,51 unequal: No Solution Exploring Operation: 9*4=36, Resulting Numbers: [36] 36,51 unequal: No Solution Exploring Operation: 9-4=5, Resulting Numbers: [5] 5,51 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: 51:[9, 4], Operations: ['72-63=9', '36/9=4'] Exploring Operation: 9+4=13, Resulting Numbers: [13] 13,51 unequal: No Solution Exploring Operation: 9*4=36, Resulting Numbers: [36] 36,51 unequal: No Solution Exploring Operation: 9-4=5, Resulting Numbers: [5] 5,51 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: 51:[9, 45], Operations: ['72-63=9', '9+36=45'] Exploring Operation: 9*45=405, Resulting Numbers: [405] 405,51 unequal: No Solution Exploring Operation: 9+45=54, Resulting Numbers: [54] 54,51 unequal: No Solution Exploring Operation: 45-9=36, Resulting Numbers: [36] 36,51 unequal: No Solution Exploring Operation: 45/9=5, Resulting Numbers: [5] 5,51 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: 51:[9, 45], Operations: ['72-63=9', '36+9=45'] Exploring Operation: 45-9=36, Resulting Numbers: [36] 36,51 unequal: No Solution Exploring Operation: 9*45=405, Resulting Numbers: [405] 405,51 unequal: No Solution Exploring Operation: 45/9=5, Resulting Numbers: [5] 5,51 unequal: No Solution Exploring Operation: 9+45=54, Resulting Numbers: [54] 54,51 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: 51:[63, 36, 8], Operations: ['72/9=8'] Exploring Operation: 63-36=27, Resulting Numbers: [8, 27] Generated Node #0,0,0: 51:[8, 27] Operation: 63-36=27 Exploring Operation: 63-8=55, Resulting Numbers: [36, 55] Generated Node #0,0,1: 51:[36, 55] Operation: 63-8=55 Exploring Operation: 36-8=28, Resulting Numbers: [63, 28] Generated Node #0,0,2: 51:[63, 28] Operation: 36-8=28 Exploring Operation: 36+8=44, Resulting Numbers: [63, 44] Generated Node #0,0,3: 51:[63, 44] Operation: 36+8=44 Moving to Node #0,3 Current State: 51:[63, 9, 36], Operations: ['72-36=36'] Exploring Operation: 63-36=27, Resulting Numbers: [9, 27] Generated Node #0,3,0: 51:[9, 27] Operation: 63-36=27 Exploring Operation: 36/9=4, Resulting Numbers: [63, 4] Generated Node #0,3,1: 51:[63, 4] Operation: 36/9=4 Exploring Operation: 63-9=54, Resulting Numbers: [36, 54] Generated Node #0,3,2: 51:[36, 54] Operation: 63-9=54 Exploring Operation: 9+36=45, Resulting Numbers: [63, 45] Generated Node #0,3,3: 51:[63, 45] Operation: 9+36=45 Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 51:[63, 4], Operations: ['72-36=36', '36/9=4'] Exploring Operation: 63+4=67, Resulting Numbers: [67] 67,51 unequal: No Solution Exploring Operation: 63-4=59, Resulting Numbers: [59] 59,51 unequal: No Solution Exploring Operation: 63*4=252, Resulting Numbers: [252] 252,51 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: 51:[9, 27], Operations: ['72-36=36', '63-36=27'] Exploring Operation: 27-9=18, Resulting Numbers: [18] 18,51 unequal: No Solution Exploring Operation: 27/9=3, Resulting Numbers: [3] 3,51 unequal: No Solution Exploring Operation: 9*27=243, Resulting Numbers: [243] 243,51 unequal: No Solution Exploring Operation: 9+27=36, Resulting Numbers: [36] 36,51 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: 51:[36, 54], Operations: ['72-36=36', '63-9=54'] Exploring Operation: 54-36=18, Resulting Numbers: [18] 18,51 unequal: No Solution Exploring Operation: 36+54=90, Resulting Numbers: [90] 90,51 unequal: No Solution Exploring Operation: 36*54=1944, Resulting Numbers: [1944] 1944,51 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: 51:[63, 45], Operations: ['72-36=36', '9+36=45'] Exploring Operation: 63-45=18, Resulting Numbers: [18] 18,51 unequal: No Solution Exploring Operation: 63*45=2835, Resulting Numbers: [2835] 2835,51 unequal: No Solution Exploring Operation: 63+45=108, Resulting Numbers: [108] 108,51 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: 51:[8, 27], Operations: ['72/9=8', '63-36=27'] Exploring Operation: 8+27=35, Resulting Numbers: [35] 35,51 unequal: No Solution Exploring Operation: 8*27=216, Resulting Numbers: [216] 216,51 unequal: No Solution Exploring Operation: 27-8=19, Resulting Numbers: [19] 19,51 unequal: No Solution Moving to Node #0,0,3 Current State: 51:[63, 44], Operations: ['72/9=8', '36+8=44'] Exploring Operation: 63-44=19, Resulting Numbers: [19] 19,51 unequal: No Solution Exploring Operation: 63+44=107, Resulting Numbers: [107] 107,51 unequal: No Solution Exploring Operation: 63*44=2772, Resulting Numbers: [2772] 2772,51 unequal: No Solution Moving to Node #0,0,1 Current State: 51:[36, 55], Operations: ['72/9=8', '63-8=55'] Exploring Operation: 36*55=1980, Resulting Numbers: [1980] 1980,51 unequal: No Solution Exploring Operation: 55-36=19, Resulting Numbers: [19] 19,51 unequal: No Solution Exploring Operation: 36+55=91, Resulting Numbers: [91] 91,51 unequal: No Solution Moving to Node #0,0,2 Current State: 51:[63, 28], Operations: ['72/9=8', '36-8=28'] Exploring Operation: 63*28=1764, Resulting Numbers: [1764] 1764,51 unequal: No Solution Exploring Operation: 63+28=91, Resulting Numbers: [91] 91,51 unequal: No Solution Exploring Operation: 63-28=35, Resulting Numbers: [35] 35,51 unequal: No Solution No solution found.
0
hs_4
sum_heuristic
[ 98, 35, 2, 24 ]
41
[ "98-35=63", "24-2=22", "63-22=41" ]
Current State: 41:[98, 35, 2, 24], Operations: [] Exploring Operation: 98-35=63, Resulting Numbers: [2, 24, 63] Generated Node #2: [2, 24, 63] from Operation: 98-35=63 Current State: 41:[2, 24, 63], Operations: ['98-35=63'] Exploring Operation: 24-2=22, Resulting Numbers: [63, 22] Generated Node #3: [63, 22] from Operation: 24-2=22 Current State: 41:[63, 22], Operations: ['98-35=63', '24-2=22'] Exploring Operation: 63-22=41, Resulting Numbers: [41] 41,41 equal: Goal Reached
4
Current State: 41:[98, 35, 2, 24], Operations: [] Exploring Operation: 2*24=48, Resulting Numbers: [98, 35, 48] Generated Node #0,0: 41:[98, 35, 48] Operation: 2*24=48 Exploring Operation: 98-35=63, Resulting Numbers: [2, 24, 63] Generated Node #0,1: 41:[2, 24, 63] Operation: 98-35=63 Exploring Operation: 98/2=49, Resulting Numbers: [35, 24, 49] Generated Node #0,2: 41:[35, 24, 49] Operation: 98/2=49 Start Sub Search at level 1: Moving to Node #0,2 Current State: 41:[35, 24, 49], Operations: ['98/2=49'] Exploring Operation: 35+24=59, Resulting Numbers: [49, 59] Generated Node #0,2,0: 41:[49, 59] Operation: 35+24=59 Exploring Operation: 35-24=11, Resulting Numbers: [49, 11] Generated Node #0,2,1: 41:[49, 11] Operation: 35-24=11 Exploring Operation: 49-24=25, Resulting Numbers: [35, 25] Generated Node #0,2,2: 41:[35, 25] Operation: 49-24=25 Moving to Node #0,2,2 Current State: 41:[35, 25], Operations: ['98/2=49', '49-24=25'] Exploring Operation: 35+25=60, Resulting Numbers: [60] 60,41 unequal: No Solution Exploring Operation: 35-25=10, Resulting Numbers: [10] 10,41 unequal: No Solution Exploring Operation: 35*25=875, Resulting Numbers: [875] 875,41 unequal: No Solution Moving to Node #0,2,0 Current State: 41:[49, 59], Operations: ['98/2=49', '35+24=59'] Exploring Operation: 59-49=10, Resulting Numbers: [10] 10,41 unequal: No Solution Exploring Operation: 49*59=2891, Resulting Numbers: [2891] 2891,41 unequal: No Solution Exploring Operation: 49+59=108, Resulting Numbers: [108] 108,41 unequal: No Solution Moving to Node #0,2,1 Current State: 41:[49, 11], Operations: ['98/2=49', '35-24=11'] Exploring Operation: 49+11=60, Resulting Numbers: [60] 60,41 unequal: No Solution Exploring Operation: 49*11=539, Resulting Numbers: [539] 539,41 unequal: No Solution Exploring Operation: 49-11=38, Resulting Numbers: [38] 38,41 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: 41:[98, 35, 48], Operations: ['2*24=48'] Exploring Operation: 48-35=13, Resulting Numbers: [98, 13] Generated Node #0,0,0: 41:[98, 13] Operation: 48-35=13 Exploring Operation: 98-48=50, Resulting Numbers: [35, 50] Generated Node #0,0,1: 41:[35, 50] Operation: 98-48=50 Exploring Operation: 98-35=63, Resulting Numbers: [48, 63] Generated Node #0,0,2: 41:[48, 63] Operation: 98-35=63 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 41:[35, 50], Operations: ['2*24=48', '98-48=50'] Exploring Operation: 35*50=1750, Resulting Numbers: [1750] 1750,41 unequal: No Solution Exploring Operation: 35+50=85, Resulting Numbers: [85] 85,41 unequal: No Solution Exploring Operation: 50-35=15, Resulting Numbers: [15] 15,41 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:[48, 63], Operations: ['2*24=48', '98-35=63'] Exploring Operation: 48*63=3024, Resulting Numbers: [3024] 3024,41 unequal: No Solution Exploring Operation: 63-48=15, Resulting Numbers: [15] 15,41 unequal: No Solution Exploring Operation: 48+63=111, Resulting Numbers: [111] 111,41 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 #0,0,0 Current State: 41:[98, 13], Operations: ['2*24=48', '48-35=13'] Exploring Operation: 98-13=85, Resulting Numbers: [85] 85,41 unequal: No Solution Exploring Operation: 98+13=111, Resulting Numbers: [111] 111,41 unequal: No Solution Exploring Operation: 98*13=1274, Resulting Numbers: [1274] 1274,41 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: 41:[2, 24, 63], Operations: ['98-35=63'] Exploring Operation: 2*24=48, Resulting Numbers: [63, 48] Generated Node #0,1,0: 41:[63, 48] Operation: 2*24=48 Exploring Operation: 63-2=61, Resulting Numbers: [24, 61] Generated Node #0,1,1: 41:[24, 61] Operation: 63-2=61 Exploring Operation: 2+24=26, Resulting Numbers: [63, 26] Generated Node #0,1,2: 41:[63, 26] Operation: 2+24=26 Moving to Node #0,1,0 Current State: 41:[63, 48], Operations: ['98-35=63', '2*24=48'] Exploring Operation: 63*48=3024, Resulting Numbers: [3024] 3024,41 unequal: No Solution Exploring Operation: 63+48=111, Resulting Numbers: [111] 111,41 unequal: No Solution Exploring Operation: 63-48=15, Resulting Numbers: [15] 15,41 unequal: No Solution Moving to Node #0,1,1 Current State: 41:[24, 61], Operations: ['98-35=63', '63-2=61'] Exploring Operation: 24+61=85, Resulting Numbers: [85] 85,41 unequal: No Solution Exploring Operation: 61-24=37, Resulting Numbers: [37] 37,41 unequal: No Solution Exploring Operation: 24*61=1464, Resulting Numbers: [1464] 1464,41 unequal: No Solution Moving to Node #0,1,2 Current State: 41:[63, 26], Operations: ['98-35=63', '2+24=26'] Exploring Operation: 63+26=89, Resulting Numbers: [89] 89,41 unequal: No Solution Exploring Operation: 63*26=1638, Resulting Numbers: [1638] 1638,41 unequal: No Solution Exploring Operation: 63-26=37, Resulting Numbers: [37] 37,41 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
[ 14, 32, 16, 1 ]
15
[ "16-14=2", "32/2=16", "16-1=15" ]
Current State: 15:[14, 32, 16, 1], Operations: [] Exploring Operation: 16-14=2, Resulting Numbers: [32, 1, 2] Generated Node #2: [32, 1, 2] from Operation: 16-14=2 Current State: 15:[32, 1, 2], Operations: ['16-14=2'] Exploring Operation: 32/2=16, Resulting Numbers: [1, 16] Generated Node #3: [1, 16] from Operation: 32/2=16 Current State: 15:[1, 16], Operations: ['16-14=2', '32/2=16'] Exploring Operation: 16-1=15, Resulting Numbers: [15] 15,15 equal: Goal Reached
4
Current State: 15:[14, 32, 16, 1], Operations: [] Exploring Operation: 32-14=18, Resulting Numbers: [16, 1, 18] Generated Node #0,0: 15:[16, 1, 18] Operation: 32-14=18 Exploring Operation: 32-16=16, Resulting Numbers: [14, 1, 16] Generated Node #0,1: 15:[14, 1, 16] Operation: 32-16=16 Exploring Operation: 32/16=2, Resulting Numbers: [14, 1, 2] Generated Node #0,2: 15:[14, 1, 2] Operation: 32/16=2 Start Sub Search at level 1: Moving to Node #0,1 Current State: 15:[14, 1, 16], Operations: ['32-16=16'] Exploring Operation: 16-1=15, Resulting Numbers: [14, 15] Generated Node #0,1,0: 15:[14, 15] Operation: 16-1=15 Exploring Operation: 14*1=14, Resulting Numbers: [16, 14] Generated Node #0,1,1: 15:[16, 14] Operation: 14*1=14 Exploring Operation: 14+1=15, Resulting Numbers: [16, 15] Generated Node #0,1,2: 15:[16, 15] Operation: 14+1=15 Moving to Node #0,1,0 Current State: 15:[14, 15], Operations: ['32-16=16', '16-1=15'] Exploring Operation: 14*15=210, Resulting Numbers: [210] 210,15 unequal: No Solution Exploring Operation: 14+15=29, Resulting Numbers: [29] 29,15 unequal: No Solution Exploring Operation: 15-14=1, Resulting Numbers: [1] 1,15 unequal: No Solution Moving to Node #0,1,2 Current State: 15:[16, 15], Operations: ['32-16=16', '14+1=15'] Exploring Operation: 16-15=1, Resulting Numbers: [1] 1,15 unequal: No Solution Exploring Operation: 16+15=31, Resulting Numbers: [31] 31,15 unequal: No Solution Exploring Operation: 16*15=240, Resulting Numbers: [240] 240,15 unequal: No Solution Moving to Node #0,1,1 Current State: 15:[16, 14], Operations: ['32-16=16', '14*1=14'] Exploring Operation: 16+14=30, Resulting Numbers: [30] 30,15 unequal: No Solution Exploring Operation: 16-14=2, Resulting Numbers: [2] 2,15 unequal: No Solution Exploring Operation: 16*14=224, Resulting Numbers: [224] 224,15 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 Current State: 15:[14, 1, 2], Operations: ['32/16=2'] Exploring Operation: 14*1=14, Resulting Numbers: [2, 14] Generated Node #0,2,0: 15:[2, 14] Operation: 14*1=14 Exploring Operation: 1+2=3, Resulting Numbers: [14, 3] Generated Node #0,2,1: 15:[14, 3] Operation: 1+2=3 Exploring Operation: 14+1=15, Resulting Numbers: [2, 15] Generated Node #0,2,2: 15:[2, 15] Operation: 14+1=15 Moving to Node #0,2,1 Current State: 15:[14, 3], Operations: ['32/16=2', '1+2=3'] Exploring Operation: 14+3=17, Resulting Numbers: [17] 17,15 unequal: No Solution Exploring Operation: 14-3=11, Resulting Numbers: [11] 11,15 unequal: No Solution Exploring Operation: 14*3=42, Resulting Numbers: [42] 42,15 unequal: No Solution Moving to Node #0,2,2 Current State: 15:[2, 15], Operations: ['32/16=2', '14+1=15'] Exploring Operation: 15-2=13, Resulting Numbers: [13] 13,15 unequal: No Solution Exploring Operation: 2*15=30, Resulting Numbers: [30] 30,15 unequal: No Solution Exploring Operation: 2+15=17, Resulting Numbers: [17] 17,15 unequal: No Solution Moving to Node #0,2,0 Current State: 15:[2, 14], Operations: ['32/16=2', '14*1=14'] Exploring Operation: 14-2=12, Resulting Numbers: [12] 12,15 unequal: No Solution Exploring Operation: 2+14=16, Resulting Numbers: [16] 16,15 unequal: No Solution Exploring Operation: 14/2=7, Resulting Numbers: [7] 7,15 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 #0,0 Current State: 15:[16, 1, 18], Operations: ['32-14=18'] Exploring Operation: 16-1=15, Resulting Numbers: [18, 15] Generated Node #0,0,0: 15:[18, 15] Operation: 16-1=15 Exploring Operation: 18-16=2, Resulting Numbers: [1, 2] Generated Node #0,0,1: 15:[1, 2] Operation: 18-16=2 Exploring Operation: 18-1=17, Resulting Numbers: [16, 17] Generated Node #0,0,2: 15:[16, 17] Operation: 18-1=17 Moving to Node #0,0,0 Current State: 15:[18, 15], Operations: ['32-14=18', '16-1=15'] Exploring Operation: 18*15=270, Resulting Numbers: [270] 270,15 unequal: No Solution Exploring Operation: 18-15=3, Resulting Numbers: [3] 3,15 unequal: No Solution Exploring Operation: 18+15=33, Resulting Numbers: [33] 33,15 unequal: No Solution Moving to Node #0,0,1 Current State: 15:[1, 2], Operations: ['32-14=18', '18-16=2'] Exploring Operation: 2/1=2, Resulting Numbers: [2] 2,15 unequal: No Solution Exploring Operation: 1+2=3, Resulting Numbers: [3] 3,15 unequal: No Solution Exploring Operation: 1*2=2, Resulting Numbers: [2] 2,15 unequal: No Solution Moving to Node #0,0,2 Current State: 15:[16, 17], Operations: ['32-14=18', '18-1=17'] Exploring Operation: 16*17=272, Resulting Numbers: [272] 272,15 unequal: No Solution Exploring Operation: 17-16=1, Resulting Numbers: [1] 1,15 unequal: No Solution Exploring Operation: 16+17=33, Resulting Numbers: [33] 33,15 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
[ 70, 91, 45, 8 ]
32
[ "91-70=21", "45+8=53", "53-21=32" ]
Current State: 32:[70, 91, 45, 8], Operations: [] Exploring Operation: 91-70=21, Resulting Numbers: [45, 8, 21] Generated Node #2: [45, 8, 21] from Operation: 91-70=21 Current State: 32:[45, 8, 21], Operations: ['91-70=21'] Exploring Operation: 45+8=53, Resulting Numbers: [21, 53] Generated Node #3: [21, 53] from Operation: 45+8=53 Current State: 32:[21, 53], Operations: ['91-70=21', '45+8=53'] Exploring Operation: 53-21=32, Resulting Numbers: [32] 32,32 equal: Goal Reached
4
Current State: 32:[70, 91, 45, 8], Operations: [] Exploring Operation: 91-70=21, Resulting Numbers: [45, 8, 21] Generated Node #0,0: 32:[45, 8, 21] Operation: 91-70=21 Moving to Node #0,0 Current State: 32:[45, 8, 21], Operations: ['91-70=21'] Exploring Operation: 45-21=24, Resulting Numbers: [8, 24] Generated Node #0,0,0: 32:[8, 24] Operation: 45-21=24 Moving to Node #0,0,0 Current State: 32:[8, 24], Operations: ['91-70=21', '45-21=24'] Exploring Operation: 8+24=32, Resulting Numbers: [32] 32,32 equal: Goal Reached Moving to Node #0 Current State: 32:[70, 91, 45, 8], Operations: [] Exploring Operation: 91-70=21, Resulting Numbers: [45, 8, 21] Generated Node #0,0: 32:[45, 8, 21] Operation: 91-70=21 Moving to Node #0,0 Current State: 32:[45, 8, 21], Operations: ['91-70=21'] Exploring Operation: 45-21=24, Resulting Numbers: [8, 24] Generated Node #0,0,0: 32:[8, 24] Operation: 45-21=24 Moving to Node #0,0,0 Current State: 32:[8, 24], Operations: ['91-70=21', '45-21=24'] Exploring Operation: 8+24=32, Resulting Numbers: [32] 32,32 equal: Goal Reached
0.993924
hs_1
mult_heuristic
[ 47, 86, 35, 34 ]
40
[ "86-47=39", "35-34=1", "39+1=40" ]
Current State: 40:[47, 86, 35, 34], Operations: [] Exploring Operation: 86-47=39, Resulting Numbers: [35, 34, 39] Generated Node #2: [35, 34, 39] from Operation: 86-47=39 Current State: 40:[35, 34, 39], Operations: ['86-47=39'] Exploring Operation: 35-34=1, Resulting Numbers: [39, 1] Generated Node #3: [39, 1] from Operation: 35-34=1 Current State: 40:[39, 1], Operations: ['86-47=39', '35-34=1'] Exploring Operation: 39+1=40, Resulting Numbers: [40] 40,40 equal: Goal Reached
4
Current State: 40:[47, 86, 35, 34], Operations: [] Exploring Operation: 86-35=51, Resulting Numbers: [47, 34, 51] Generated Node #0,0: 40:[47, 34, 51] Operation: 86-35=51 Exploring Operation: 47-35=12, Resulting Numbers: [86, 34, 12] Generated Node #0,1: 40:[86, 34, 12] Operation: 47-35=12 Exploring Operation: 86-34=52, Resulting Numbers: [47, 35, 52] Generated Node #0,2: 40:[47, 35, 52] Operation: 86-34=52 Exploring Operation: 86-47=39, Resulting Numbers: [35, 34, 39] Generated Node #0,3: 40:[35, 34, 39] Operation: 86-47=39 Start Sub Search at level 1: Moving to Node #0,3 Current State: 40:[35, 34, 39], Operations: ['86-47=39'] Exploring Operation: 35+34=69, Resulting Numbers: [39, 69] Generated Node #0,3,0: 40:[39, 69] Operation: 35+34=69 Exploring Operation: 39-35=4, Resulting Numbers: [34, 4] Generated Node #0,3,1: 40:[34, 4] Operation: 39-35=4 Exploring Operation: 35-34=1, Resulting Numbers: [39, 1] Generated Node #0,3,2: 40:[39, 1] Operation: 35-34=1 Exploring Operation: 39-34=5, Resulting Numbers: [35, 5] Generated Node #0,3,3: 40:[35, 5] Operation: 39-34=5 Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 40:[39, 1], Operations: ['86-47=39', '35-34=1'] Exploring Operation: 39-1=38, Resulting Numbers: [38] 38,40 unequal: No Solution Exploring Operation: 39+1=40, Resulting Numbers: [40] 40,40 equal: Goal Reached Moving to Node #0 Current State: 40:[47, 86, 35, 34], Operations: [] Exploring Operation: 86-47=39, Resulting Numbers: [35, 34, 39] Generated Node #0,3: 40:[35, 34, 39] Operation: 86-47=39 Moving to Node #0,3 Current State: 40:[35, 34, 39], Operations: ['86-47=39'] Exploring Operation: 35-34=1, Resulting Numbers: [39, 1] Generated Node #0,3,2: 40:[39, 1] Operation: 35-34=1 Moving to Node #0,3,2 Current State: 40:[39, 1], Operations: ['86-47=39', '35-34=1'] Exploring Operation: 39+1=40, Resulting Numbers: [40] 40,40 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.987847
hs_4
sum_heuristic
[ 41, 66, 91, 20 ]
22
[ "41+91=132", "132/66=2", "20+2=22" ]
Current State: 22:[41, 66, 91, 20], Operations: [] Exploring Operation: 41+91=132, Resulting Numbers: [66, 20, 132] Generated Node #2: [66, 20, 132] from Operation: 41+91=132 Current State: 22:[66, 20, 132], Operations: ['41+91=132'] Exploring Operation: 132/66=2, Resulting Numbers: [20, 2] Generated Node #3: [20, 2] from Operation: 132/66=2 Current State: 22:[20, 2], Operations: ['41+91=132', '132/66=2'] Exploring Operation: 20+2=22, Resulting Numbers: [22] 22,22 equal: Goal Reached
4
Current State: 22:[41, 66, 91, 20], Operations: [] Exploring Operation: 91-66=25, Resulting Numbers: [41, 20, 25] Generated Node #0,0: 22:[41, 20, 25] Operation: 91-66=25 Exploring Operation: 66-41=25, Resulting Numbers: [91, 20, 25] Generated Node #0,1: 22:[91, 20, 25] Operation: 66-41=25 Start Sub Search at level 1: Moving to Node #0,0 Current State: 22:[41, 20, 25], Operations: ['91-66=25'] Exploring Operation: 41-25=16, Resulting Numbers: [20, 16] Generated Node #0,0,0: 22:[20, 16] Operation: 41-25=16 Exploring Operation: 41-20=21, Resulting Numbers: [25, 21] Generated Node #0,0,1: 22:[25, 21] Operation: 41-20=21 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 22:[25, 21], Operations: ['91-66=25', '41-20=21'] Exploring Operation: 25+21=46, Resulting Numbers: [46] 46,22 unequal: No Solution Exploring Operation: 25-21=4, Resulting Numbers: [4] 4,22 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: 22:[20, 16], Operations: ['91-66=25', '41-25=16'] Exploring Operation: 20-16=4, Resulting Numbers: [4] 4,22 unequal: No Solution Exploring Operation: 20+16=36, Resulting Numbers: [36] 36,22 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: 22:[91, 20, 25], Operations: ['66-41=25'] Exploring Operation: 91-20=71, Resulting Numbers: [25, 71] Generated Node #0,1,0: 22:[25, 71] Operation: 91-20=71 Exploring Operation: 91-25=66, Resulting Numbers: [20, 66] Generated Node #0,1,1: 22:[20, 66] Operation: 91-25=66 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 22:[20, 66], Operations: ['66-41=25', '91-25=66'] Exploring Operation: 20+66=86, Resulting Numbers: [86] 86,22 unequal: No Solution Exploring Operation: 66-20=46, Resulting Numbers: [46] 46,22 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: 22:[25, 71], Operations: ['66-41=25', '91-20=71'] Exploring Operation: 25+71=96, Resulting Numbers: [96] 96,22 unequal: No Solution Exploring Operation: 71-25=46, Resulting Numbers: [46] 46,22 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
[ 85, 33, 34, 6 ]
17
[ "34-33=1", "6-1=5", "85/5=17" ]
Current State: 17:[85, 33, 34, 6], Operations: [] Exploring Operation: 34-33=1, Resulting Numbers: [85, 6, 1] Generated Node #2: [85, 6, 1] from Operation: 34-33=1 Current State: 17:[85, 6, 1], Operations: ['34-33=1'] Exploring Operation: 6-1=5, Resulting Numbers: [85, 5] Generated Node #3: [85, 5] from Operation: 6-1=5 Current State: 17:[85, 5], Operations: ['34-33=1', '6-1=5'] Exploring Operation: 85/5=17, Resulting Numbers: [17] 17,17 equal: Goal Reached
4
Current State: 17:[85, 33, 34, 6], Operations: [] Exploring Operation: 85-33=52, Resulting Numbers: [34, 6, 52] Generated Node #0,0: 17:[34, 6, 52] Operation: 85-33=52 Exploring Operation: 85-34=51, Resulting Numbers: [33, 6, 51] Generated Node #0,1: 17:[33, 6, 51] Operation: 85-34=51 Moving to Node #0,1 Current State: 17:[33, 6, 51], Operations: ['85-34=51'] Exploring Operation: 51-33=18, Resulting Numbers: [6, 18] Generated Node #0,1,0: 17:[6, 18] Operation: 51-33=18 Exploring Operation: 33-6=27, Resulting Numbers: [51, 27] Generated Node #0,1,1: 17:[51, 27] Operation: 33-6=27 Moving to Node #0,0 Current State: 17:[34, 6, 52], Operations: ['85-33=52'] Exploring Operation: 34-6=28, Resulting Numbers: [52, 28] Generated Node #0,0,0: 17:[52, 28] Operation: 34-6=28 Exploring Operation: 52-34=18, Resulting Numbers: [6, 18] Generated Node #0,0,1: 17:[6, 18] Operation: 52-34=18 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 17:[6, 18], Operations: ['85-33=52', '52-34=18'] Exploring Operation: 6+18=24, Resulting Numbers: [24] 24,17 unequal: No Solution Exploring Operation: 18-6=12, Resulting Numbers: [12] 12,17 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 #0,0,0 Current State: 17:[52, 28], Operations: ['85-33=52', '34-6=28'] Exploring Operation: 52+28=80, Resulting Numbers: [80] 80,17 unequal: No Solution Exploring Operation: 52-28=24, Resulting Numbers: [24] 24,17 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: 17:[6, 18], Operations: ['85-34=51', '51-33=18'] Exploring Operation: 18-6=12, Resulting Numbers: [12] 12,17 unequal: No Solution Exploring Operation: 6+18=24, Resulting Numbers: [24] 24,17 unequal: No Solution Moving to Node #0,1,1 Current State: 17:[51, 27], Operations: ['85-34=51', '33-6=27'] Exploring Operation: 51+27=78, Resulting Numbers: [78] 78,17 unequal: No Solution Exploring Operation: 51-27=24, Resulting Numbers: [24] 24,17 unequal: No Solution No solution found.
0
hs_2
sum_heuristic
[ 94, 35, 45, 86 ]
39
[ "94+86=180", "180/45=4", "35+4=39" ]
Current State: 39:[94, 35, 45, 86], Operations: [] Exploring Operation: 94+86=180, Resulting Numbers: [35, 45, 180] Generated Node #2: [35, 45, 180] from Operation: 94+86=180 Current State: 39:[35, 45, 180], Operations: ['94+86=180'] Exploring Operation: 180/45=4, Resulting Numbers: [35, 4] Generated Node #3: [35, 4] from Operation: 180/45=4 Current State: 39:[35, 4], Operations: ['94+86=180', '180/45=4'] Exploring Operation: 35+4=39, Resulting Numbers: [39] 39,39 equal: Goal Reached
4
Current State: 39:[94, 35, 45, 86], Operations: [] Exploring Operation: 94-86=8, Resulting Numbers: [35, 45, 8] Generated Node #0,0: 39:[35, 45, 8] Operation: 94-86=8 Moving to Node #0,0 Current State: 39:[35, 45, 8], Operations: ['94-86=8'] Exploring Operation: 45-8=37, Resulting Numbers: [35, 37] Generated Node #0,0,0: 39:[35, 37] Operation: 45-8=37 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 39:[35, 37], Operations: ['94-86=8', '45-8=37'] Exploring Operation: 37-35=2, Resulting Numbers: [2] 2,39 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
[ 35, 29, 21, 67 ]
59
[ "35-29=6", "21*6=126", "126-67=59" ]
Current State: 59:[35, 29, 21, 67], Operations: [] Exploring Operation: 35-29=6, Resulting Numbers: [21, 67, 6] Generated Node #2: [21, 67, 6] from Operation: 35-29=6 Current State: 59:[21, 67, 6], Operations: ['35-29=6'] Exploring Operation: 21*6=126, Resulting Numbers: [67, 126] Generated Node #3: [67, 126] from Operation: 21*6=126 Current State: 59:[67, 126], Operations: ['35-29=6', '21*6=126'] Exploring Operation: 126-67=59, Resulting Numbers: [59] 59,59 equal: Goal Reached
4
Current State: 59:[35, 29, 21, 67], Operations: [] Exploring Operation: 29+21=50, Resulting Numbers: [35, 67, 50] Generated Node #0,0: 59:[35, 67, 50] Operation: 29+21=50 Exploring Operation: 35+21=56, Resulting Numbers: [29, 67, 56] Generated Node #0,1: 59:[29, 67, 56] Operation: 35+21=56 Exploring Operation: 35+29=64, Resulting Numbers: [21, 67, 64] Generated Node #0,2: 59:[21, 67, 64] Operation: 35+29=64 Moving to Node #0,0 Current State: 59:[35, 67, 50], Operations: ['29+21=50'] Exploring Operation: 35+50=85, Resulting Numbers: [67, 85] Generated Node #0,0,0: 59:[67, 85] Operation: 35+50=85 Exploring Operation: 67-35=32, Resulting Numbers: [50, 32] Generated Node #0,0,1: 59:[50, 32] Operation: 67-35=32 Exploring Operation: 35+67=102, Resulting Numbers: [50, 102] Generated Node #0,0,2: 59:[50, 102] Operation: 35+67=102 Moving to Node #0,1 Current State: 59:[29, 67, 56], Operations: ['35+21=56'] Exploring Operation: 29+67=96, Resulting Numbers: [56, 96] Generated Node #0,1,0: 59:[56, 96] Operation: 29+67=96 Exploring Operation: 29+56=85, Resulting Numbers: [67, 85] Generated Node #0,1,1: 59:[67, 85] Operation: 29+56=85 Exploring Operation: 67-29=38, Resulting Numbers: [56, 38] Generated Node #0,1,2: 59:[56, 38] Operation: 67-29=38 Moving to Node #0,2 Current State: 59:[21, 67, 64], Operations: ['35+29=64'] Exploring Operation: 64-21=43, Resulting Numbers: [67, 43] Generated Node #0,2,0: 59:[67, 43] Operation: 64-21=43 Exploring Operation: 21+67=88, Resulting Numbers: [64, 88] Generated Node #0,2,1: 59:[64, 88] Operation: 21+67=88 Exploring Operation: 67-21=46, Resulting Numbers: [64, 46] Generated Node #0,2,2: 59:[64, 46] Operation: 67-21=46 Moving to Node #0,2,2 Current State: 59:[64, 46], Operations: ['35+29=64', '67-21=46'] Exploring Operation: 64+46=110, Resulting Numbers: [110] 110,59 unequal: No Solution Exploring Operation: 64-46=18, Resulting Numbers: [18] 18,59 unequal: No Solution Exploring Operation: 64*46=2944, Resulting Numbers: [2944] 2944,59 unequal: No Solution Moving to Node #0,1,2 Current State: 59:[56, 38], Operations: ['35+21=56', '67-29=38'] Exploring Operation: 56+38=94, Resulting Numbers: [94] 94,59 unequal: No Solution Exploring Operation: 56-38=18, Resulting Numbers: [18] 18,59 unequal: No Solution Exploring Operation: 56*38=2128, Resulting Numbers: [2128] 2128,59 unequal: No Solution Moving to Node #0,2,0 Current State: 59:[67, 43], Operations: ['35+29=64', '64-21=43'] Exploring Operation: 67*43=2881, Resulting Numbers: [2881] 2881,59 unequal: No Solution Exploring Operation: 67-43=24, Resulting Numbers: [24] 24,59 unequal: No Solution Exploring Operation: 67+43=110, Resulting Numbers: [110] 110,59 unequal: No Solution Moving to Node #0,2,1 Current State: 59:[64, 88], Operations: ['35+29=64', '21+67=88'] Exploring Operation: 88-64=24, Resulting Numbers: [24] 24,59 unequal: No Solution Exploring Operation: 64+88=152, Resulting Numbers: [152] 152,59 unequal: No Solution Exploring Operation: 64*88=5632, Resulting Numbers: [5632] 5632,59 unequal: No Solution Moving to Node #0,1,1 Current State: 59:[67, 85], Operations: ['35+21=56', '29+56=85'] Exploring Operation: 67+85=152, Resulting Numbers: [152] 152,59 unequal: No Solution Exploring Operation: 85-67=18, Resulting Numbers: [18] 18,59 unequal: No Solution Exploring Operation: 67*85=5695, Resulting Numbers: [5695] 5695,59 unequal: No Solution Moving to Node #0,0,0 Current State: 59:[67, 85], Operations: ['29+21=50', '35+50=85'] Exploring Operation: 67+85=152, Resulting Numbers: [152] 152,59 unequal: No Solution Exploring Operation: 85-67=18, Resulting Numbers: [18] 18,59 unequal: No Solution Exploring Operation: 67*85=5695, Resulting Numbers: [5695] 5695,59 unequal: No Solution Moving to Node #0,0,1 Current State: 59:[50, 32], Operations: ['29+21=50', '67-35=32'] Exploring Operation: 50+32=82, Resulting Numbers: [82] 82,59 unequal: No Solution Exploring Operation: 50*32=1600, Resulting Numbers: [1600] 1600,59 unequal: No Solution Exploring Operation: 50-32=18, Resulting Numbers: [18] 18,59 unequal: No Solution Moving to Node #0,1,0 Current State: 59:[56, 96], Operations: ['35+21=56', '29+67=96'] Exploring Operation: 56+96=152, Resulting Numbers: [152] 152,59 unequal: No Solution Exploring Operation: 56*96=5376, Resulting Numbers: [5376] 5376,59 unequal: No Solution Exploring Operation: 96-56=40, Resulting Numbers: [40] 40,59 unequal: No Solution Moving to Node #0,0,2 Current State: 59:[50, 102], Operations: ['29+21=50', '35+67=102'] Exploring Operation: 50*102=5100, Resulting Numbers: [5100] 5100,59 unequal: No Solution Exploring Operation: 50+102=152, Resulting Numbers: [152] 152,59 unequal: No Solution Exploring Operation: 102-50=52, Resulting Numbers: [52] 52,59 unequal: No Solution No solution found.
0
hs_3
mult_heuristic
[ 90, 31, 25, 18 ]
87
[ "31-25=6", "18/6=3", "90-3=87" ]
Current State: 87:[90, 31, 25, 18], Operations: [] Exploring Operation: 31-25=6, Resulting Numbers: [90, 18, 6] Generated Node #2: [90, 18, 6] from Operation: 31-25=6 Current State: 87:[90, 18, 6], Operations: ['31-25=6'] Exploring Operation: 18/6=3, Resulting Numbers: [90, 3] Generated Node #3: [90, 3] from Operation: 18/6=3 Current State: 87:[90, 3], Operations: ['31-25=6', '18/6=3'] Exploring Operation: 90-3=87, Resulting Numbers: [87] 87,87 equal: Goal Reached
4
Current State: 87:[90, 31, 25, 18], Operations: [] Exploring Operation: 25-18=7, Resulting Numbers: [90, 31, 7] Generated Node #0,0: 87:[90, 31, 7] Operation: 25-18=7 Exploring Operation: 31-25=6, Resulting Numbers: [90, 18, 6] Generated Node #0,1: 87:[90, 18, 6] Operation: 31-25=6 Exploring Operation: 31-18=13, Resulting Numbers: [90, 25, 13] Generated Node #0,2: 87:[90, 25, 13] Operation: 31-18=13 Exploring Operation: 90/18=5, Resulting Numbers: [31, 25, 5] Generated Node #0,3: 87:[31, 25, 5] Operation: 90/18=5 Moving to Node #0,3 Current State: 87:[31, 25, 5], Operations: ['90/18=5'] Exploring Operation: 31-5=26, Resulting Numbers: [25, 26] Generated Node #0,3,0: 87:[25, 26] Operation: 31-5=26 Exploring Operation: 31-25=6, Resulting Numbers: [5, 6] Generated Node #0,3,1: 87:[5, 6] Operation: 31-25=6 Exploring Operation: 25+5=30, Resulting Numbers: [31, 30] Generated Node #0,3,2: 87:[31, 30] Operation: 25+5=30 Exploring Operation: 25/5=5, Resulting Numbers: [31, 5] Generated Node #0,3,3: 87:[31, 5] Operation: 25/5=5 Moving to Node #0,0 Current State: 87:[90, 31, 7], Operations: ['25-18=7'] Exploring Operation: 31+7=38, Resulting Numbers: [90, 38] Generated Node #0,0,0: 87:[90, 38] Operation: 31+7=38 Exploring Operation: 90-7=83, Resulting Numbers: [31, 83] Generated Node #0,0,1: 87:[31, 83] Operation: 90-7=83 Exploring Operation: 90+7=97, Resulting Numbers: [31, 97] Generated Node #0,0,2: 87:[31, 97] Operation: 90+7=97 Exploring Operation: 31-7=24, Resulting Numbers: [90, 24] Generated Node #0,0,3: 87:[90, 24] Operation: 31-7=24 Moving to Node #0,2 Current State: 87:[90, 25, 13], Operations: ['31-18=13'] Exploring Operation: 90+13=103, Resulting Numbers: [25, 103] Generated Node #0,2,0: 87:[25, 103] Operation: 90+13=103 Exploring Operation: 90-13=77, Resulting Numbers: [25, 77] Generated Node #0,2,1: 87:[25, 77] Operation: 90-13=77 Exploring Operation: 25+13=38, Resulting Numbers: [90, 38] Generated Node #0,2,2: 87:[90, 38] Operation: 25+13=38 Exploring Operation: 25-13=12, Resulting Numbers: [90, 12] Generated Node #0,2,3: 87:[90, 12] Operation: 25-13=12 Moving to Node #0,1 Current State: 87:[90, 18, 6], Operations: ['31-25=6'] Exploring Operation: 90/18=5, Resulting Numbers: [6, 5] Generated Node #0,1,0: 87:[6, 5] Operation: 90/18=5 Exploring Operation: 18-6=12, Resulting Numbers: [90, 12] Generated Node #0,1,1: 87:[90, 12] Operation: 18-6=12 Exploring Operation: 18+6=24, Resulting Numbers: [90, 24] Generated Node #0,1,2: 87:[90, 24] Operation: 18+6=24 Exploring Operation: 18/6=3, Resulting Numbers: [90, 3] Generated Node #0,1,3: 87:[90, 3] Operation: 18/6=3 Moving to Node #0,3,2 Current State: 87:[31, 30], Operations: ['90/18=5', '25+5=30'] Exploring Operation: 31+30=61, Resulting Numbers: [61] 61,87 unequal: No Solution Exploring Operation: 31*30=930, Resulting Numbers: [930] 930,87 unequal: No Solution Exploring Operation: 31-30=1, Resulting Numbers: [1] 1,87 unequal: No Solution Moving to Node #0,1,3 Current State: 87:[90, 3], Operations: ['31-25=6', '18/6=3'] Exploring Operation: 90+3=93, Resulting Numbers: [93] 93,87 unequal: No Solution Exploring Operation: 90/3=30, Resulting Numbers: [30] 30,87 unequal: No Solution Exploring Operation: 90*3=270, Resulting Numbers: [270] 270,87 unequal: No Solution Exploring Operation: 90-3=87, Resulting Numbers: [87] 87,87 equal: Goal Reached Moving to Node #0 Current State: 87:[90, 31, 25, 18], Operations: [] Exploring Operation: 31-25=6, Resulting Numbers: [90, 18, 6] Generated Node #0,1: 87:[90, 18, 6] Operation: 31-25=6 Moving to Node #0,1 Current State: 87:[90, 18, 6], Operations: ['31-25=6'] Exploring Operation: 18/6=3, Resulting Numbers: [90, 3] Generated Node #0,1,3: 87:[90, 3] Operation: 18/6=3 Moving to Node #0,1,3 Current State: 87:[90, 3], Operations: ['31-25=6', '18/6=3'] Exploring Operation: 90-3=87, Resulting Numbers: [87] 87,87 equal: Goal Reached
0.97309
hs_4
sum_heuristic
[ 77, 18, 2, 20 ]
93
[ "77-20=57", "18*2=36", "57+36=93" ]
Current State: 93:[77, 18, 2, 20], Operations: [] Exploring Operation: 77-20=57, Resulting Numbers: [18, 2, 57] Generated Node #2: [18, 2, 57] from Operation: 77-20=57 Current State: 93:[18, 2, 57], Operations: ['77-20=57'] Exploring Operation: 18*2=36, Resulting Numbers: [57, 36] Generated Node #3: [57, 36] from Operation: 18*2=36 Current State: 93:[57, 36], Operations: ['77-20=57', '18*2=36'] Exploring Operation: 57+36=93, Resulting Numbers: [93] 93,93 equal: Goal Reached
4
Current State: 93:[77, 18, 2, 20], Operations: [] Exploring Operation: 77+18=95, Resulting Numbers: [2, 20, 95] Generated Node #0,0: 93:[2, 20, 95] Operation: 77+18=95 Exploring Operation: 77+20=97, Resulting Numbers: [18, 2, 97] Generated Node #0,1: 93:[18, 2, 97] Operation: 77+20=97 Moving to Node #0,0 Current State: 93:[2, 20, 95], Operations: ['77+18=95'] Exploring Operation: 20/2=10, Resulting Numbers: [95, 10] Generated Node #0,0,0: 93:[95, 10] Operation: 20/2=10 Exploring Operation: 2+20=22, Resulting Numbers: [95, 22] Generated Node #0,0,1: 93:[95, 22] Operation: 2+20=22 Moving to Node #0,1 Current State: 93:[18, 2, 97], Operations: ['77+20=97'] Exploring Operation: 18/2=9, Resulting Numbers: [97, 9] Generated Node #0,1,0: 93:[97, 9] Operation: 18/2=9 Exploring Operation: 18*2=36, Resulting Numbers: [97, 36] Generated Node #0,1,1: 93:[97, 36] Operation: 18*2=36 Moving to Node #0,0,0 Current State: 93:[95, 10], Operations: ['77+18=95', '20/2=10'] Exploring Operation: 95+10=105, Resulting Numbers: [105] 105,93 unequal: No Solution Exploring Operation: 95-10=85, Resulting Numbers: [85] 85,93 unequal: No Solution Moving to Node #0,1,1 Current State: 93:[97, 36], Operations: ['77+20=97', '18*2=36'] Exploring Operation: 97-36=61, Resulting Numbers: [61] 61,93 unequal: No Solution Exploring Operation: 97+36=133, Resulting Numbers: [133] 133,93 unequal: No Solution Moving to Node #0,1,0 Current State: 93:[97, 9], Operations: ['77+20=97', '18/2=9'] Exploring Operation: 97-9=88, Resulting Numbers: [88] 88,93 unequal: No Solution Exploring Operation: 97+9=106, Resulting Numbers: [106] 106,93 unequal: No Solution Moving to Node #0,0,1 Current State: 93:[95, 22], Operations: ['77+18=95', '2+20=22'] Exploring Operation: 95-22=73, Resulting Numbers: [73] 73,93 unequal: No Solution Exploring Operation: 95+22=117, Resulting Numbers: [117] 117,93 unequal: No Solution No solution found.
0
hs_2
sum_heuristic
[ 23, 64, 4, 48 ]
92
[ "64-48=16", "23*16=368", "368/4=92" ]
Current State: 92:[23, 64, 4, 48], Operations: [] Exploring Operation: 64-48=16, Resulting Numbers: [23, 4, 16] Generated Node #2: [23, 4, 16] from Operation: 64-48=16 Current State: 92:[23, 4, 16], Operations: ['64-48=16'] Exploring Operation: 23*16=368, Resulting Numbers: [4, 368] Generated Node #3: [4, 368] from Operation: 23*16=368 Current State: 92:[4, 368], Operations: ['64-48=16', '23*16=368'] Exploring Operation: 368/4=92, Resulting Numbers: [92] 92,92 equal: Goal Reached
4
Current State: 92:[23, 64, 4, 48], Operations: [] Exploring Operation: 23+64=87, Resulting Numbers: [4, 48, 87] Generated Node #0,0: 92:[4, 48, 87] Operation: 23+64=87 Exploring Operation: 64-48=16, Resulting Numbers: [23, 4, 16] Generated Node #0,1: 92:[23, 4, 16] Operation: 64-48=16 Exploring Operation: 64-23=41, Resulting Numbers: [4, 48, 41] Generated Node #0,2: 92:[4, 48, 41] Operation: 64-23=41 Moving to Node #0,0 Current State: 92:[4, 48, 87], Operations: ['23+64=87'] Exploring Operation: 4+87=91, Resulting Numbers: [48, 91] Generated Node #0,0,0: 92:[48, 91] Operation: 4+87=91 Exploring Operation: 48-4=44, Resulting Numbers: [87, 44] Generated Node #0,0,1: 92:[87, 44] Operation: 48-4=44 Exploring Operation: 87-48=39, Resulting Numbers: [4, 39] Generated Node #0,0,2: 92:[4, 39] Operation: 87-48=39 Moving to Node #0,1 Current State: 92:[23, 4, 16], Operations: ['64-48=16'] Exploring Operation: 16/4=4, Resulting Numbers: [23, 4] Generated Node #0,1,0: 92:[23, 4] Operation: 16/4=4 Exploring Operation: 4+16=20, Resulting Numbers: [23, 20] Generated Node #0,1,1: 92:[23, 20] Operation: 4+16=20 Exploring Operation: 23-16=7, Resulting Numbers: [4, 7] Generated Node #0,1,2: 92:[4, 7] Operation: 23-16=7 Moving to Node #0,2 Current State: 92:[4, 48, 41], Operations: ['64-23=41'] Exploring Operation: 4+41=45, Resulting Numbers: [48, 45] Generated Node #0,2,0: 92:[48, 45] Operation: 4+41=45 Exploring Operation: 48+41=89, Resulting Numbers: [4, 89] Generated Node #0,2,1: 92:[4, 89] Operation: 48+41=89 Exploring Operation: 48-41=7, Resulting Numbers: [4, 7] Generated Node #0,2,2: 92:[4, 7] Operation: 48-41=7 Moving to Node #0,1,0 Current State: 92:[23, 4], Operations: ['64-48=16', '16/4=4'] Exploring Operation: 23*4=92, Resulting Numbers: [92] 92,92 equal: Goal Reached Moving to Node #0 Current State: 92:[23, 64, 4, 48], Operations: [] Exploring Operation: 64-48=16, Resulting Numbers: [23, 4, 16] Generated Node #0,1: 92:[23, 4, 16] Operation: 64-48=16 Moving to Node #0,1 Current State: 92:[23, 4, 16], Operations: ['64-48=16'] Exploring Operation: 16/4=4, Resulting Numbers: [23, 4] Generated Node #0,1,0: 92:[23, 4] Operation: 16/4=4 Moving to Node #0,1,0 Current State: 92:[23, 4], Operations: ['64-48=16', '16/4=4'] Exploring Operation: 23*4=92, Resulting Numbers: [92] 92,92 equal: Goal Reached
0.985243
hs_3
mult_heuristic
[ 42, 32, 38, 89 ]
53
[ "42+32=74", "38+89=127", "127-74=53" ]
Current State: 53:[42, 32, 38, 89], Operations: [] Exploring Operation: 42+32=74, Resulting Numbers: [38, 89, 74] Generated Node #2: [38, 89, 74] from Operation: 42+32=74 Current State: 53:[38, 89, 74], Operations: ['42+32=74'] Exploring Operation: 38+89=127, Resulting Numbers: [74, 127] Generated Node #3: [74, 127] from Operation: 38+89=127 Current State: 53:[74, 127], Operations: ['42+32=74', '38+89=127'] Exploring Operation: 127-74=53, Resulting Numbers: [53] 53,53 equal: Goal Reached
4
Current State: 53:[42, 32, 38, 89], Operations: [] Exploring Operation: 89-38=51, Resulting Numbers: [42, 32, 51] Generated Node #0,0: 53:[42, 32, 51] Operation: 89-38=51 Exploring Operation: 89-32=57, Resulting Numbers: [42, 38, 57] Generated Node #0,1: 53:[42, 38, 57] Operation: 89-32=57 Exploring Operation: 89-42=47, Resulting Numbers: [32, 38, 47] Generated Node #0,2: 53:[32, 38, 47] Operation: 89-42=47 Moving to Node #0,1 Current State: 53:[42, 38, 57], Operations: ['89-32=57'] Exploring Operation: 57-38=19, Resulting Numbers: [42, 19] Generated Node #0,1,0: 53:[42, 19] Operation: 57-38=19 Exploring Operation: 42+38=80, Resulting Numbers: [57, 80] Generated Node #0,1,1: 53:[57, 80] Operation: 42+38=80 Exploring Operation: 42-38=4, Resulting Numbers: [57, 4] Generated Node #0,1,2: 53:[57, 4] Operation: 42-38=4 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 53:[57, 80], Operations: ['89-32=57', '42+38=80'] Exploring Operation: 57+80=137, Resulting Numbers: [137] 137,53 unequal: No Solution Exploring Operation: 57*80=4560, Resulting Numbers: [4560] 4560,53 unequal: No Solution Exploring Operation: 80-57=23, Resulting Numbers: [23] 23,53 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: 53:[42, 19], Operations: ['89-32=57', '57-38=19'] Exploring Operation: 42-19=23, Resulting Numbers: [23] 23,53 unequal: No Solution Exploring Operation: 42*19=798, Resulting Numbers: [798] 798,53 unequal: No Solution Exploring Operation: 42+19=61, Resulting Numbers: [61] 61,53 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: 53:[57, 4], Operations: ['89-32=57', '42-38=4'] Exploring Operation: 57+4=61, Resulting Numbers: [61] 61,53 unequal: No Solution Exploring Operation: 57-4=53, Resulting Numbers: [53] 53,53 equal: Goal Reached Moving to Node #0 Current State: 53:[42, 32, 38, 89], Operations: [] Exploring Operation: 89-32=57, Resulting Numbers: [42, 38, 57] Generated Node #0,1: 53:[42, 38, 57] Operation: 89-32=57 Moving to Node #0,1 Current State: 53:[42, 38, 57], Operations: ['89-32=57'] Exploring Operation: 42-38=4, Resulting Numbers: [57, 4] Generated Node #0,1,2: 53:[57, 4] Operation: 42-38=4 Moving to Node #0,1,2 Current State: 53:[57, 4], Operations: ['89-32=57', '42-38=4'] Exploring Operation: 57-4=53, Resulting Numbers: [53] 53,53 equal: Goal Reached Exit Sub Search at level 1
0.984375
hs_3
sum_heuristic
[ 8, 61, 95, 63 ]
99
[ "63-61=2", "8/2=4", "95+4=99" ]
Current State: 99:[8, 61, 95, 63], Operations: [] Exploring Operation: 63-61=2, Resulting Numbers: [8, 95, 2] Generated Node #2: [8, 95, 2] from Operation: 63-61=2 Current State: 99:[8, 95, 2], Operations: ['63-61=2'] Exploring Operation: 8/2=4, Resulting Numbers: [95, 4] Generated Node #3: [95, 4] from Operation: 8/2=4 Current State: 99:[95, 4], Operations: ['63-61=2', '8/2=4'] Exploring Operation: 95+4=99, Resulting Numbers: [99] 99,99 equal: Goal Reached
4
Current State: 99:[8, 61, 95, 63], Operations: [] Exploring Operation: 95-61=34, Resulting Numbers: [8, 63, 34] Generated Node #0,0: 99:[8, 63, 34] Operation: 95-61=34 Exploring Operation: 95-63=32, Resulting Numbers: [8, 61, 32] Generated Node #0,1: 99:[8, 61, 32] Operation: 95-63=32 Exploring Operation: 63-61=2, Resulting Numbers: [8, 95, 2] Generated Node #0,2: 99:[8, 95, 2] Operation: 63-61=2 Exploring Operation: 61+63=124, Resulting Numbers: [8, 95, 124] Generated Node #0,3: 99:[8, 95, 124] Operation: 61+63=124 Moving to Node #0,2 Current State: 99:[8, 95, 2], Operations: ['63-61=2'] Exploring Operation: 95+2=97, Resulting Numbers: [8, 97] Generated Node #0,2,0: 99:[8, 97] Operation: 95+2=97 Exploring Operation: 8+2=10, Resulting Numbers: [95, 10] Generated Node #0,2,1: 99:[95, 10] Operation: 8+2=10 Exploring Operation: 8+95=103, Resulting Numbers: [2, 103] Generated Node #0,2,2: 99:[2, 103] Operation: 8+95=103 Exploring Operation: 8/2=4, Resulting Numbers: [95, 4] Generated Node #0,2,3: 99:[95, 4] Operation: 8/2=4 Moving to Node #0,3 Current State: 99:[8, 95, 124], Operations: ['61+63=124'] Exploring Operation: 95-8=87, Resulting Numbers: [124, 87] Generated Node #0,3,0: 99:[124, 87] Operation: 95-8=87 Exploring Operation: 8+95=103, Resulting Numbers: [124, 103] Generated Node #0,3,1: 99:[124, 103] Operation: 8+95=103 Exploring Operation: 124-95=29, Resulting Numbers: [8, 29] Generated Node #0,3,2: 99:[8, 29] Operation: 124-95=29 Exploring Operation: 124-8=116, Resulting Numbers: [95, 116] Generated Node #0,3,3: 99:[95, 116] Operation: 124-8=116 Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 99:[8, 29], Operations: ['61+63=124', '124-95=29'] Exploring Operation: 8+29=37, Resulting Numbers: [37] 37,99 unequal: No Solution Exploring Operation: 29-8=21, Resulting Numbers: [21] 21,99 unequal: No Solution Exploring Operation: 8*29=232, Resulting Numbers: [232] 232,99 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 #0,3,3 Current State: 99:[95, 116], Operations: ['61+63=124', '124-8=116'] Exploring Operation: 95*116=11020, Resulting Numbers: [11020] 11020,99 unequal: No Solution Exploring Operation: 116-95=21, Resulting Numbers: [21] 21,99 unequal: No Solution Exploring Operation: 95+116=211, Resulting Numbers: [211] 211,99 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 #0,3,1 Current State: 99:[124, 103], Operations: ['61+63=124', '8+95=103'] Exploring Operation: 124+103=227, Resulting Numbers: [227] 227,99 unequal: No Solution Exploring Operation: 124-103=21, Resulting Numbers: [21] 21,99 unequal: No Solution Exploring Operation: 124*103=12772, Resulting Numbers: [12772] 12772,99 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 #0,3,0 Current State: 99:[124, 87], Operations: ['61+63=124', '95-8=87'] Exploring Operation: 124-87=37, Resulting Numbers: [37] 37,99 unequal: No Solution Exploring Operation: 124*87=10788, Resulting Numbers: [10788] 10788,99 unequal: No Solution Exploring Operation: 124+87=211, Resulting Numbers: [211] 211,99 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: 99:[8, 61, 32], Operations: ['95-63=32'] Exploring Operation: 61-32=29, Resulting Numbers: [8, 29] Generated Node #0,1,0: 99:[8, 29] Operation: 61-32=29 Exploring Operation: 32/8=4, Resulting Numbers: [61, 4] Generated Node #0,1,1: 99:[61, 4] Operation: 32/8=4 Exploring Operation: 61+32=93, Resulting Numbers: [8, 93] Generated Node #0,1,2: 99:[8, 93] Operation: 61+32=93 Exploring Operation: 61-8=53, Resulting Numbers: [32, 53] Generated Node #0,1,3: 99:[32, 53] Operation: 61-8=53 Moving to Node #0,0 Current State: 99:[8, 63, 34], Operations: ['95-61=34'] Exploring Operation: 8+63=71, Resulting Numbers: [34, 71] Generated Node #0,0,0: 99:[34, 71] Operation: 8+63=71 Exploring Operation: 63-8=55, Resulting Numbers: [34, 55] Generated Node #0,0,1: 99:[34, 55] Operation: 63-8=55 Exploring Operation: 63-34=29, Resulting Numbers: [8, 29] Generated Node #0,0,2: 99:[8, 29] Operation: 63-34=29 Exploring Operation: 63+34=97, Resulting Numbers: [8, 97] Generated Node #0,0,3: 99:[8, 97] Operation: 63+34=97 Moving to Node #0,2,0 Current State: 99:[8, 97], Operations: ['63-61=2', '95+2=97'] Exploring Operation: 8*97=776, Resulting Numbers: [776] 776,99 unequal: No Solution Exploring Operation: 8+97=105, Resulting Numbers: [105] 105,99 unequal: No Solution Exploring Operation: 97-8=89, Resulting Numbers: [89] 89,99 unequal: No Solution Moving to Node #0,0,3 Current State: 99:[8, 97], Operations: ['95-61=34', '63+34=97'] Exploring Operation: 97-8=89, Resulting Numbers: [89] 89,99 unequal: No Solution Exploring Operation: 8+97=105, Resulting Numbers: [105] 105,99 unequal: No Solution Exploring Operation: 8*97=776, Resulting Numbers: [776] 776,99 unequal: No Solution Moving to Node #0,2,2 Current State: 99:[2, 103], Operations: ['63-61=2', '8+95=103'] Exploring Operation: 2*103=206, Resulting Numbers: [206] 206,99 unequal: No Solution Exploring Operation: 103-2=101, Resulting Numbers: [101] 101,99 unequal: No Solution Exploring Operation: 2+103=105, Resulting Numbers: [105] 105,99 unequal: No Solution Moving to Node #0,1,0 Current State: 99:[8, 29], Operations: ['95-63=32', '61-32=29'] Exploring Operation: 8*29=232, Resulting Numbers: [232] 232,99 unequal: No Solution Exploring Operation: 29-8=21, Resulting Numbers: [21] 21,99 unequal: No Solution Exploring Operation: 8+29=37, Resulting Numbers: [37] 37,99 unequal: No Solution Moving to Node #0,0,2 Current State: 99:[8, 29], Operations: ['95-61=34', '63-34=29'] Exploring Operation: 8+29=37, Resulting Numbers: [37] 37,99 unequal: No Solution Exploring Operation: 29-8=21, Resulting Numbers: [21] 21,99 unequal: No Solution Exploring Operation: 8*29=232, Resulting Numbers: [232] 232,99 unequal: No Solution Moving to Node #0,2,1 Current State: 99:[95, 10], Operations: ['63-61=2', '8+2=10'] Exploring Operation: 95-10=85, Resulting Numbers: [85] 85,99 unequal: No Solution Exploring Operation: 95+10=105, Resulting Numbers: [105] 105,99 unequal: No Solution Exploring Operation: 95*10=950, Resulting Numbers: [950] 950,99 unequal: No Solution Moving to Node #0,2,3 Current State: 99:[95, 4], Operations: ['63-61=2', '8/2=4'] Exploring Operation: 95*4=380, Resulting Numbers: [380] 380,99 unequal: No Solution Exploring Operation: 95-4=91, Resulting Numbers: [91] 91,99 unequal: No Solution Exploring Operation: 95+4=99, Resulting Numbers: [99] 99,99 equal: Goal Reached Moving to Node #0 Current State: 99:[8, 61, 95, 63], Operations: [] Exploring Operation: 63-61=2, Resulting Numbers: [8, 95, 2] Generated Node #0,2: 99:[8, 95, 2] Operation: 63-61=2 Moving to Node #0,2 Current State: 99:[8, 95, 2], Operations: ['63-61=2'] Exploring Operation: 8/2=4, Resulting Numbers: [95, 4] Generated Node #0,2,3: 99:[95, 4] Operation: 8/2=4 Moving to Node #0,2,3 Current State: 99:[95, 4], Operations: ['63-61=2', '8/2=4'] Exploring Operation: 95+4=99, Resulting Numbers: [99] 99,99 equal: Goal Reached
0.950521
hs_4
sum_heuristic
[ 98, 38, 98, 88 ]
88
[ "98-98=0", "38*0=0", "88+0=88" ]
Current State: 88:[98, 38, 98, 88], Operations: [] Exploring Operation: 98-98=0, Resulting Numbers: [38, 88, 0] Generated Node #2: [38, 88, 0] from Operation: 98-98=0 Current State: 88:[38, 88, 0], Operations: ['98-98=0'] Exploring Operation: 38*0=0, Resulting Numbers: [88, 0] Generated Node #3: [88, 0] from Operation: 38*0=0 Current State: 88:[88, 0], Operations: ['98-98=0', '38*0=0'] Exploring Operation: 88+0=88, Resulting Numbers: [88] 88,88 equal: Goal Reached
4
Current State: 88:[98, 38, 98, 88], Operations: [] Exploring Operation: 98-98=0, Resulting Numbers: [38, 88, 0] Generated Node #0,0: 88:[38, 88, 0] Operation: 98-98=0 Exploring Operation: 98-88=10, Resulting Numbers: [38, 98, 10] Generated Node #0,1: 88:[38, 98, 10] Operation: 98-88=10 Exploring Operation: 98/98=1, Resulting Numbers: [38, 88, 1] Generated Node #0,2: 88:[38, 88, 1] Operation: 98/98=1 Exploring Operation: 98-38=60, Resulting Numbers: [98, 88, 60] Generated Node #0,3: 88:[98, 88, 60] Operation: 98-38=60 Exploring Operation: 98-88=10, Resulting Numbers: [98, 38, 10] Generated Node #0,4: 88:[98, 38, 10] Operation: 98-88=10 Start Sub Search at level 1: Moving to Node #0,2 Current State: 88:[38, 88, 1], Operations: ['98/98=1'] Exploring Operation: 38+1=39, Resulting Numbers: [88, 39] Generated Node #0,2,0: 88:[88, 39] Operation: 38+1=39 Exploring Operation: 38/1=38, Resulting Numbers: [88, 38] Generated Node #0,2,1: 88:[88, 38] Operation: 38/1=38 Exploring Operation: 88/1=88, Resulting Numbers: [38, 88] Generated Node #0,2,2: 88:[38, 88] Operation: 88/1=88 Exploring Operation: 38*1=38, Resulting Numbers: [88, 38] Generated Node #0,2,3: 88:[88, 38] Operation: 38*1=38 Exploring Operation: 88*1=88, Resulting Numbers: [38, 88] Generated Node #0,2,4: 88:[38, 88] Operation: 88*1=88 Moving to Node #0,2,0 Current State: 88:[88, 39], Operations: ['98/98=1', '38+1=39'] Exploring Operation: 88+39=127, Resulting Numbers: [127] 127,88 unequal: No Solution Exploring Operation: 88*39=3432, Resulting Numbers: [3432] 3432,88 unequal: No Solution Exploring Operation: 88-39=49, Resulting Numbers: [49] 49,88 unequal: No Solution Moving to Node #0,2,2 Current State: 88:[38, 88], Operations: ['98/98=1', '88/1=88'] Exploring Operation: 38*88=3344, Resulting Numbers: [3344] 3344,88 unequal: No Solution Exploring Operation: 38+88=126, Resulting Numbers: [126] 126,88 unequal: No Solution Exploring Operation: 88-38=50, Resulting Numbers: [50] 50,88 unequal: No Solution Moving to Node #0,2,4 Current State: 88:[38, 88], Operations: ['98/98=1', '88*1=88'] Exploring Operation: 38+88=126, Resulting Numbers: [126] 126,88 unequal: No Solution Exploring Operation: 38*88=3344, Resulting Numbers: [3344] 3344,88 unequal: No Solution Exploring Operation: 88-38=50, Resulting Numbers: [50] 50,88 unequal: No Solution Moving to Node #0,2,1 Current State: 88:[88, 38], Operations: ['98/98=1', '38/1=38'] Exploring Operation: 88+38=126, Resulting Numbers: [126] 126,88 unequal: No Solution Exploring Operation: 88*38=3344, Resulting Numbers: [3344] 3344,88 unequal: No Solution Exploring Operation: 88-38=50, Resulting Numbers: [50] 50,88 unequal: No Solution Moving to Node #0,2,3 Current State: 88:[88, 38], Operations: ['98/98=1', '38*1=38'] Exploring Operation: 88+38=126, Resulting Numbers: [126] 126,88 unequal: No Solution Exploring Operation: 88-38=50, Resulting Numbers: [50] 50,88 unequal: No Solution Exploring Operation: 88*38=3344, Resulting Numbers: [3344] 3344,88 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: 88:[38, 88, 0], Operations: ['98-98=0'] Exploring Operation: 88-0=88, Resulting Numbers: [38, 88] Generated Node #0,0,0: 88:[38, 88] Operation: 88-0=88 Exploring Operation: 38+0=38, Resulting Numbers: [88, 38] Generated Node #0,0,1: 88:[88, 38] Operation: 38+0=38 Exploring Operation: 38*0=0, Resulting Numbers: [88, 0] Generated Node #0,0,2: 88:[88, 0] Operation: 38*0=0 Exploring Operation: 88+0=88, Resulting Numbers: [38, 88] Generated Node #0,0,3: 88:[38, 88] Operation: 88+0=88 Exploring Operation: 38-0=38, Resulting Numbers: [88, 38] Generated Node #0,0,4: 88:[88, 38] Operation: 38-0=38 Moving to Node #0,0,2 Current State: 88:[88, 0], Operations: ['98-98=0', '38*0=0'] Exploring Operation: 88*0=0, Resulting Numbers: [0] 0,88 unequal: No Solution Exploring Operation: 88+0=88, Resulting Numbers: [88] 88,88 equal: Goal Reached Moving to Node #0 Current State: 88:[98, 38, 98, 88], Operations: [] Exploring Operation: 98-98=0, Resulting Numbers: [38, 88, 0] Generated Node #0,0: 88:[38, 88, 0] Operation: 98-98=0 Moving to Node #0,0 Current State: 88:[38, 88, 0], Operations: ['98-98=0'] Exploring Operation: 38*0=0, Resulting Numbers: [88, 0] Generated Node #0,0,2: 88:[88, 0] Operation: 38*0=0 Moving to Node #0,0,2 Current State: 88:[88, 0], Operations: ['98-98=0', '38*0=0'] Exploring Operation: 88+0=88, Resulting Numbers: [88] 88,88 equal: Goal Reached Exit Sub Search at level 1
0.96875
hs_5
sum_heuristic
[ 45, 73, 67, 69 ]
19
[ "45+69=114", "73-67=6", "114/6=19" ]
Current State: 19:[45, 73, 67, 69], Operations: [] Exploring Operation: 45+69=114, Resulting Numbers: [73, 67, 114] Generated Node #2: [73, 67, 114] from Operation: 45+69=114 Current State: 19:[73, 67, 114], Operations: ['45+69=114'] Exploring Operation: 73-67=6, Resulting Numbers: [114, 6] Generated Node #3: [114, 6] from Operation: 73-67=6 Current State: 19:[114, 6], Operations: ['45+69=114', '73-67=6'] Exploring Operation: 114/6=19, Resulting Numbers: [19] 19,19 equal: Goal Reached
4
Current State: 19:[45, 73, 67, 69], Operations: [] Exploring Operation: 73-69=4, Resulting Numbers: [45, 67, 4] Generated Node #0,0: 19:[45, 67, 4] Operation: 73-69=4 Exploring Operation: 73-67=6, Resulting Numbers: [45, 69, 6] Generated Node #0,1: 19:[45, 69, 6] Operation: 73-67=6 Start Sub Search at level 1: Moving to Node #0,0 Current State: 19:[45, 67, 4], Operations: ['73-69=4'] Exploring Operation: 67-45=22, Resulting Numbers: [4, 22] Generated Node #0,0,0: 19:[4, 22] Operation: 67-45=22 Exploring Operation: 45-4=41, Resulting Numbers: [67, 41] Generated Node #0,0,1: 19:[67, 41] Operation: 45-4=41 Moving to Node #0,0,0 Current State: 19:[4, 22], Operations: ['73-69=4', '67-45=22'] Exploring Operation: 4+22=26, Resulting Numbers: [26] 26,19 unequal: No Solution Exploring Operation: 22-4=18, Resulting Numbers: [18] 18,19 unequal: No Solution Moving to Node #0,0,1 Current State: 19:[67, 41], Operations: ['73-69=4', '45-4=41'] Exploring Operation: 67+41=108, Resulting Numbers: [108] 108,19 unequal: No Solution Exploring Operation: 67-41=26, Resulting Numbers: [26] 26,19 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: 19:[45, 69, 6], Operations: ['73-67=6'] Exploring Operation: 69-45=24, Resulting Numbers: [6, 24] Generated Node #0,1,0: 19:[6, 24] Operation: 69-45=24 Exploring Operation: 45-6=39, Resulting Numbers: [69, 39] Generated Node #0,1,1: 19:[69, 39] Operation: 45-6=39 Moving to Node #0,1,0 Current State: 19:[6, 24], Operations: ['73-67=6', '69-45=24'] Exploring Operation: 24-6=18, Resulting Numbers: [18] 18,19 unequal: No Solution Exploring Operation: 6+24=30, Resulting Numbers: [30] 30,19 unequal: No Solution Moving to Node #0,1,1 Current State: 19:[69, 39], Operations: ['73-67=6', '45-6=39'] Exploring Operation: 69+39=108, Resulting Numbers: [108] 108,19 unequal: No Solution Exploring Operation: 69-39=30, Resulting Numbers: [30] 30,19 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
[ 72, 8, 86, 2 ]
75
[ "72-8=64", "86+64=150", "150/2=75" ]
Current State: 75:[72, 8, 86, 2], Operations: [] Exploring Operation: 72-8=64, Resulting Numbers: [86, 2, 64] Generated Node #2: [86, 2, 64] from Operation: 72-8=64 Current State: 75:[86, 2, 64], Operations: ['72-8=64'] Exploring Operation: 86+64=150, Resulting Numbers: [2, 150] Generated Node #3: [2, 150] from Operation: 86+64=150 Current State: 75:[2, 150], Operations: ['72-8=64', '86+64=150'] Exploring Operation: 150/2=75, Resulting Numbers: [75] 75,75 equal: Goal Reached
4
Current State: 75:[72, 8, 86, 2], Operations: [] Exploring Operation: 86-8=78, Resulting Numbers: [72, 2, 78] Generated Node #0,0: 75:[72, 2, 78] Operation: 86-8=78 Exploring Operation: 8-2=6, Resulting Numbers: [72, 86, 6] Generated Node #0,1: 75:[72, 86, 6] Operation: 8-2=6 Exploring Operation: 8*2=16, Resulting Numbers: [72, 86, 16] Generated Node #0,2: 75:[72, 86, 16] Operation: 8*2=16 Exploring Operation: 72+2=74, Resulting Numbers: [8, 86, 74] Generated Node #0,3: 75:[8, 86, 74] Operation: 72+2=74 Exploring Operation: 86-72=14, Resulting Numbers: [8, 2, 14] Generated Node #0,4: 75:[8, 2, 14] Operation: 86-72=14 Moving to Node #0,4 Current State: 75:[8, 2, 14], Operations: ['86-72=14'] Exploring Operation: 8*2=16, Resulting Numbers: [14, 16] Generated Node #0,4,0: 75:[14, 16] Operation: 8*2=16 Exploring Operation: 8+14=22, Resulting Numbers: [2, 22] Generated Node #0,4,1: 75:[2, 22] Operation: 8+14=22 Exploring Operation: 8/2=4, Resulting Numbers: [14, 4] Generated Node #0,4,2: 75:[14, 4] Operation: 8/2=4 Exploring Operation: 8-2=6, Resulting Numbers: [14, 6] Generated Node #0,4,3: 75:[14, 6] Operation: 8-2=6 Exploring Operation: 14-8=6, Resulting Numbers: [2, 6] Generated Node #0,4,4: 75:[2, 6] Operation: 14-8=6 Start Sub Search at level 1: Moving to Node #0,4,0 Current State: 75:[14, 16], Operations: ['86-72=14', '8*2=16'] Exploring Operation: 14*16=224, Resulting Numbers: [224] 224,75 unequal: No Solution Exploring Operation: 16-14=2, Resulting Numbers: [2] 2,75 unequal: No Solution Exploring Operation: 14+16=30, Resulting Numbers: [30] 30,75 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: 75:[14, 4], Operations: ['86-72=14', '8/2=4'] Exploring Operation: 14-4=10, Resulting Numbers: [10] 10,75 unequal: No Solution Exploring Operation: 14+4=18, Resulting Numbers: [18] 18,75 unequal: No Solution Exploring Operation: 14*4=56, Resulting Numbers: [56] 56,75 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: 75:[14, 6], Operations: ['86-72=14', '8-2=6'] Exploring Operation: 14*6=84, Resulting Numbers: [84] 84,75 unequal: No Solution Exploring Operation: 14-6=8, Resulting Numbers: [8] 8,75 unequal: No Solution Exploring Operation: 14+6=20, Resulting Numbers: [20] 20,75 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: 75:[2, 6], Operations: ['86-72=14', '14-8=6'] Exploring Operation: 6/2=3, Resulting Numbers: [3] 3,75 unequal: No Solution Exploring Operation: 2+6=8, Resulting Numbers: [8] 8,75 unequal: No Solution Exploring Operation: 2*6=12, Resulting Numbers: [12] 12,75 unequal: No Solution Exploring Operation: 6-2=4, Resulting Numbers: [4] 4,75 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: 75:[2, 22], Operations: ['86-72=14', '8+14=22'] Exploring Operation: 2*22=44, Resulting Numbers: [44] 44,75 unequal: No Solution Exploring Operation: 22/2=11, Resulting Numbers: [11] 11,75 unequal: No Solution Exploring Operation: 22-2=20, Resulting Numbers: [20] 20,75 unequal: No Solution Exploring Operation: 2+22=24, Resulting Numbers: [24] 24,75 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: 75:[72, 2, 78], Operations: ['86-8=78'] Exploring Operation: 78-2=76, Resulting Numbers: [72, 76] Generated Node #0,0,0: 75:[72, 76] Operation: 78-2=76 Exploring Operation: 72-2=70, Resulting Numbers: [78, 70] Generated Node #0,0,1: 75:[78, 70] Operation: 72-2=70 Exploring Operation: 2+78=80, Resulting Numbers: [72, 80] Generated Node #0,0,2: 75:[72, 80] Operation: 2+78=80 Exploring Operation: 72+2=74, Resulting Numbers: [78, 74] Generated Node #0,0,3: 75:[78, 74] Operation: 72+2=74 Exploring Operation: 78-72=6, Resulting Numbers: [2, 6] Generated Node #0,0,4: 75:[2, 6] Operation: 78-72=6 Moving to Node #0,1 Current State: 75:[72, 86, 6], Operations: ['8-2=6'] Exploring Operation: 72/6=12, Resulting Numbers: [86, 12] Generated Node #0,1,0: 75:[86, 12] Operation: 72/6=12 Exploring Operation: 86-72=14, Resulting Numbers: [6, 14] Generated Node #0,1,1: 75:[6, 14] Operation: 86-72=14 Exploring Operation: 72+6=78, Resulting Numbers: [86, 78] Generated Node #0,1,2: 75:[86, 78] Operation: 72+6=78 Exploring Operation: 86-6=80, Resulting Numbers: [72, 80] Generated Node #0,1,3: 75:[72, 80] Operation: 86-6=80 Exploring Operation: 72-6=66, Resulting Numbers: [86, 66] Generated Node #0,1,4: 75:[86, 66] Operation: 72-6=66 Moving to Node #0,2 Current State: 75:[72, 86, 16], Operations: ['8*2=16'] Exploring Operation: 86-16=70, Resulting Numbers: [72, 70] Generated Node #0,2,0: 75:[72, 70] Operation: 86-16=70 Exploring Operation: 72-16=56, Resulting Numbers: [86, 56] Generated Node #0,2,1: 75:[86, 56] Operation: 72-16=56 Exploring Operation: 86-72=14, Resulting Numbers: [16, 14] Generated Node #0,2,2: 75:[16, 14] Operation: 86-72=14 Exploring Operation: 86+16=102, Resulting Numbers: [72, 102] Generated Node #0,2,3: 75:[72, 102] Operation: 86+16=102 Exploring Operation: 72+16=88, Resulting Numbers: [86, 88] Generated Node #0,2,4: 75:[86, 88] Operation: 72+16=88 Moving to Node #0,3 Current State: 75:[8, 86, 74], Operations: ['72+2=74'] Exploring Operation: 8+86=94, Resulting Numbers: [74, 94] Generated Node #0,3,0: 75:[74, 94] Operation: 8+86=94 Exploring Operation: 86-74=12, Resulting Numbers: [8, 12] Generated Node #0,3,1: 75:[8, 12] Operation: 86-74=12 Exploring Operation: 74-8=66, Resulting Numbers: [86, 66] Generated Node #0,3,2: 75:[86, 66] Operation: 74-8=66 Exploring Operation: 8+74=82, Resulting Numbers: [86, 82] Generated Node #0,3,3: 75:[86, 82] Operation: 8+74=82 Exploring Operation: 86-8=78, Resulting Numbers: [74, 78] Generated Node #0,3,4: 75:[74, 78] Operation: 86-8=78 Start Sub Search at level 1: Moving to Node #0,3,4 Current State: 75:[74, 78], Operations: ['72+2=74', '86-8=78'] Exploring Operation: 74*78=5772, Resulting Numbers: [5772] 5772,75 unequal: No Solution Exploring Operation: 74+78=152, Resulting Numbers: [152] 152,75 unequal: No Solution Exploring Operation: 78-74=4, Resulting Numbers: [4] 4,75 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: 75:[8, 12], Operations: ['72+2=74', '86-74=12'] Exploring Operation: 8+12=20, Resulting Numbers: [20] 20,75 unequal: No Solution Exploring Operation: 12-8=4, Resulting Numbers: [4] 4,75 unequal: No Solution Exploring Operation: 8*12=96, Resulting Numbers: [96] 96,75 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: 75:[86, 82], Operations: ['72+2=74', '8+74=82'] Exploring Operation: 86*82=7052, Resulting Numbers: [7052] 7052,75 unequal: No Solution Exploring Operation: 86+82=168, Resulting Numbers: [168] 168,75 unequal: No Solution Exploring Operation: 86-82=4, Resulting Numbers: [4] 4,75 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: 75:[74, 94], Operations: ['72+2=74', '8+86=94'] Exploring Operation: 74*94=6956, Resulting Numbers: [6956] 6956,75 unequal: No Solution Exploring Operation: 74+94=168, Resulting Numbers: [168] 168,75 unequal: No Solution Exploring Operation: 94-74=20, Resulting Numbers: [20] 20,75 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: 75:[86, 66], Operations: ['72+2=74', '74-8=66'] Exploring Operation: 86*66=5676, Resulting Numbers: [5676] 5676,75 unequal: No Solution Exploring Operation: 86+66=152, Resulting Numbers: [152] 152,75 unequal: No Solution Exploring Operation: 86-66=20, Resulting Numbers: [20] 20,75 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0,4 Current State: 75:[2, 6], Operations: ['86-8=78', '78-72=6'] Exploring Operation: 6-2=4, Resulting Numbers: [4] 4,75 unequal: No Solution Exploring Operation: 6/2=3, Resulting Numbers: [3] 3,75 unequal: No Solution Exploring Operation: 2+6=8, Resulting Numbers: [8] 8,75 unequal: No Solution Exploring Operation: 2*6=12, Resulting Numbers: [12] 12,75 unequal: No Solution Moving to Node #0,1,1 Current State: 75:[6, 14], Operations: ['8-2=6', '86-72=14'] Exploring Operation: 14-6=8, Resulting Numbers: [8] 8,75 unequal: No Solution Exploring Operation: 6+14=20, Resulting Numbers: [20] 20,75 unequal: No Solution Exploring Operation: 6*14=84, Resulting Numbers: [84] 84,75 unequal: No Solution Moving to Node #0,2,2 Current State: 75:[16, 14], Operations: ['8*2=16', '86-72=14'] Exploring Operation: 16*14=224, Resulting Numbers: [224] 224,75 unequal: No Solution Exploring Operation: 16-14=2, Resulting Numbers: [2] 2,75 unequal: No Solution Exploring Operation: 16+14=30, Resulting Numbers: [30] 30,75 unequal: No Solution Moving to Node #0,0,3 Current State: 75:[78, 74], Operations: ['86-8=78', '72+2=74'] Exploring Operation: 78-74=4, Resulting Numbers: [4] 4,75 unequal: No Solution Exploring Operation: 78*74=5772, Resulting Numbers: [5772] 5772,75 unequal: No Solution Exploring Operation: 78+74=152, Resulting Numbers: [152] 152,75 unequal: No Solution Moving to Node #0,0,0 Current State: 75:[72, 76], Operations: ['86-8=78', '78-2=76'] Exploring Operation: 76-72=4, Resulting Numbers: [4] 4,75 unequal: No Solution Exploring Operation: 72+76=148, Resulting Numbers: [148] 148,75 unequal: No Solution Exploring Operation: 72*76=5472, Resulting Numbers: [5472] 5472,75 unequal: No Solution Moving to Node #0,1,3 Current State: 75:[72, 80], Operations: ['8-2=6', '86-6=80'] Exploring Operation: 80-72=8, Resulting Numbers: [8] 8,75 unequal: No Solution Exploring Operation: 72*80=5760, Resulting Numbers: [5760] 5760,75 unequal: No Solution Exploring Operation: 72+80=152, Resulting Numbers: [152] 152,75 unequal: No Solution Moving to Node #0,2,0 Current State: 75:[72, 70], Operations: ['8*2=16', '86-16=70'] Exploring Operation: 72*70=5040, Resulting Numbers: [5040] 5040,75 unequal: No Solution Exploring Operation: 72-70=2, Resulting Numbers: [2] 2,75 unequal: No Solution Exploring Operation: 72+70=142, Resulting Numbers: [142] 142,75 unequal: No Solution Moving to Node #0,0,2 Current State: 75:[72, 80], Operations: ['86-8=78', '2+78=80'] Exploring Operation: 72+80=152, Resulting Numbers: [152] 152,75 unequal: No Solution Exploring Operation: 72*80=5760, Resulting Numbers: [5760] 5760,75 unequal: No Solution Exploring Operation: 80-72=8, Resulting Numbers: [8] 8,75 unequal: No Solution Moving to Node #0,0,1 Current State: 75:[78, 70], Operations: ['86-8=78', '72-2=70'] Exploring Operation: 78+70=148, Resulting Numbers: [148] 148,75 unequal: No Solution Exploring Operation: 78*70=5460, Resulting Numbers: [5460] 5460,75 unequal: No Solution Exploring Operation: 78-70=8, Resulting Numbers: [8] 8,75 unequal: No Solution Moving to Node #0,1,0 Current State: 75:[86, 12], Operations: ['8-2=6', '72/6=12'] Exploring Operation: 86*12=1032, Resulting Numbers: [1032] 1032,75 unequal: No Solution Exploring Operation: 86+12=98, Resulting Numbers: [98] 98,75 unequal: No Solution Exploring Operation: 86-12=74, Resulting Numbers: [74] 74,75 unequal: No Solution Moving to Node #0,1,2 Current State: 75:[86, 78], Operations: ['8-2=6', '72+6=78'] Exploring Operation: 86+78=164, Resulting Numbers: [164] 164,75 unequal: No Solution Exploring Operation: 86*78=6708, Resulting Numbers: [6708] 6708,75 unequal: No Solution Exploring Operation: 86-78=8, Resulting Numbers: [8] 8,75 unequal: No Solution Moving to Node #0,1,4 Current State: 75:[86, 66], Operations: ['8-2=6', '72-6=66'] Exploring Operation: 86-66=20, Resulting Numbers: [20] 20,75 unequal: No Solution Exploring Operation: 86+66=152, Resulting Numbers: [152] 152,75 unequal: No Solution Exploring Operation: 86*66=5676, Resulting Numbers: [5676] 5676,75 unequal: No Solution Moving to Node #0,2,4 Current State: 75:[86, 88], Operations: ['8*2=16', '72+16=88'] Exploring Operation: 86*88=7568, Resulting Numbers: [7568] 7568,75 unequal: No Solution Exploring Operation: 86+88=174, Resulting Numbers: [174] 174,75 unequal: No Solution Exploring Operation: 88-86=2, Resulting Numbers: [2] 2,75 unequal: No Solution Moving to Node #0,2,3 Current State: 75:[72, 102], Operations: ['8*2=16', '86+16=102'] Exploring Operation: 72+102=174, Resulting Numbers: [174] 174,75 unequal: No Solution Exploring Operation: 102-72=30, Resulting Numbers: [30] 30,75 unequal: No Solution Exploring Operation: 72*102=7344, Resulting Numbers: [7344] 7344,75 unequal: No Solution Moving to Node #0,2,1 Current State: 75:[86, 56], Operations: ['8*2=16', '72-16=56'] Exploring Operation: 86-56=30, Resulting Numbers: [30] 30,75 unequal: No Solution Exploring Operation: 86*56=4816, Resulting Numbers: [4816] 4816,75 unequal: No Solution Exploring Operation: 86+56=142, Resulting Numbers: [142] 142,75 unequal: No Solution No solution found.
0
hs_5
sum_heuristic
[ 25, 65, 53, 99 ]
86
[ "65-25=40", "99-53=46", "40+46=86" ]
Current State: 86:[25, 65, 53, 99], Operations: [] Exploring Operation: 65-25=40, Resulting Numbers: [53, 99, 40] Generated Node #2: [53, 99, 40] from Operation: 65-25=40 Current State: 86:[53, 99, 40], Operations: ['65-25=40'] Exploring Operation: 99-53=46, Resulting Numbers: [40, 46] Generated Node #3: [40, 46] from Operation: 99-53=46 Current State: 86:[40, 46], Operations: ['65-25=40', '99-53=46'] Exploring Operation: 40+46=86, Resulting Numbers: [86] 86,86 equal: Goal Reached
4
Current State: 86:[25, 65, 53, 99], Operations: [] Exploring Operation: 65-25=40, Resulting Numbers: [53, 99, 40] Generated Node #0,0: 86:[53, 99, 40] Operation: 65-25=40 Moving to Node #0,0 Current State: 86:[53, 99, 40], Operations: ['65-25=40'] Exploring Operation: 99-53=46, Resulting Numbers: [40, 46] Generated Node #0,0,0: 86:[40, 46] Operation: 99-53=46 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 86:[40, 46], Operations: ['65-25=40', '99-53=46'] Exploring Operation: 40+46=86, Resulting Numbers: [86] 86,86 equal: Goal Reached Moving to Node #0 Current State: 86:[25, 65, 53, 99], Operations: [] Exploring Operation: 65-25=40, Resulting Numbers: [53, 99, 40] Generated Node #0,0: 86:[53, 99, 40] Operation: 65-25=40 Moving to Node #0,0 Current State: 86:[53, 99, 40], Operations: ['65-25=40'] Exploring Operation: 99-53=46, Resulting Numbers: [40, 46] Generated Node #0,0,0: 86:[40, 46] Operation: 99-53=46 Moving to Node #0,0,0 Current State: 86:[40, 46], Operations: ['65-25=40', '99-53=46'] Exploring Operation: 40+46=86, Resulting Numbers: [86] 86,86 equal: Goal Reached Exit Sub Search at level 1
0.993924
hs_1
mult_heuristic
[ 7, 11, 14, 4 ]
84
[ "7*4=28", "14-11=3", "28*3=84" ]
Current State: 84:[7, 11, 14, 4], Operations: [] Exploring Operation: 7*4=28, Resulting Numbers: [11, 14, 28] Generated Node #2: [11, 14, 28] from Operation: 7*4=28 Current State: 84:[11, 14, 28], Operations: ['7*4=28'] Exploring Operation: 14-11=3, Resulting Numbers: [28, 3] Generated Node #3: [28, 3] from Operation: 14-11=3 Current State: 84:[28, 3], Operations: ['7*4=28', '14-11=3'] Exploring Operation: 28*3=84, Resulting Numbers: [84] 84,84 equal: Goal Reached
4
Current State: 84:[7, 11, 14, 4], Operations: [] Exploring Operation: 11-7=4, Resulting Numbers: [14, 4, 4] Generated Node #0,0: 84:[14, 4, 4] Operation: 11-7=4 Exploring Operation: 7+14=21, Resulting Numbers: [11, 4, 21] Generated Node #0,1: 84:[11, 4, 21] Operation: 7+14=21 Exploring Operation: 14-11=3, Resulting Numbers: [7, 4, 3] Generated Node #0,2: 84:[7, 4, 3] Operation: 14-11=3 Exploring Operation: 11-4=7, Resulting Numbers: [7, 14, 7] Generated Node #0,3: 84:[7, 14, 7] Operation: 11-4=7 Start Sub Search at level 1: Moving to Node #0,0 Current State: 84:[14, 4, 4], Operations: ['11-7=4'] Exploring Operation: 4/4=1, Resulting Numbers: [14, 1] Generated Node #0,0,0: 84:[14, 1] Operation: 4/4=1 Exploring Operation: 14-4=10, Resulting Numbers: [4, 10] Generated Node #0,0,1: 84:[4, 10] Operation: 14-4=10 Exploring Operation: 14-4=10, Resulting Numbers: [4, 10] Generated Node #0,0,2: 84:[4, 10] Operation: 14-4=10 Exploring Operation: 4+4=8, Resulting Numbers: [14, 8] Generated Node #0,0,3: 84:[14, 8] Operation: 4+4=8 Moving to Node #0,0,0 Current State: 84:[14, 1], Operations: ['11-7=4', '4/4=1'] Exploring Operation: 14-1=13, Resulting Numbers: [13] 13,84 unequal: No Solution Exploring Operation: 14/1=14, Resulting Numbers: [14] 14,84 unequal: No Solution Exploring Operation: 14*1=14, Resulting Numbers: [14] 14,84 unequal: No Solution Exploring Operation: 14+1=15, Resulting Numbers: [15] 15,84 unequal: No Solution Moving to Node #0,0,3 Current State: 84:[14, 8], Operations: ['11-7=4', '4+4=8'] Exploring Operation: 14-8=6, Resulting Numbers: [6] 6,84 unequal: No Solution Exploring Operation: 14*8=112, Resulting Numbers: [112] 112,84 unequal: No Solution Exploring Operation: 14+8=22, Resulting Numbers: [22] 22,84 unequal: No Solution Moving to Node #0,0,2 Current State: 84:[4, 10], Operations: ['11-7=4', '14-4=10'] Exploring Operation: 4+10=14, Resulting Numbers: [14] 14,84 unequal: No Solution Exploring Operation: 4*10=40, Resulting Numbers: [40] 40,84 unequal: No Solution Exploring Operation: 10-4=6, Resulting Numbers: [6] 6,84 unequal: No Solution Moving to Node #0,0,1 Current State: 84:[4, 10], Operations: ['11-7=4', '14-4=10'] Exploring Operation: 4*10=40, Resulting Numbers: [40] 40,84 unequal: No Solution Exploring Operation: 4+10=14, Resulting Numbers: [14] 14,84 unequal: No Solution Exploring Operation: 10-4=6, Resulting Numbers: [6] 6,84 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 #0,2 Current State: 84:[7, 4, 3], Operations: ['14-11=3'] Exploring Operation: 7*4=28, Resulting Numbers: [3, 28] Generated Node #0,2,0: 84:[3, 28] Operation: 7*4=28 Exploring Operation: 7*3=21, Resulting Numbers: [4, 21] Generated Node #0,2,1: 84:[4, 21] Operation: 7*3=21 Exploring Operation: 7-3=4, Resulting Numbers: [4, 4] Generated Node #0,2,2: 84:[4, 4] Operation: 7-3=4 Exploring Operation: 7-4=3, Resulting Numbers: [3, 3] Generated Node #0,2,3: 84:[3, 3] Operation: 7-4=3 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 84:[3, 28], Operations: ['14-11=3', '7*4=28'] Exploring Operation: 3*28=84, Resulting Numbers: [84] 84,84 equal: Goal Reached Moving to Node #0 Current State: 84:[7, 11, 14, 4], Operations: [] Exploring Operation: 14-11=3, Resulting Numbers: [7, 4, 3] Generated Node #0,2: 84:[7, 4, 3] Operation: 14-11=3 Moving to Node #0,2 Current State: 84:[7, 4, 3], Operations: ['14-11=3'] Exploring Operation: 7*4=28, Resulting Numbers: [3, 28] Generated Node #0,2,0: 84:[3, 28] Operation: 7*4=28 Moving to Node #0,2,0 Current State: 84:[3, 28], Operations: ['14-11=3', '7*4=28'] Exploring Operation: 3*28=84, Resulting Numbers: [84] 84,84 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.973958
hs_4
mult_heuristic
[ 93, 79, 26, 1 ]
96
[ "79-1=78", "78/26=3", "93+3=96" ]
Current State: 96:[93, 79, 26, 1], Operations: [] Exploring Operation: 79-1=78, Resulting Numbers: [93, 26, 78] Generated Node #2: [93, 26, 78] from Operation: 79-1=78 Current State: 96:[93, 26, 78], Operations: ['79-1=78'] Exploring Operation: 78/26=3, Resulting Numbers: [93, 3] Generated Node #3: [93, 3] from Operation: 78/26=3 Current State: 96:[93, 3], Operations: ['79-1=78', '78/26=3'] Exploring Operation: 93+3=96, Resulting Numbers: [96] 96,96 equal: Goal Reached
4
Current State: 96:[93, 79, 26, 1], Operations: [] Exploring Operation: 79+26=105, Resulting Numbers: [93, 1, 105] Generated Node #0,0: 96:[93, 1, 105] Operation: 79+26=105 Exploring Operation: 93-79=14, Resulting Numbers: [26, 1, 14] Generated Node #0,1: 96:[26, 1, 14] Operation: 93-79=14 Exploring Operation: 79-26=53, Resulting Numbers: [93, 1, 53] Generated Node #0,2: 96:[93, 1, 53] Operation: 79-26=53 Moving to Node #0,1 Current State: 96:[26, 1, 14], Operations: ['93-79=14'] Exploring Operation: 26-14=12, Resulting Numbers: [1, 12] Generated Node #0,1,0: 96:[1, 12] Operation: 26-14=12 Exploring Operation: 26-1=25, Resulting Numbers: [14, 25] Generated Node #0,1,1: 96:[14, 25] Operation: 26-1=25 Exploring Operation: 1+14=15, Resulting Numbers: [26, 15] Generated Node #0,1,2: 96:[26, 15] Operation: 1+14=15 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 96:[1, 12], Operations: ['93-79=14', '26-14=12'] Exploring Operation: 1+12=13, Resulting Numbers: [13] 13,96 unequal: No Solution Exploring Operation: 1*12=12, Resulting Numbers: [12] 12,96 unequal: No Solution Exploring Operation: 12/1=12, Resulting Numbers: [12] 12,96 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: 96:[14, 25], Operations: ['93-79=14', '26-1=25'] Exploring Operation: 25-14=11, Resulting Numbers: [11] 11,96 unequal: No Solution Exploring Operation: 14+25=39, Resulting Numbers: [39] 39,96 unequal: No Solution Exploring Operation: 14*25=350, Resulting Numbers: [350] 350,96 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: 96:[26, 15], Operations: ['93-79=14', '1+14=15'] Exploring Operation: 26*15=390, Resulting Numbers: [390] 390,96 unequal: No Solution Exploring Operation: 26-15=11, Resulting Numbers: [11] 11,96 unequal: No Solution Exploring Operation: 26+15=41, Resulting Numbers: [41] 41,96 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: 96:[93, 1, 53], Operations: ['79-26=53'] Exploring Operation: 53-1=52, Resulting Numbers: [93, 52] Generated Node #0,2,0: 96:[93, 52] Operation: 53-1=52 Exploring Operation: 93*1=93, Resulting Numbers: [53, 93] Generated Node #0,2,1: 96:[53, 93] Operation: 93*1=93 Exploring Operation: 93+1=94, Resulting Numbers: [53, 94] Generated Node #0,2,2: 96:[53, 94] Operation: 93+1=94 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 96:[93, 52], Operations: ['79-26=53', '53-1=52'] Exploring Operation: 93*52=4836, Resulting Numbers: [4836] 4836,96 unequal: No Solution Exploring Operation: 93+52=145, Resulting Numbers: [145] 145,96 unequal: No Solution Exploring Operation: 93-52=41, Resulting Numbers: [41] 41,96 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: 96:[53, 94], Operations: ['79-26=53', '93+1=94'] Exploring Operation: 94-53=41, Resulting Numbers: [41] 41,96 unequal: No Solution Exploring Operation: 53+94=147, Resulting Numbers: [147] 147,96 unequal: No Solution Exploring Operation: 53*94=4982, Resulting Numbers: [4982] 4982,96 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: 96:[53, 93], Operations: ['79-26=53', '93*1=93'] Exploring Operation: 53+93=146, Resulting Numbers: [146] 146,96 unequal: No Solution Exploring Operation: 53*93=4929, Resulting Numbers: [4929] 4929,96 unequal: No Solution Exploring Operation: 93-53=40, Resulting Numbers: [40] 40,96 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: 96:[93, 1, 105], Operations: ['79+26=105'] Exploring Operation: 105-93=12, Resulting Numbers: [1, 12] Generated Node #0,0,0: 96:[1, 12] Operation: 105-93=12 Exploring Operation: 105-1=104, Resulting Numbers: [93, 104] Generated Node #0,0,1: 96:[93, 104] Operation: 105-1=104 Exploring Operation: 93+1=94, Resulting Numbers: [105, 94] Generated Node #0,0,2: 96:[105, 94] Operation: 93+1=94 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 96:[1, 12], Operations: ['79+26=105', '105-93=12'] Exploring Operation: 1+12=13, Resulting Numbers: [13] 13,96 unequal: No Solution Exploring Operation: 1*12=12, Resulting Numbers: [12] 12,96 unequal: No Solution Exploring Operation: 12/1=12, Resulting Numbers: [12] 12,96 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: 96:[93, 104], Operations: ['79+26=105', '105-1=104'] Exploring Operation: 104-93=11, Resulting Numbers: [11] 11,96 unequal: No Solution Exploring Operation: 93+104=197, Resulting Numbers: [197] 197,96 unequal: No Solution Exploring Operation: 93*104=9672, Resulting Numbers: [9672] 9672,96 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: 96:[105, 94], Operations: ['79+26=105', '93+1=94'] Exploring Operation: 105*94=9870, Resulting Numbers: [9870] 9870,96 unequal: No Solution Exploring Operation: 105+94=199, Resulting Numbers: [199] 199,96 unequal: No Solution Exploring Operation: 105-94=11, Resulting Numbers: [11] 11,96 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
[ 30, 83, 73, 76 ]
50
[ "83-30=53", "76-73=3", "53-3=50" ]
Current State: 50:[30, 83, 73, 76], Operations: [] Exploring Operation: 83-30=53, Resulting Numbers: [73, 76, 53] Generated Node #2: [73, 76, 53] from Operation: 83-30=53 Current State: 50:[73, 76, 53], Operations: ['83-30=53'] Exploring Operation: 76-73=3, Resulting Numbers: [53, 3] Generated Node #3: [53, 3] from Operation: 76-73=3 Current State: 50:[53, 3], Operations: ['83-30=53', '76-73=3'] Exploring Operation: 53-3=50, Resulting Numbers: [50] 50,50 equal: Goal Reached
4
Current State: 50:[30, 83, 73, 76], Operations: [] Exploring Operation: 83-76=7, Resulting Numbers: [30, 73, 7] Generated Node #0,0: 50:[30, 73, 7] Operation: 83-76=7 Exploring Operation: 83-73=10, Resulting Numbers: [30, 76, 10] Generated Node #0,1: 50:[30, 76, 10] Operation: 83-73=10 Exploring Operation: 83-30=53, Resulting Numbers: [73, 76, 53] Generated Node #0,2: 50:[73, 76, 53] Operation: 83-30=53 Exploring Operation: 76-73=3, Resulting Numbers: [30, 83, 3] Generated Node #0,3: 50:[30, 83, 3] Operation: 76-73=3 Moving to Node #0,0 Current State: 50:[30, 73, 7], Operations: ['83-76=7'] Exploring Operation: 30-7=23, Resulting Numbers: [73, 23] Generated Node #0,0,0: 50:[73, 23] Operation: 30-7=23 Exploring Operation: 30+7=37, Resulting Numbers: [73, 37] Generated Node #0,0,1: 50:[73, 37] Operation: 30+7=37 Exploring Operation: 73-30=43, Resulting Numbers: [7, 43] Generated Node #0,0,2: 50:[7, 43] Operation: 73-30=43 Exploring Operation: 73-7=66, Resulting Numbers: [30, 66] Generated Node #0,0,3: 50:[30, 66] Operation: 73-7=66 Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 50:[7, 43], Operations: ['83-76=7', '73-30=43'] Exploring Operation: 7*43=301, Resulting Numbers: [301] 301,50 unequal: No Solution Exploring Operation: 7+43=50, Resulting Numbers: [50] 50,50 equal: Goal Reached Moving to Node #0 Current State: 50:[30, 83, 73, 76], Operations: [] Exploring Operation: 83-76=7, Resulting Numbers: [30, 73, 7] Generated Node #0,0: 50:[30, 73, 7] Operation: 83-76=7 Moving to Node #0,0 Current State: 50:[30, 73, 7], Operations: ['83-76=7'] Exploring Operation: 73-30=43, Resulting Numbers: [7, 43] Generated Node #0,0,2: 50:[7, 43] Operation: 73-30=43 Moving to Node #0,0,2 Current State: 50:[7, 43], Operations: ['83-76=7', '73-30=43'] Exploring Operation: 7+43=50, Resulting Numbers: [50] 50,50 equal: Goal Reached Exit Sub Search at level 1
0.987847
hs_4
sum_heuristic
[ 51, 20, 74, 90 ]
93
[ "51+20=71", "74+90=164", "164-71=93" ]
Current State: 93:[51, 20, 74, 90], Operations: [] Exploring Operation: 51+20=71, Resulting Numbers: [74, 90, 71] Generated Node #2: [74, 90, 71] from Operation: 51+20=71 Current State: 93:[74, 90, 71], Operations: ['51+20=71'] Exploring Operation: 74+90=164, Resulting Numbers: [71, 164] Generated Node #3: [71, 164] from Operation: 74+90=164 Current State: 93:[71, 164], Operations: ['51+20=71', '74+90=164'] Exploring Operation: 164-71=93, Resulting Numbers: [93] 93,93 equal: Goal Reached
4
Current State: 93:[51, 20, 74, 90], Operations: [] Exploring Operation: 20+74=94, Resulting Numbers: [51, 90, 94] Generated Node #0,0: 93:[51, 90, 94] Operation: 20+74=94 Exploring Operation: 90-51=39, Resulting Numbers: [20, 74, 39] Generated Node #0,1: 93:[20, 74, 39] Operation: 90-51=39 Exploring Operation: 51-20=31, Resulting Numbers: [74, 90, 31] Generated Node #0,2: 93:[74, 90, 31] Operation: 51-20=31 Exploring Operation: 74-51=23, Resulting Numbers: [20, 90, 23] Generated Node #0,3: 93:[20, 90, 23] Operation: 74-51=23 Moving to Node #0,2 Current State: 93:[74, 90, 31], Operations: ['51-20=31'] Exploring Operation: 90+31=121, Resulting Numbers: [74, 121] Generated Node #0,2,0: 93:[74, 121] Operation: 90+31=121 Exploring Operation: 74-31=43, Resulting Numbers: [90, 43] Generated Node #0,2,1: 93:[90, 43] Operation: 74-31=43 Exploring Operation: 74+31=105, Resulting Numbers: [90, 105] Generated Node #0,2,2: 93:[90, 105] Operation: 74+31=105 Exploring Operation: 90-74=16, Resulting Numbers: [31, 16] Generated Node #0,2,3: 93:[31, 16] Operation: 90-74=16 Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 93:[31, 16], Operations: ['51-20=31', '90-74=16'] Exploring Operation: 31+16=47, Resulting Numbers: [47] 47,93 unequal: No Solution Exploring Operation: 31*16=496, Resulting Numbers: [496] 496,93 unequal: No Solution Exploring Operation: 31-16=15, Resulting Numbers: [15] 15,93 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 #0,2,1 Current State: 93:[90, 43], Operations: ['51-20=31', '74-31=43'] Exploring Operation: 90*43=3870, Resulting Numbers: [3870] 3870,93 unequal: No Solution Exploring Operation: 90+43=133, Resulting Numbers: [133] 133,93 unequal: No Solution Exploring Operation: 90-43=47, Resulting Numbers: [47] 47,93 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 #0,2,2 Current State: 93:[90, 105], Operations: ['51-20=31', '74+31=105'] Exploring Operation: 90*105=9450, Resulting Numbers: [9450] 9450,93 unequal: No Solution Exploring Operation: 90+105=195, Resulting Numbers: [195] 195,93 unequal: No Solution Exploring Operation: 105-90=15, Resulting Numbers: [15] 15,93 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 #0,2,0 Current State: 93:[74, 121], Operations: ['51-20=31', '90+31=121'] Exploring Operation: 74+121=195, Resulting Numbers: [195] 195,93 unequal: No Solution Exploring Operation: 74*121=8954, Resulting Numbers: [8954] 8954,93 unequal: No Solution Exploring Operation: 121-74=47, Resulting Numbers: [47] 47,93 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: 93:[20, 90, 23], Operations: ['74-51=23'] Exploring Operation: 23-20=3, Resulting Numbers: [90, 3] Generated Node #0,3,0: 93:[90, 3] Operation: 23-20=3 Exploring Operation: 20+90=110, Resulting Numbers: [23, 110] Generated Node #0,3,1: 93:[23, 110] Operation: 20+90=110 Exploring Operation: 90-20=70, Resulting Numbers: [23, 70] Generated Node #0,3,2: 93:[23, 70] Operation: 90-20=70 Exploring Operation: 20+23=43, Resulting Numbers: [90, 43] Generated Node #0,3,3: 93:[90, 43] Operation: 20+23=43 Moving to Node #0,0 Current State: 93:[51, 90, 94], Operations: ['20+74=94'] Exploring Operation: 94-51=43, Resulting Numbers: [90, 43] Generated Node #0,0,0: 93:[90, 43] Operation: 94-51=43 Exploring Operation: 94-90=4, Resulting Numbers: [51, 4] Generated Node #0,0,1: 93:[51, 4] Operation: 94-90=4 Exploring Operation: 90-51=39, Resulting Numbers: [94, 39] Generated Node #0,0,2: 93:[94, 39] Operation: 90-51=39 Exploring Operation: 51+90=141, Resulting Numbers: [94, 141] Generated Node #0,0,3: 93:[94, 141] Operation: 51+90=141 Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 93:[94, 39], Operations: ['20+74=94', '90-51=39'] Exploring Operation: 94+39=133, Resulting Numbers: [133] 133,93 unequal: No Solution Exploring Operation: 94*39=3666, Resulting Numbers: [3666] 3666,93 unequal: No Solution Exploring Operation: 94-39=55, Resulting Numbers: [55] 55,93 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 #0,0,0 Current State: 93:[90, 43], Operations: ['20+74=94', '94-51=43'] Exploring Operation: 90+43=133, Resulting Numbers: [133] 133,93 unequal: No Solution Exploring Operation: 90-43=47, Resulting Numbers: [47] 47,93 unequal: No Solution Exploring Operation: 90*43=3870, Resulting Numbers: [3870] 3870,93 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 #0,0,1 Current State: 93:[51, 4], Operations: ['20+74=94', '94-90=4'] Exploring Operation: 51*4=204, Resulting Numbers: [204] 204,93 unequal: No Solution Exploring Operation: 51+4=55, Resulting Numbers: [55] 55,93 unequal: No Solution Exploring Operation: 51-4=47, Resulting Numbers: [47] 47,93 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 #0,0,3 Current State: 93:[94, 141], Operations: ['20+74=94', '51+90=141'] Exploring Operation: 141-94=47, Resulting Numbers: [47] 47,93 unequal: No Solution Exploring Operation: 94*141=13254, Resulting Numbers: [13254] 13254,93 unequal: No Solution Exploring Operation: 94+141=235, Resulting Numbers: [235] 235,93 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: 93:[20, 74, 39], Operations: ['90-51=39'] Exploring Operation: 39-20=19, Resulting Numbers: [74, 19] Generated Node #0,1,0: 93:[74, 19] Operation: 39-20=19 Exploring Operation: 20+74=94, Resulting Numbers: [39, 94] Generated Node #0,1,1: 93:[39, 94] Operation: 20+74=94 Exploring Operation: 74-39=35, Resulting Numbers: [20, 35] Generated Node #0,1,2: 93:[20, 35] Operation: 74-39=35 Exploring Operation: 74-20=54, Resulting Numbers: [39, 54] Generated Node #0,1,3: 93:[39, 54] Operation: 74-20=54 Moving to Node #0,3,0 Current State: 93:[90, 3], Operations: ['74-51=23', '23-20=3'] Exploring Operation: 90-3=87, Resulting Numbers: [87] 87,93 unequal: No Solution Exploring Operation: 90*3=270, Resulting Numbers: [270] 270,93 unequal: No Solution Exploring Operation: 90+3=93, Resulting Numbers: [93] 93,93 equal: Goal Reached Moving to Node #0 Current State: 93:[51, 20, 74, 90], Operations: [] Exploring Operation: 74-51=23, Resulting Numbers: [20, 90, 23] Generated Node #0,3: 93:[20, 90, 23] Operation: 74-51=23 Moving to Node #0,3 Current State: 93:[20, 90, 23], Operations: ['74-51=23'] Exploring Operation: 23-20=3, Resulting Numbers: [90, 3] Generated Node #0,3,0: 93:[90, 3] Operation: 23-20=3 Moving to Node #0,3,0 Current State: 93:[90, 3], Operations: ['74-51=23', '23-20=3'] Exploring Operation: 90+3=93, Resulting Numbers: [93] 93,93 equal: Goal Reached
0.955729
hs_4
sum_heuristic
[ 23, 51, 39, 26 ]
37
[ "51-23=28", "39+26=65", "65-28=37" ]
Current State: 37:[23, 51, 39, 26], Operations: [] Exploring Operation: 51-23=28, Resulting Numbers: [39, 26, 28] Generated Node #2: [39, 26, 28] from Operation: 51-23=28 Current State: 37:[39, 26, 28], Operations: ['51-23=28'] Exploring Operation: 39+26=65, Resulting Numbers: [28, 65] Generated Node #3: [28, 65] from Operation: 39+26=65 Current State: 37:[28, 65], Operations: ['51-23=28', '39+26=65'] Exploring Operation: 65-28=37, Resulting Numbers: [37] 37,37 equal: Goal Reached
4
Current State: 37:[23, 51, 39, 26], Operations: [] Exploring Operation: 51-23=28, Resulting Numbers: [39, 26, 28] Generated Node #0,0: 37:[39, 26, 28] Operation: 51-23=28 Exploring Operation: 23+26=49, Resulting Numbers: [51, 39, 49] Generated Node #0,1: 37:[51, 39, 49] Operation: 23+26=49 Start Sub Search at level 1: Moving to Node #0,0 Current State: 37:[39, 26, 28], Operations: ['51-23=28'] Exploring Operation: 39-26=13, Resulting Numbers: [28, 13] Generated Node #0,0,0: 37:[28, 13] Operation: 39-26=13 Exploring Operation: 26+28=54, Resulting Numbers: [39, 54] Generated Node #0,0,1: 37:[39, 54] Operation: 26+28=54 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 37:[39, 54], Operations: ['51-23=28', '26+28=54'] Exploring Operation: 39+54=93, Resulting Numbers: [93] 93,37 unequal: No Solution Exploring Operation: 54-39=15, Resulting Numbers: [15] 15,37 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 #0,0,0 Current State: 37:[28, 13], Operations: ['51-23=28', '39-26=13'] Exploring Operation: 28-13=15, Resulting Numbers: [15] 15,37 unequal: No Solution Exploring Operation: 28+13=41, Resulting Numbers: [41] 41,37 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 #0,1 Current State: 37:[51, 39, 49], Operations: ['23+26=49'] Exploring Operation: 51-49=2, Resulting Numbers: [39, 2] Generated Node #0,1,0: 37:[39, 2] Operation: 51-49=2 Exploring Operation: 51-39=12, Resulting Numbers: [49, 12] Generated Node #0,1,1: 37:[49, 12] Operation: 51-39=12 Moving to Node #0,1,0 Current State: 37:[39, 2], Operations: ['23+26=49', '51-49=2'] Exploring Operation: 39+2=41, Resulting Numbers: [41] 41,37 unequal: No Solution Exploring Operation: 39-2=37, Resulting Numbers: [37] 37,37 equal: Goal Reached Moving to Node #0 Current State: 37:[23, 51, 39, 26], Operations: [] Exploring Operation: 23+26=49, Resulting Numbers: [51, 39, 49] Generated Node #0,1: 37:[51, 39, 49] Operation: 23+26=49 Moving to Node #0,1 Current State: 37:[51, 39, 49], Operations: ['23+26=49'] Exploring Operation: 51-49=2, Resulting Numbers: [39, 2] Generated Node #0,1,0: 37:[39, 2] Operation: 51-49=2 Moving to Node #0,1,0 Current State: 37:[39, 2], Operations: ['23+26=49', '51-49=2'] Exploring Operation: 39-2=37, Resulting Numbers: [37] 37,37 equal: Goal Reached Exit Sub Search at level 1
0.986111
hs_2
mult_heuristic
[ 56, 44, 88, 11 ]
28
[ "88-56=32", "44/11=4", "32-4=28" ]
Current State: 28:[56, 44, 88, 11], Operations: [] Exploring Operation: 88-56=32, Resulting Numbers: [44, 11, 32] Generated Node #2: [44, 11, 32] from Operation: 88-56=32 Current State: 28:[44, 11, 32], Operations: ['88-56=32'] Exploring Operation: 44/11=4, Resulting Numbers: [32, 4] Generated Node #3: [32, 4] from Operation: 44/11=4 Current State: 28:[32, 4], Operations: ['88-56=32', '44/11=4'] Exploring Operation: 32-4=28, Resulting Numbers: [28] 28,28 equal: Goal Reached
4
Current State: 28:[56, 44, 88, 11], Operations: [] Exploring Operation: 88/44=2, Resulting Numbers: [56, 11, 2] Generated Node #0,0: 28:[56, 11, 2] Operation: 88/44=2 Exploring Operation: 88/11=8, Resulting Numbers: [56, 44, 8] Generated Node #0,1: 28:[56, 44, 8] Operation: 88/11=8 Exploring Operation: 88-56=32, Resulting Numbers: [44, 11, 32] Generated Node #0,2: 28:[44, 11, 32] Operation: 88-56=32 Moving to Node #0,2 Current State: 28:[44, 11, 32], Operations: ['88-56=32'] Exploring Operation: 44-11=33, Resulting Numbers: [32, 33] Generated Node #0,2,0: 28:[32, 33] Operation: 44-11=33 Exploring Operation: 44-32=12, Resulting Numbers: [11, 12] Generated Node #0,2,1: 28:[11, 12] Operation: 44-32=12 Exploring Operation: 44/11=4, Resulting Numbers: [32, 4] Generated Node #0,2,2: 28:[32, 4] Operation: 44/11=4 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 28:[32, 4], Operations: ['88-56=32', '44/11=4'] Exploring Operation: 32+4=36, Resulting Numbers: [36] 36,28 unequal: No Solution Exploring Operation: 32-4=28, Resulting Numbers: [28] 28,28 equal: Goal Reached Moving to Node #0 Current State: 28:[56, 44, 88, 11], Operations: [] Exploring Operation: 88-56=32, Resulting Numbers: [44, 11, 32] Generated Node #0,2: 28:[44, 11, 32] Operation: 88-56=32 Moving to Node #0,2 Current State: 28:[44, 11, 32], Operations: ['88-56=32'] Exploring Operation: 44/11=4, Resulting Numbers: [32, 4] Generated Node #0,2,2: 28:[32, 4] Operation: 44/11=4 Moving to Node #0,2,2 Current State: 28:[32, 4], Operations: ['88-56=32', '44/11=4'] Exploring Operation: 32-4=28, Resulting Numbers: [28] 28,28 equal: Goal Reached Exit Sub Search at level 1
0.989583
hs_3
mult_heuristic
[ 52, 35, 66, 88 ]
74
[ "52*66=3432", "3432/88=39", "35+39=74" ]
Current State: 74:[52, 35, 66, 88], Operations: [] Exploring Operation: 52*66=3432, Resulting Numbers: [35, 88, 3432] Generated Node #2: [35, 88, 3432] from Operation: 52*66=3432 Current State: 74:[35, 88, 3432], Operations: ['52*66=3432'] Exploring Operation: 3432/88=39, Resulting Numbers: [35, 39] Generated Node #3: [35, 39] from Operation: 3432/88=39 Current State: 74:[35, 39], Operations: ['52*66=3432', '3432/88=39'] Exploring Operation: 35+39=74, Resulting Numbers: [74] 74,74 equal: Goal Reached
4
Current State: 74:[52, 35, 66, 88], Operations: [] Exploring Operation: 88-52=36, Resulting Numbers: [35, 66, 36] Generated Node #0,0: 74:[35, 66, 36] Operation: 88-52=36 Start Sub Search at level 1: Moving to Node #0,0 Current State: 74:[35, 66, 36], Operations: ['88-52=36'] Exploring Operation: 66-35=31, Resulting Numbers: [36, 31] Generated Node #0,0,0: 74:[36, 31] Operation: 66-35=31 Moving to Node #0,0,0 Current State: 74:[36, 31], Operations: ['88-52=36', '66-35=31'] Exploring Operation: 36-31=5, Resulting Numbers: [5] 5,74 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
[ 65, 58, 8, 19 ]
61
[ "65-8=57", "57/19=3", "58+3=61" ]
Current State: 61:[65, 58, 8, 19], Operations: [] Exploring Operation: 65-8=57, Resulting Numbers: [58, 19, 57] Generated Node #2: [58, 19, 57] from Operation: 65-8=57 Current State: 61:[58, 19, 57], Operations: ['65-8=57'] Exploring Operation: 57/19=3, Resulting Numbers: [58, 3] Generated Node #3: [58, 3] from Operation: 57/19=3 Current State: 61:[58, 3], Operations: ['65-8=57', '57/19=3'] Exploring Operation: 58+3=61, Resulting Numbers: [61] 61,61 equal: Goal Reached
4
Current State: 61:[65, 58, 8, 19], Operations: [] Exploring Operation: 58+8=66, Resulting Numbers: [65, 19, 66] Generated Node #0,0: 61:[65, 19, 66] Operation: 58+8=66 Exploring Operation: 65-8=57, Resulting Numbers: [58, 19, 57] Generated Node #0,1: 61:[58, 19, 57] Operation: 65-8=57 Exploring Operation: 65+8=73, Resulting Numbers: [58, 19, 73] Generated Node #0,2: 61:[58, 19, 73] Operation: 65+8=73 Exploring Operation: 8+19=27, Resulting Numbers: [65, 58, 27] Generated Node #0,3: 61:[65, 58, 27] Operation: 8+19=27 Moving to Node #0,3 Current State: 61:[65, 58, 27], Operations: ['8+19=27'] Exploring Operation: 65+27=92, Resulting Numbers: [58, 92] Generated Node #0,3,0: 61:[58, 92] Operation: 65+27=92 Exploring Operation: 58-27=31, Resulting Numbers: [65, 31] Generated Node #0,3,1: 61:[65, 31] Operation: 58-27=31 Exploring Operation: 65-27=38, Resulting Numbers: [58, 38] Generated Node #0,3,2: 61:[58, 38] Operation: 65-27=38 Exploring Operation: 58+27=85, Resulting Numbers: [65, 85] Generated Node #0,3,3: 61:[65, 85] Operation: 58+27=85 Moving to Node #0,1 Current State: 61:[58, 19, 57], Operations: ['65-8=57'] Exploring Operation: 57-19=38, Resulting Numbers: [58, 38] Generated Node #0,1,0: 61:[58, 38] Operation: 57-19=38 Exploring Operation: 19+57=76, Resulting Numbers: [58, 76] Generated Node #0,1,1: 61:[58, 76] Operation: 19+57=76 Exploring Operation: 58+19=77, Resulting Numbers: [57, 77] Generated Node #0,1,2: 61:[57, 77] Operation: 58+19=77 Exploring Operation: 58-19=39, Resulting Numbers: [57, 39] Generated Node #0,1,3: 61:[57, 39] Operation: 58-19=39 Moving to Node #0,0 Current State: 61:[65, 19, 66], Operations: ['58+8=66'] Exploring Operation: 19+66=85, Resulting Numbers: [65, 85] Generated Node #0,0,0: 61:[65, 85] Operation: 19+66=85 Exploring Operation: 65+19=84, Resulting Numbers: [66, 84] Generated Node #0,0,1: 61:[66, 84] Operation: 65+19=84 Exploring Operation: 65-19=46, Resulting Numbers: [66, 46] Generated Node #0,0,2: 61:[66, 46] Operation: 65-19=46 Exploring Operation: 66-19=47, Resulting Numbers: [65, 47] Generated Node #0,0,3: 61:[65, 47] Operation: 66-19=47 Moving to Node #0,2 Current State: 61:[58, 19, 73], Operations: ['65+8=73'] Exploring Operation: 58+19=77, Resulting Numbers: [73, 77] Generated Node #0,2,0: 61:[73, 77] Operation: 58+19=77 Exploring Operation: 58-19=39, Resulting Numbers: [73, 39] Generated Node #0,2,1: 61:[73, 39] Operation: 58-19=39 Exploring Operation: 73-19=54, Resulting Numbers: [58, 54] Generated Node #0,2,2: 61:[58, 54] Operation: 73-19=54 Exploring Operation: 19+73=92, Resulting Numbers: [58, 92] Generated Node #0,2,3: 61:[58, 92] Operation: 19+73=92 Moving to Node #0,2,2 Current State: 61:[58, 54], Operations: ['65+8=73', '73-19=54'] Exploring Operation: 58+54=112, Resulting Numbers: [112] 112,61 unequal: No Solution Exploring Operation: 58*54=3132, Resulting Numbers: [3132] 3132,61 unequal: No Solution Exploring Operation: 58-54=4, Resulting Numbers: [4] 4,61 unequal: No Solution Moving to Node #0,1,1 Current State: 61:[58, 76], Operations: ['65-8=57', '19+57=76'] Exploring Operation: 76-58=18, Resulting Numbers: [18] 18,61 unequal: No Solution Exploring Operation: 58+76=134, Resulting Numbers: [134] 134,61 unequal: No Solution Exploring Operation: 58*76=4408, Resulting Numbers: [4408] 4408,61 unequal: No Solution Moving to Node #0,0,3 Current State: 61:[65, 47], Operations: ['58+8=66', '66-19=47'] Exploring Operation: 65*47=3055, Resulting Numbers: [3055] 3055,61 unequal: No Solution Exploring Operation: 65-47=18, Resulting Numbers: [18] 18,61 unequal: No Solution Exploring Operation: 65+47=112, Resulting Numbers: [112] 112,61 unequal: No Solution Moving to Node #0,1,2 Current State: 61:[57, 77], Operations: ['65-8=57', '58+19=77'] Exploring Operation: 57*77=4389, Resulting Numbers: [4389] 4389,61 unequal: No Solution Exploring Operation: 57+77=134, Resulting Numbers: [134] 134,61 unequal: No Solution Exploring Operation: 77-57=20, Resulting Numbers: [20] 20,61 unequal: No Solution Moving to Node #0,0,2 Current State: 61:[66, 46], Operations: ['58+8=66', '65-19=46'] Exploring Operation: 66+46=112, Resulting Numbers: [112] 112,61 unequal: No Solution Exploring Operation: 66-46=20, Resulting Numbers: [20] 20,61 unequal: No Solution Exploring Operation: 66*46=3036, Resulting Numbers: [3036] 3036,61 unequal: No Solution Moving to Node #0,1,0 Current State: 61:[58, 38], Operations: ['65-8=57', '57-19=38'] Exploring Operation: 58-38=20, Resulting Numbers: [20] 20,61 unequal: No Solution Exploring Operation: 58+38=96, Resulting Numbers: [96] 96,61 unequal: No Solution Exploring Operation: 58*38=2204, Resulting Numbers: [2204] 2204,61 unequal: No Solution Moving to Node #0,3,2 Current State: 61:[58, 38], Operations: ['8+19=27', '65-27=38'] Exploring Operation: 58+38=96, Resulting Numbers: [96] 96,61 unequal: No Solution Exploring Operation: 58-38=20, Resulting Numbers: [20] 20,61 unequal: No Solution Exploring Operation: 58*38=2204, Resulting Numbers: [2204] 2204,61 unequal: No Solution Moving to Node #0,1,3 Current State: 61:[57, 39], Operations: ['65-8=57', '58-19=39'] Exploring Operation: 57-39=18, Resulting Numbers: [18] 18,61 unequal: No Solution Exploring Operation: 57+39=96, Resulting Numbers: [96] 96,61 unequal: No Solution Exploring Operation: 57*39=2223, Resulting Numbers: [2223] 2223,61 unequal: No Solution Moving to Node #0,2,0 Current State: 61:[73, 77], Operations: ['65+8=73', '58+19=77'] Exploring Operation: 73*77=5621, Resulting Numbers: [5621] 5621,61 unequal: No Solution Exploring Operation: 77-73=4, Resulting Numbers: [4] 4,61 unequal: No Solution Exploring Operation: 73+77=150, Resulting Numbers: [150] 150,61 unequal: No Solution Moving to Node #0,0,1 Current State: 61:[66, 84], Operations: ['58+8=66', '65+19=84'] Exploring Operation: 66*84=5544, Resulting Numbers: [5544] 5544,61 unequal: No Solution Exploring Operation: 66+84=150, Resulting Numbers: [150] 150,61 unequal: No Solution Exploring Operation: 84-66=18, Resulting Numbers: [18] 18,61 unequal: No Solution Moving to Node #0,0,0 Current State: 61:[65, 85], Operations: ['58+8=66', '19+66=85'] Exploring Operation: 65+85=150, Resulting Numbers: [150] 150,61 unequal: No Solution Exploring Operation: 85-65=20, Resulting Numbers: [20] 20,61 unequal: No Solution Exploring Operation: 65*85=5525, Resulting Numbers: [5525] 5525,61 unequal: No Solution Moving to Node #0,3,3 Current State: 61:[65, 85], Operations: ['8+19=27', '58+27=85'] Exploring Operation: 65+85=150, Resulting Numbers: [150] 150,61 unequal: No Solution Exploring Operation: 85-65=20, Resulting Numbers: [20] 20,61 unequal: No Solution Exploring Operation: 65*85=5525, Resulting Numbers: [5525] 5525,61 unequal: No Solution Moving to Node #0,3,0 Current State: 61:[58, 92], Operations: ['8+19=27', '65+27=92'] Exploring Operation: 92-58=34, Resulting Numbers: [34] 34,61 unequal: No Solution Exploring Operation: 58+92=150, Resulting Numbers: [150] 150,61 unequal: No Solution Exploring Operation: 58*92=5336, Resulting Numbers: [5336] 5336,61 unequal: No Solution Moving to Node #0,2,1 Current State: 61:[73, 39], Operations: ['65+8=73', '58-19=39'] Exploring Operation: 73-39=34, Resulting Numbers: [34] 34,61 unequal: No Solution Exploring Operation: 73*39=2847, Resulting Numbers: [2847] 2847,61 unequal: No Solution Exploring Operation: 73+39=112, Resulting Numbers: [112] 112,61 unequal: No Solution Moving to Node #0,3,1 Current State: 61:[65, 31], Operations: ['8+19=27', '58-27=31'] Exploring Operation: 65-31=34, Resulting Numbers: [34] 34,61 unequal: No Solution Exploring Operation: 65*31=2015, Resulting Numbers: [2015] 2015,61 unequal: No Solution Exploring Operation: 65+31=96, Resulting Numbers: [96] 96,61 unequal: No Solution Moving to Node #0,2,3 Current State: 61:[58, 92], Operations: ['65+8=73', '19+73=92'] Exploring Operation: 58+92=150, Resulting Numbers: [150] 150,61 unequal: No Solution Exploring Operation: 58*92=5336, Resulting Numbers: [5336] 5336,61 unequal: No Solution Exploring Operation: 92-58=34, Resulting Numbers: [34] 34,61 unequal: No Solution No solution found.
0
hs_4
mult_heuristic
[ 2, 38, 62, 54 ]
73
[ "54/2=27", "38+62=100", "100-27=73" ]
Current State: 73:[2, 38, 62, 54], Operations: [] Exploring Operation: 54/2=27, Resulting Numbers: [38, 62, 27] Generated Node #2: [38, 62, 27] from Operation: 54/2=27 Current State: 73:[38, 62, 27], Operations: ['54/2=27'] Exploring Operation: 38+62=100, Resulting Numbers: [27, 100] Generated Node #3: [27, 100] from Operation: 38+62=100 Current State: 73:[27, 100], Operations: ['54/2=27', '38+62=100'] Exploring Operation: 100-27=73, Resulting Numbers: [73] 73,73 equal: Goal Reached
4
Current State: 73:[2, 38, 62, 54], Operations: [] Exploring Operation: 2+62=64, Resulting Numbers: [38, 54, 64] Generated Node #0,0: 73:[38, 54, 64] Operation: 2+62=64 Exploring Operation: 2+54=56, Resulting Numbers: [38, 62, 56] Generated Node #0,1: 73:[38, 62, 56] Operation: 2+54=56 Exploring Operation: 2*38=76, Resulting Numbers: [62, 54, 76] Generated Node #0,2: 73:[62, 54, 76] Operation: 2*38=76 Exploring Operation: 2+38=40, Resulting Numbers: [62, 54, 40] Generated Node #0,3: 73:[62, 54, 40] Operation: 2+38=40 Start Sub Search at level 1: Moving to Node #0,2 Current State: 73:[62, 54, 76], Operations: ['2*38=76'] Exploring Operation: 62+54=116, Resulting Numbers: [76, 116] Generated Node #0,2,0: 73:[76, 116] Operation: 62+54=116 Exploring Operation: 54+76=130, Resulting Numbers: [62, 130] Generated Node #0,2,1: 73:[62, 130] Operation: 54+76=130 Exploring Operation: 76-54=22, Resulting Numbers: [62, 22] Generated Node #0,2,2: 73:[62, 22] Operation: 76-54=22 Exploring Operation: 62-54=8, Resulting Numbers: [76, 8] Generated Node #0,2,3: 73:[76, 8] Operation: 62-54=8 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 73:[76, 116], Operations: ['2*38=76', '62+54=116'] Exploring Operation: 76+116=192, Resulting Numbers: [192] 192,73 unequal: No Solution Exploring Operation: 116-76=40, Resulting Numbers: [40] 40,73 unequal: No Solution Exploring Operation: 76*116=8816, Resulting Numbers: [8816] 8816,73 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:[62, 22], Operations: ['2*38=76', '76-54=22'] Exploring Operation: 62-22=40, Resulting Numbers: [40] 40,73 unequal: No Solution Exploring Operation: 62+22=84, Resulting Numbers: [84] 84,73 unequal: No Solution Exploring Operation: 62*22=1364, Resulting Numbers: [1364] 1364,73 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 #0,2,1 Current State: 73:[62, 130], Operations: ['2*38=76', '54+76=130'] Exploring Operation: 62*130=8060, Resulting Numbers: [8060] 8060,73 unequal: No Solution Exploring Operation: 62+130=192, Resulting Numbers: [192] 192,73 unequal: No Solution Exploring Operation: 130-62=68, Resulting Numbers: [68] 68,73 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:[76, 8], Operations: ['2*38=76', '62-54=8'] Exploring Operation: 76+8=84, Resulting Numbers: [84] 84,73 unequal: No Solution Exploring Operation: 76-8=68, Resulting Numbers: [68] 68,73 unequal: No Solution Exploring Operation: 76*8=608, Resulting Numbers: [608] 608,73 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:[38, 54, 64], Operations: ['2+62=64'] Exploring Operation: 38+54=92, Resulting Numbers: [64, 92] Generated Node #0,0,0: 73:[64, 92] Operation: 38+54=92 Exploring Operation: 64-38=26, Resulting Numbers: [54, 26] Generated Node #0,0,1: 73:[54, 26] Operation: 64-38=26 Exploring Operation: 38+64=102, Resulting Numbers: [54, 102] Generated Node #0,0,2: 73:[54, 102] Operation: 38+64=102 Exploring Operation: 54-38=16, Resulting Numbers: [64, 16] Generated Node #0,0,3: 73:[64, 16] Operation: 54-38=16 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 73:[64, 92], Operations: ['2+62=64', '38+54=92'] Exploring Operation: 92-64=28, Resulting Numbers: [28] 28,73 unequal: No Solution Exploring Operation: 64*92=5888, Resulting Numbers: [5888] 5888,73 unequal: No Solution Exploring Operation: 64+92=156, Resulting Numbers: [156] 156,73 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:[54, 102], Operations: ['2+62=64', '38+64=102'] Exploring Operation: 102-54=48, Resulting Numbers: [48] 48,73 unequal: No Solution Exploring Operation: 54+102=156, Resulting Numbers: [156] 156,73 unequal: No Solution Exploring Operation: 54*102=5508, Resulting Numbers: [5508] 5508,73 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:[54, 26], Operations: ['2+62=64', '64-38=26'] Exploring Operation: 54*26=1404, Resulting Numbers: [1404] 1404,73 unequal: No Solution Exploring Operation: 54+26=80, Resulting Numbers: [80] 80,73 unequal: No Solution Exploring Operation: 54-26=28, Resulting Numbers: [28] 28,73 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 #0,0,3 Current State: 73:[64, 16], Operations: ['2+62=64', '54-38=16'] Exploring Operation: 64-16=48, Resulting Numbers: [48] 48,73 unequal: No Solution Exploring Operation: 64+16=80, Resulting Numbers: [80] 80,73 unequal: No Solution Exploring Operation: 64/16=4, Resulting Numbers: [4] 4,73 unequal: No Solution Exploring Operation: 64*16=1024, Resulting Numbers: [1024] 1024,73 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:[38, 62, 56], Operations: ['2+54=56'] Exploring Operation: 38+56=94, Resulting Numbers: [62, 94] Generated Node #0,1,0: 73:[62, 94] Operation: 38+56=94 Exploring Operation: 56-38=18, Resulting Numbers: [62, 18] Generated Node #0,1,1: 73:[62, 18] Operation: 56-38=18 Exploring Operation: 62-38=24, Resulting Numbers: [56, 24] Generated Node #0,1,2: 73:[56, 24] Operation: 62-38=24 Exploring Operation: 38+62=100, Resulting Numbers: [56, 100] Generated Node #0,1,3: 73:[56, 100] Operation: 38+62=100 Moving to Node #0,1,0 Current State: 73:[62, 94], Operations: ['2+54=56', '38+56=94'] Exploring Operation: 62+94=156, Resulting Numbers: [156] 156,73 unequal: No Solution Exploring Operation: 94-62=32, Resulting Numbers: [32] 32,73 unequal: No Solution Exploring Operation: 62*94=5828, Resulting Numbers: [5828] 5828,73 unequal: No Solution Moving to Node #0,1,3 Current State: 73:[56, 100], Operations: ['2+54=56', '38+62=100'] Exploring Operation: 100-56=44, Resulting Numbers: [44] 44,73 unequal: No Solution Exploring Operation: 56+100=156, Resulting Numbers: [156] 156,73 unequal: No Solution Exploring Operation: 56*100=5600, Resulting Numbers: [5600] 5600,73 unequal: No Solution Moving to Node #0,1,2 Current State: 73:[56, 24], Operations: ['2+54=56', '62-38=24'] Exploring Operation: 56-24=32, Resulting Numbers: [32] 32,73 unequal: No Solution Exploring Operation: 56+24=80, Resulting Numbers: [80] 80,73 unequal: No Solution Exploring Operation: 56*24=1344, Resulting Numbers: [1344] 1344,73 unequal: No Solution Moving to Node #0,1,1 Current State: 73:[62, 18], Operations: ['2+54=56', '56-38=18'] Exploring Operation: 62*18=1116, Resulting Numbers: [1116] 1116,73 unequal: No Solution Exploring Operation: 62-18=44, Resulting Numbers: [44] 44,73 unequal: No Solution Exploring Operation: 62+18=80, Resulting Numbers: [80] 80,73 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 Current State: 73:[62, 54, 40], Operations: ['2+38=40'] Exploring Operation: 54+40=94, Resulting Numbers: [62, 94] Generated Node #0,3,0: 73:[62, 94] Operation: 54+40=94 Exploring Operation: 62+40=102, Resulting Numbers: [54, 102] Generated Node #0,3,1: 73:[54, 102] Operation: 62+40=102 Exploring Operation: 54-40=14, Resulting Numbers: [62, 14] Generated Node #0,3,2: 73:[62, 14] Operation: 54-40=14 Exploring Operation: 62-40=22, Resulting Numbers: [54, 22] Generated Node #0,3,3: 73:[54, 22] Operation: 62-40=22 Moving to Node #0,3,0 Current State: 73:[62, 94], Operations: ['2+38=40', '54+40=94'] Exploring Operation: 62+94=156, Resulting Numbers: [156] 156,73 unequal: No Solution Exploring Operation: 62*94=5828, Resulting Numbers: [5828] 5828,73 unequal: No Solution Exploring Operation: 94-62=32, Resulting Numbers: [32] 32,73 unequal: No Solution Moving to Node #0,3,1 Current State: 73:[54, 102], Operations: ['2+38=40', '62+40=102'] Exploring Operation: 54+102=156, Resulting Numbers: [156] 156,73 unequal: No Solution Exploring Operation: 102-54=48, Resulting Numbers: [48] 48,73 unequal: No Solution Exploring Operation: 54*102=5508, Resulting Numbers: [5508] 5508,73 unequal: No Solution Moving to Node #0,3,3 Current State: 73:[54, 22], Operations: ['2+38=40', '62-40=22'] Exploring Operation: 54-22=32, Resulting Numbers: [32] 32,73 unequal: No Solution Exploring Operation: 54+22=76, Resulting Numbers: [76] 76,73 unequal: No Solution Exploring Operation: 54*22=1188, Resulting Numbers: [1188] 1188,73 unequal: No Solution Moving to Node #0,3,2 Current State: 73:[62, 14], Operations: ['2+38=40', '54-40=14'] Exploring Operation: 62+14=76, Resulting Numbers: [76] 76,73 unequal: No Solution Exploring Operation: 62*14=868, Resulting Numbers: [868] 868,73 unequal: No Solution Exploring Operation: 62-14=48, Resulting Numbers: [48] 48,73 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
[ 80, 86, 20, 78 ]
80
[ "86-78=8", "20*8=160", "160-80=80" ]
Current State: 80:[80, 86, 20, 78], Operations: [] Exploring Operation: 86-78=8, Resulting Numbers: [80, 20, 8] Generated Node #2: [80, 20, 8] from Operation: 86-78=8 Current State: 80:[80, 20, 8], Operations: ['86-78=8'] Exploring Operation: 20*8=160, Resulting Numbers: [80, 160] Generated Node #3: [80, 160] from Operation: 20*8=160 Current State: 80:[80, 160], Operations: ['86-78=8', '20*8=160'] Exploring Operation: 160-80=80, Resulting Numbers: [80] 80,80 equal: Goal Reached
4
Current State: 80:[80, 86, 20, 78], Operations: [] Exploring Operation: 86-80=6, Resulting Numbers: [20, 78, 6] Generated Node #0,0: 80:[20, 78, 6] Operation: 86-80=6 Exploring Operation: 86-78=8, Resulting Numbers: [80, 20, 8] Generated Node #0,1: 80:[80, 20, 8] Operation: 86-78=8 Exploring Operation: 80-78=2, Resulting Numbers: [86, 20, 2] Generated Node #0,2: 80:[86, 20, 2] Operation: 80-78=2 Exploring Operation: 80/20=4, Resulting Numbers: [86, 78, 4] Generated Node #0,3: 80:[86, 78, 4] Operation: 80/20=4 Start Sub Search at level 1: Moving to Node #0,1 Current State: 80:[80, 20, 8], Operations: ['86-78=8'] Exploring Operation: 80/8=10, Resulting Numbers: [20, 10] Generated Node #0,1,0: 80:[20, 10] Operation: 80/8=10 Exploring Operation: 80+8=88, Resulting Numbers: [20, 88] Generated Node #0,1,1: 80:[20, 88] Operation: 80+8=88 Exploring Operation: 20-8=12, Resulting Numbers: [80, 12] Generated Node #0,1,2: 80:[80, 12] Operation: 20-8=12 Exploring Operation: 80/20=4, Resulting Numbers: [8, 4] Generated Node #0,1,3: 80:[8, 4] Operation: 80/20=4 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 80:[20, 10], Operations: ['86-78=8', '80/8=10'] Exploring Operation: 20+10=30, Resulting Numbers: [30] 30,80 unequal: No Solution Exploring Operation: 20*10=200, Resulting Numbers: [200] 200,80 unequal: No Solution Exploring Operation: 20-10=10, Resulting Numbers: [10] 10,80 unequal: No Solution Exploring Operation: 20/10=2, Resulting Numbers: [2] 2,80 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: 80:[8, 4], Operations: ['86-78=8', '80/20=4'] Exploring Operation: 8+4=12, Resulting Numbers: [12] 12,80 unequal: No Solution Exploring Operation: 8/4=2, Resulting Numbers: [2] 2,80 unequal: No Solution Exploring Operation: 8*4=32, Resulting Numbers: [32] 32,80 unequal: No Solution Exploring Operation: 8-4=4, Resulting Numbers: [4] 4,80 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: 80:[80, 12], Operations: ['86-78=8', '20-8=12'] Exploring Operation: 80*12=960, Resulting Numbers: [960] 960,80 unequal: No Solution Exploring Operation: 80-12=68, Resulting Numbers: [68] 68,80 unequal: No Solution Exploring Operation: 80+12=92, Resulting Numbers: [92] 92,80 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: 80:[20, 88], Operations: ['86-78=8', '80+8=88'] Exploring Operation: 20+88=108, Resulting Numbers: [108] 108,80 unequal: No Solution Exploring Operation: 20*88=1760, Resulting Numbers: [1760] 1760,80 unequal: No Solution Exploring Operation: 88-20=68, Resulting Numbers: [68] 68,80 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: 80:[20, 78, 6], Operations: ['86-80=6'] Exploring Operation: 78+6=84, Resulting Numbers: [20, 84] Generated Node #0,0,0: 80:[20, 84] Operation: 78+6=84 Exploring Operation: 78/6=13, Resulting Numbers: [20, 13] Generated Node #0,0,1: 80:[20, 13] Operation: 78/6=13 Exploring Operation: 20-6=14, Resulting Numbers: [78, 14] Generated Node #0,0,2: 80:[78, 14] Operation: 20-6=14 Exploring Operation: 20+6=26, Resulting Numbers: [78, 26] Generated Node #0,0,3: 80:[78, 26] Operation: 20+6=26 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 80:[20, 13], Operations: ['86-80=6', '78/6=13'] Exploring Operation: 20-13=7, Resulting Numbers: [7] 7,80 unequal: No Solution Exploring Operation: 20+13=33, Resulting Numbers: [33] 33,80 unequal: No Solution Exploring Operation: 20*13=260, Resulting Numbers: [260] 260,80 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: 80:[20, 84], Operations: ['86-80=6', '78+6=84'] Exploring Operation: 84-20=64, Resulting Numbers: [64] 64,80 unequal: No Solution Exploring Operation: 20*84=1680, Resulting Numbers: [1680] 1680,80 unequal: No Solution Exploring Operation: 20+84=104, Resulting Numbers: [104] 104,80 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: 80:[78, 14], Operations: ['86-80=6', '20-6=14'] Exploring Operation: 78+14=92, Resulting Numbers: [92] 92,80 unequal: No Solution Exploring Operation: 78-14=64, Resulting Numbers: [64] 64,80 unequal: No Solution Exploring Operation: 78*14=1092, Resulting Numbers: [1092] 1092,80 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: 80:[78, 26], Operations: ['86-80=6', '20+6=26'] Exploring Operation: 78-26=52, Resulting Numbers: [52] 52,80 unequal: No Solution Exploring Operation: 78*26=2028, Resulting Numbers: [2028] 2028,80 unequal: No Solution Exploring Operation: 78+26=104, Resulting Numbers: [104] 104,80 unequal: No Solution Exploring Operation: 78/26=3, Resulting Numbers: [3] 3,80 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: 80:[86, 20, 2], Operations: ['80-78=2'] Exploring Operation: 20/2=10, Resulting Numbers: [86, 10] Generated Node #0,2,0: 80:[86, 10] Operation: 20/2=10 Exploring Operation: 86-2=84, Resulting Numbers: [20, 84] Generated Node #0,2,1: 80:[20, 84] Operation: 86-2=84 Exploring Operation: 86/2=43, Resulting Numbers: [20, 43] Generated Node #0,2,2: 80:[20, 43] Operation: 86/2=43 Exploring Operation: 20*2=40, Resulting Numbers: [86, 40] Generated Node #0,2,3: 80:[86, 40] Operation: 20*2=40 Moving to Node #0,2,2 Current State: 80:[20, 43], Operations: ['80-78=2', '86/2=43'] Exploring Operation: 20+43=63, Resulting Numbers: [63] 63,80 unequal: No Solution Exploring Operation: 43-20=23, Resulting Numbers: [23] 23,80 unequal: No Solution Exploring Operation: 20*43=860, Resulting Numbers: [860] 860,80 unequal: No Solution Moving to Node #0,2,1 Current State: 80:[20, 84], Operations: ['80-78=2', '86-2=84'] Exploring Operation: 20*84=1680, Resulting Numbers: [1680] 1680,80 unequal: No Solution Exploring Operation: 20+84=104, Resulting Numbers: [104] 104,80 unequal: No Solution Exploring Operation: 84-20=64, Resulting Numbers: [64] 64,80 unequal: No Solution Moving to Node #0,2,3 Current State: 80:[86, 40], Operations: ['80-78=2', '20*2=40'] Exploring Operation: 86-40=46, Resulting Numbers: [46] 46,80 unequal: No Solution Exploring Operation: 86+40=126, Resulting Numbers: [126] 126,80 unequal: No Solution Exploring Operation: 86*40=3440, Resulting Numbers: [3440] 3440,80 unequal: No Solution Moving to Node #0,2,0 Current State: 80:[86, 10], Operations: ['80-78=2', '20/2=10'] Exploring Operation: 86-10=76, Resulting Numbers: [76] 76,80 unequal: No Solution Exploring Operation: 86+10=96, Resulting Numbers: [96] 96,80 unequal: No Solution Exploring Operation: 86*10=860, Resulting Numbers: [860] 860,80 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: 80:[86, 78, 4], Operations: ['80/20=4'] Exploring Operation: 86+4=90, Resulting Numbers: [78, 90] Generated Node #0,3,0: 80:[78, 90] Operation: 86+4=90 Exploring Operation: 78+4=82, Resulting Numbers: [86, 82] Generated Node #0,3,1: 80:[86, 82] Operation: 78+4=82 Exploring Operation: 86-78=8, Resulting Numbers: [4, 8] Generated Node #0,3,2: 80:[4, 8] Operation: 86-78=8 Exploring Operation: 86-4=82, Resulting Numbers: [78, 82] Generated Node #0,3,3: 80:[78, 82] Operation: 86-4=82 Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 80:[4, 8], Operations: ['80/20=4', '86-78=8'] Exploring Operation: 4*8=32, Resulting Numbers: [32] 32,80 unequal: No Solution Exploring Operation: 8-4=4, Resulting Numbers: [4] 4,80 unequal: No Solution Exploring Operation: 4+8=12, Resulting Numbers: [12] 12,80 unequal: No Solution Exploring Operation: 8/4=2, Resulting Numbers: [2] 2,80 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: 80:[78, 82], Operations: ['80/20=4', '86-4=82'] Exploring Operation: 78*82=6396, Resulting Numbers: [6396] 6396,80 unequal: No Solution Exploring Operation: 78+82=160, Resulting Numbers: [160] 160,80 unequal: No Solution Exploring Operation: 82-78=4, Resulting Numbers: [4] 4,80 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: 80:[86, 82], Operations: ['80/20=4', '78+4=82'] Exploring Operation: 86-82=4, Resulting Numbers: [4] 4,80 unequal: No Solution Exploring Operation: 86*82=7052, Resulting Numbers: [7052] 7052,80 unequal: No Solution Exploring Operation: 86+82=168, Resulting Numbers: [168] 168,80 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: 80:[78, 90], Operations: ['80/20=4', '86+4=90'] Exploring Operation: 78*90=7020, Resulting Numbers: [7020] 7020,80 unequal: No Solution Exploring Operation: 90-78=12, Resulting Numbers: [12] 12,80 unequal: No Solution Exploring Operation: 78+90=168, Resulting Numbers: [168] 168,80 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
[ 5, 84, 5, 88 ]
21
[ "5*5=25", "88-84=4", "25-4=21" ]
Current State: 21:[5, 84, 5, 88], Operations: [] Exploring Operation: 5*5=25, Resulting Numbers: [84, 88, 25] Generated Node #2: [84, 88, 25] from Operation: 5*5=25 Current State: 21:[84, 88, 25], Operations: ['5*5=25'] Exploring Operation: 88-84=4, Resulting Numbers: [25, 4] Generated Node #3: [25, 4] from Operation: 88-84=4 Current State: 21:[25, 4], Operations: ['5*5=25', '88-84=4'] Exploring Operation: 25-4=21, Resulting Numbers: [21] 21,21 equal: Goal Reached
4
Current State: 21:[5, 84, 5, 88], Operations: [] Exploring Operation: 88-84=4, Resulting Numbers: [5, 5, 4] Generated Node #0,0: 21:[5, 5, 4] Operation: 88-84=4 Exploring Operation: 84-5=79, Resulting Numbers: [5, 88, 79] Generated Node #0,1: 21:[5, 88, 79] Operation: 84-5=79 Exploring Operation: 88-5=83, Resulting Numbers: [84, 5, 83] Generated Node #0,2: 21:[84, 5, 83] Operation: 88-5=83 Exploring Operation: 84-5=79, Resulting Numbers: [5, 88, 79] Generated Node #0,3: 21:[5, 88, 79] Operation: 84-5=79 Start Sub Search at level 1: Moving to Node #0,0 Current State: 21:[5, 5, 4], Operations: ['88-84=4'] Exploring Operation: 5/5=1, Resulting Numbers: [4, 1] Generated Node #0,0,0: 21:[4, 1] Operation: 5/5=1 Exploring Operation: 5*4=20, Resulting Numbers: [5, 20] Generated Node #0,0,1: 21:[5, 20] Operation: 5*4=20 Exploring Operation: 5*4=20, Resulting Numbers: [5, 20] Generated Node #0,0,2: 21:[5, 20] Operation: 5*4=20 Exploring Operation: 5+5=10, Resulting Numbers: [4, 10] Generated Node #0,0,3: 21:[4, 10] Operation: 5+5=10 Moving to Node #0,0,0 Current State: 21:[4, 1], Operations: ['88-84=4', '5/5=1'] Exploring Operation: 4+1=5, Resulting Numbers: [5] 5,21 unequal: No Solution Exploring Operation: 4-1=3, Resulting Numbers: [3] 3,21 unequal: No Solution Exploring Operation: 4*1=4, Resulting Numbers: [4] 4,21 unequal: No Solution Exploring Operation: 4/1=4, Resulting Numbers: [4] 4,21 unequal: No Solution Moving to Node #0,0,2 Current State: 21:[5, 20], Operations: ['88-84=4', '5*4=20'] Exploring Operation: 20/5=4, Resulting Numbers: [4] 4,21 unequal: No Solution Exploring Operation: 20-5=15, Resulting Numbers: [15] 15,21 unequal: No Solution Exploring Operation: 5+20=25, Resulting Numbers: [25] 25,21 unequal: No Solution Exploring Operation: 5*20=100, Resulting Numbers: [100] 100,21 unequal: No Solution Moving to Node #0,0,1 Current State: 21:[5, 20], Operations: ['88-84=4', '5*4=20'] Exploring Operation: 20-5=15, Resulting Numbers: [15] 15,21 unequal: No Solution Exploring Operation: 5+20=25, Resulting Numbers: [25] 25,21 unequal: No Solution Exploring Operation: 5*20=100, Resulting Numbers: [100] 100,21 unequal: No Solution Exploring Operation: 20/5=4, Resulting Numbers: [4] 4,21 unequal: No Solution Moving to Node #0,0,3 Current State: 21:[4, 10], Operations: ['88-84=4', '5+5=10'] Exploring Operation: 4*10=40, Resulting Numbers: [40] 40,21 unequal: No Solution Exploring Operation: 10-4=6, Resulting Numbers: [6] 6,21 unequal: No Solution Exploring Operation: 4+10=14, Resulting Numbers: [14] 14,21 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: 21:[5, 88, 79], Operations: ['84-5=79'] Exploring Operation: 88-5=83, Resulting Numbers: [79, 83] Generated Node #0,1,0: 21:[79, 83] Operation: 88-5=83 Exploring Operation: 79-5=74, Resulting Numbers: [88, 74] Generated Node #0,1,1: 21:[88, 74] Operation: 79-5=74 Exploring Operation: 5+88=93, Resulting Numbers: [79, 93] Generated Node #0,1,2: 21:[79, 93] Operation: 5+88=93 Exploring Operation: 88-79=9, Resulting Numbers: [5, 9] Generated Node #0,1,3: 21:[5, 9] Operation: 88-79=9 Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 21:[5, 9], Operations: ['84-5=79', '88-79=9'] Exploring Operation: 9-5=4, Resulting Numbers: [4] 4,21 unequal: No Solution Exploring Operation: 5+9=14, Resulting Numbers: [14] 14,21 unequal: No Solution Exploring Operation: 5*9=45, Resulting Numbers: [45] 45,21 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: 21:[79, 83], Operations: ['84-5=79', '88-5=83'] Exploring Operation: 79+83=162, Resulting Numbers: [162] 162,21 unequal: No Solution Exploring Operation: 79*83=6557, Resulting Numbers: [6557] 6557,21 unequal: No Solution Exploring Operation: 83-79=4, Resulting Numbers: [4] 4,21 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: 21:[88, 74], Operations: ['84-5=79', '79-5=74'] Exploring Operation: 88*74=6512, Resulting Numbers: [6512] 6512,21 unequal: No Solution Exploring Operation: 88+74=162, Resulting Numbers: [162] 162,21 unequal: No Solution Exploring Operation: 88-74=14, Resulting Numbers: [14] 14,21 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: 21:[79, 93], Operations: ['84-5=79', '5+88=93'] Exploring Operation: 79+93=172, Resulting Numbers: [172] 172,21 unequal: No Solution Exploring Operation: 93-79=14, Resulting Numbers: [14] 14,21 unequal: No Solution Exploring Operation: 79*93=7347, Resulting Numbers: [7347] 7347,21 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: 21:[84, 5, 83], Operations: ['88-5=83'] Exploring Operation: 84-83=1, Resulting Numbers: [5, 1] Generated Node #0,2,0: 21:[5, 1] Operation: 84-83=1 Exploring Operation: 84+5=89, Resulting Numbers: [83, 89] Generated Node #0,2,1: 21:[83, 89] Operation: 84+5=89 Exploring Operation: 84-5=79, Resulting Numbers: [83, 79] Generated Node #0,2,2: 21:[83, 79] Operation: 84-5=79 Exploring Operation: 83-5=78, Resulting Numbers: [84, 78] Generated Node #0,2,3: 21:[84, 78] Operation: 83-5=78 Moving to Node #0,2,0 Current State: 21:[5, 1], Operations: ['88-5=83', '84-83=1'] Exploring Operation: 5+1=6, Resulting Numbers: [6] 6,21 unequal: No Solution Exploring Operation: 5/1=5, Resulting Numbers: [5] 5,21 unequal: No Solution Exploring Operation: 5-1=4, Resulting Numbers: [4] 4,21 unequal: No Solution Exploring Operation: 5*1=5, Resulting Numbers: [5] 5,21 unequal: No Solution Moving to Node #0,2,3 Current State: 21:[84, 78], Operations: ['88-5=83', '83-5=78'] Exploring Operation: 84*78=6552, Resulting Numbers: [6552] 6552,21 unequal: No Solution Exploring Operation: 84+78=162, Resulting Numbers: [162] 162,21 unequal: No Solution Exploring Operation: 84-78=6, Resulting Numbers: [6] 6,21 unequal: No Solution Moving to Node #0,2,2 Current State: 21:[83, 79], Operations: ['88-5=83', '84-5=79'] Exploring Operation: 83+79=162, Resulting Numbers: [162] 162,21 unequal: No Solution Exploring Operation: 83-79=4, Resulting Numbers: [4] 4,21 unequal: No Solution Exploring Operation: 83*79=6557, Resulting Numbers: [6557] 6557,21 unequal: No Solution Moving to Node #0,2,1 Current State: 21:[83, 89], Operations: ['88-5=83', '84+5=89'] Exploring Operation: 89-83=6, Resulting Numbers: [6] 6,21 unequal: No Solution Exploring Operation: 83*89=7387, Resulting Numbers: [7387] 7387,21 unequal: No Solution Exploring Operation: 83+89=172, Resulting Numbers: [172] 172,21 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: 21:[5, 88, 79], Operations: ['84-5=79'] Exploring Operation: 88-5=83, Resulting Numbers: [79, 83] Generated Node #0,3,0: 21:[79, 83] Operation: 88-5=83 Exploring Operation: 5+88=93, Resulting Numbers: [79, 93] Generated Node #0,3,1: 21:[79, 93] Operation: 5+88=93 Exploring Operation: 79-5=74, Resulting Numbers: [88, 74] Generated Node #0,3,2: 21:[88, 74] Operation: 79-5=74 Exploring Operation: 88-79=9, Resulting Numbers: [5, 9] Generated Node #0,3,3: 21:[5, 9] Operation: 88-79=9 Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 21:[5, 9], Operations: ['84-5=79', '88-79=9'] Exploring Operation: 5*9=45, Resulting Numbers: [45] 45,21 unequal: No Solution Exploring Operation: 9-5=4, Resulting Numbers: [4] 4,21 unequal: No Solution Exploring Operation: 5+9=14, Resulting Numbers: [14] 14,21 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: 21:[79, 83], Operations: ['84-5=79', '88-5=83'] Exploring Operation: 79+83=162, Resulting Numbers: [162] 162,21 unequal: No Solution Exploring Operation: 79*83=6557, Resulting Numbers: [6557] 6557,21 unequal: No Solution Exploring Operation: 83-79=4, Resulting Numbers: [4] 4,21 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: 21:[88, 74], Operations: ['84-5=79', '79-5=74'] Exploring Operation: 88-74=14, Resulting Numbers: [14] 14,21 unequal: No Solution Exploring Operation: 88*74=6512, Resulting Numbers: [6512] 6512,21 unequal: No Solution Exploring Operation: 88+74=162, Resulting Numbers: [162] 162,21 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: 21:[79, 93], Operations: ['84-5=79', '5+88=93'] Exploring Operation: 93-79=14, Resulting Numbers: [14] 14,21 unequal: No Solution Exploring Operation: 79*93=7347, Resulting Numbers: [7347] 7347,21 unequal: No Solution Exploring Operation: 79+93=172, Resulting Numbers: [172] 172,21 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
[ 25, 97, 78, 90 ]
84
[ "97-25=72", "90-78=12", "72+12=84" ]
Current State: 84:[25, 97, 78, 90], Operations: [] Exploring Operation: 97-25=72, Resulting Numbers: [78, 90, 72] Generated Node #2: [78, 90, 72] from Operation: 97-25=72 Current State: 84:[78, 90, 72], Operations: ['97-25=72'] Exploring Operation: 90-78=12, Resulting Numbers: [72, 12] Generated Node #3: [72, 12] from Operation: 90-78=12 Current State: 84:[72, 12], Operations: ['97-25=72', '90-78=12'] Exploring Operation: 72+12=84, Resulting Numbers: [84] 84,84 equal: Goal Reached
4
Current State: 84:[25, 97, 78, 90], Operations: [] Exploring Operation: 97-90=7, Resulting Numbers: [25, 78, 7] Generated Node #0,0: 84:[25, 78, 7] Operation: 97-90=7 Exploring Operation: 97-78=19, Resulting Numbers: [25, 90, 19] Generated Node #0,1: 84:[25, 90, 19] Operation: 97-78=19 Exploring Operation: 90-78=12, Resulting Numbers: [25, 97, 12] Generated Node #0,2: 84:[25, 97, 12] Operation: 90-78=12 Exploring Operation: 97-25=72, Resulting Numbers: [78, 90, 72] Generated Node #0,3: 84:[78, 90, 72] Operation: 97-25=72 Start Sub Search at level 1: Moving to Node #0,0 Current State: 84:[25, 78, 7], Operations: ['97-90=7'] Exploring Operation: 25+7=32, Resulting Numbers: [78, 32] Generated Node #0,0,0: 84:[78, 32] Operation: 25+7=32 Exploring Operation: 25-7=18, Resulting Numbers: [78, 18] Generated Node #0,0,1: 84:[78, 18] Operation: 25-7=18 Exploring Operation: 78+7=85, Resulting Numbers: [25, 85] Generated Node #0,0,2: 84:[25, 85] Operation: 78+7=85 Exploring Operation: 78-25=53, Resulting Numbers: [7, 53] Generated Node #0,0,3: 84:[7, 53] Operation: 78-25=53 Moving to Node #0,0,2 Current State: 84:[25, 85], Operations: ['97-90=7', '78+7=85'] Exploring Operation: 25+85=110, Resulting Numbers: [110] 110,84 unequal: No Solution Exploring Operation: 85-25=60, Resulting Numbers: [60] 60,84 unequal: No Solution Exploring Operation: 25*85=2125, Resulting Numbers: [2125] 2125,84 unequal: No Solution Moving to Node #0,0,1 Current State: 84:[78, 18], Operations: ['97-90=7', '25-7=18'] Exploring Operation: 78+18=96, Resulting Numbers: [96] 96,84 unequal: No Solution Exploring Operation: 78*18=1404, Resulting Numbers: [1404] 1404,84 unequal: No Solution Exploring Operation: 78-18=60, Resulting Numbers: [60] 60,84 unequal: No Solution Moving to Node #0,0,0 Current State: 84:[78, 32], Operations: ['97-90=7', '25+7=32'] Exploring Operation: 78+32=110, Resulting Numbers: [110] 110,84 unequal: No Solution Exploring Operation: 78*32=2496, Resulting Numbers: [2496] 2496,84 unequal: No Solution Exploring Operation: 78-32=46, Resulting Numbers: [46] 46,84 unequal: No Solution Moving to Node #0,0,3 Current State: 84:[7, 53], Operations: ['97-90=7', '78-25=53'] Exploring Operation: 7*53=371, Resulting Numbers: [371] 371,84 unequal: No Solution Exploring Operation: 7+53=60, Resulting Numbers: [60] 60,84 unequal: No Solution Exploring Operation: 53-7=46, Resulting Numbers: [46] 46,84 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 #0,1 Current State: 84:[25, 90, 19], Operations: ['97-78=19'] Exploring Operation: 25-19=6, Resulting Numbers: [90, 6] Generated Node #0,1,0: 84:[90, 6] Operation: 25-19=6 Exploring Operation: 25+19=44, Resulting Numbers: [90, 44] Generated Node #0,1,1: 84:[90, 44] Operation: 25+19=44 Exploring Operation: 90-19=71, Resulting Numbers: [25, 71] Generated Node #0,1,2: 84:[25, 71] Operation: 90-19=71 Exploring Operation: 90-25=65, Resulting Numbers: [19, 65] Generated Node #0,1,3: 84:[19, 65] Operation: 90-25=65 Moving to Node #0,1,0 Current State: 84:[90, 6], Operations: ['97-78=19', '25-19=6'] Exploring Operation: 90+6=96, Resulting Numbers: [96] 96,84 unequal: No Solution Exploring Operation: 90*6=540, Resulting Numbers: [540] 540,84 unequal: No Solution Exploring Operation: 90-6=84, Resulting Numbers: [84] 84,84 equal: Goal Reached Moving to Node #0 Current State: 84:[25, 97, 78, 90], Operations: [] Exploring Operation: 97-78=19, Resulting Numbers: [25, 90, 19] Generated Node #0,1: 84:[25, 90, 19] Operation: 97-78=19 Moving to Node #0,1 Current State: 84:[25, 90, 19], Operations: ['97-78=19'] Exploring Operation: 25-19=6, Resulting Numbers: [90, 6] Generated Node #0,1,0: 84:[90, 6] Operation: 25-19=6 Moving to Node #0,1,0 Current State: 84:[90, 6], Operations: ['97-78=19', '25-19=6'] Exploring Operation: 90-6=84, Resulting Numbers: [84] 84,84 equal: Goal Reached Exit Sub Search at level 1
0.97309
hs_4
mult_heuristic
[ 35, 12, 20, 18 ]
11
[ "20-18=2", "12*2=24", "35-24=11" ]
Current State: 11:[35, 12, 20, 18], Operations: [] Exploring Operation: 20-18=2, Resulting Numbers: [35, 12, 2] Generated Node #2: [35, 12, 2] from Operation: 20-18=2 Current State: 11:[35, 12, 2], Operations: ['20-18=2'] Exploring Operation: 12*2=24, Resulting Numbers: [35, 24] Generated Node #3: [35, 24] from Operation: 12*2=24 Current State: 11:[35, 24], Operations: ['20-18=2', '12*2=24'] Exploring Operation: 35-24=11, Resulting Numbers: [11] 11,11 equal: Goal Reached
4
Current State: 11:[35, 12, 20, 18], Operations: [] Exploring Operation: 35-12=23, Resulting Numbers: [20, 18, 23] Generated Node #0,0: 11:[20, 18, 23] Operation: 35-12=23 Exploring Operation: 35-18=17, Resulting Numbers: [12, 20, 17] Generated Node #0,1: 11:[12, 20, 17] Operation: 35-18=17 Exploring Operation: 35-20=15, Resulting Numbers: [12, 18, 15] Generated Node #0,2: 11:[12, 18, 15] Operation: 35-20=15 Exploring Operation: 20-12=8, Resulting Numbers: [35, 18, 8] Generated Node #0,3: 11:[35, 18, 8] Operation: 20-12=8 Exploring Operation: 20-18=2, Resulting Numbers: [35, 12, 2] Generated Node #0,4: 11:[35, 12, 2] Operation: 20-18=2 Moving to Node #0,2 Current State: 11:[12, 18, 15], Operations: ['35-20=15'] Exploring Operation: 18-12=6, Resulting Numbers: [15, 6] Generated Node #0,2,0: 11:[15, 6] Operation: 18-12=6 Exploring Operation: 15-12=3, Resulting Numbers: [18, 3] Generated Node #0,2,1: 11:[18, 3] Operation: 15-12=3 Exploring Operation: 12+18=30, Resulting Numbers: [15, 30] Generated Node #0,2,2: 11:[15, 30] Operation: 12+18=30 Exploring Operation: 12+15=27, Resulting Numbers: [18, 27] Generated Node #0,2,3: 11:[18, 27] Operation: 12+15=27 Exploring Operation: 18-15=3, Resulting Numbers: [12, 3] Generated Node #0,2,4: 11:[12, 3] Operation: 18-15=3 Moving to Node #0,1 Current State: 11:[12, 20, 17], Operations: ['35-18=17'] Exploring Operation: 17-12=5, Resulting Numbers: [20, 5] Generated Node #0,1,0: 11:[20, 5] Operation: 17-12=5 Exploring Operation: 12+17=29, Resulting Numbers: [20, 29] Generated Node #0,1,1: 11:[20, 29] Operation: 12+17=29 Exploring Operation: 20-12=8, Resulting Numbers: [17, 8] Generated Node #0,1,2: 11:[17, 8] Operation: 20-12=8 Exploring Operation: 20-17=3, Resulting Numbers: [12, 3] Generated Node #0,1,3: 11:[12, 3] Operation: 20-17=3 Exploring Operation: 12+20=32, Resulting Numbers: [17, 32] Generated Node #0,1,4: 11:[17, 32] Operation: 12+20=32 Moving to Node #0,0 Current State: 11:[20, 18, 23], Operations: ['35-12=23'] Exploring Operation: 20+18=38, Resulting Numbers: [23, 38] Generated Node #0,0,0: 11:[23, 38] Operation: 20+18=38 Exploring Operation: 20+23=43, Resulting Numbers: [18, 43] Generated Node #0,0,1: 11:[18, 43] Operation: 20+23=43 Exploring Operation: 20-18=2, Resulting Numbers: [23, 2] Generated Node #0,0,2: 11:[23, 2] Operation: 20-18=2 Exploring Operation: 23-18=5, Resulting Numbers: [20, 5] Generated Node #0,0,3: 11:[20, 5] Operation: 23-18=5 Exploring Operation: 23-20=3, Resulting Numbers: [18, 3] Generated Node #0,0,4: 11:[18, 3] Operation: 23-20=3 Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 11:[20, 5], Operations: ['35-12=23', '23-18=5'] Exploring Operation: 20+5=25, Resulting Numbers: [25] 25,11 unequal: No Solution Exploring Operation: 20/5=4, Resulting Numbers: [4] 4,11 unequal: No Solution Exploring Operation: 20-5=15, Resulting Numbers: [15] 15,11 unequal: No Solution Exploring Operation: 20*5=100, Resulting Numbers: [100] 100,11 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 #0,0,4 Current State: 11:[18, 3], Operations: ['35-12=23', '23-20=3'] Exploring Operation: 18/3=6, Resulting Numbers: [6] 6,11 unequal: No Solution Exploring Operation: 18-3=15, Resulting Numbers: [15] 15,11 unequal: No Solution Exploring Operation: 18*3=54, Resulting Numbers: [54] 54,11 unequal: No Solution Exploring Operation: 18+3=21, Resulting Numbers: [21] 21,11 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: 11:[23, 2], Operations: ['35-12=23', '20-18=2'] Exploring Operation: 23-2=21, Resulting Numbers: [21] 21,11 unequal: No Solution Exploring Operation: 23*2=46, Resulting Numbers: [46] 46,11 unequal: No Solution Exploring Operation: 23+2=25, Resulting Numbers: [25] 25,11 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: 11:[23, 38], Operations: ['35-12=23', '20+18=38'] Exploring Operation: 23*38=874, Resulting Numbers: [874] 874,11 unequal: No Solution Exploring Operation: 23+38=61, Resulting Numbers: [61] 61,11 unequal: No Solution Exploring Operation: 38-23=15, Resulting Numbers: [15] 15,11 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: 11:[18, 43], Operations: ['35-12=23', '20+23=43'] Exploring Operation: 43-18=25, Resulting Numbers: [25] 25,11 unequal: No Solution Exploring Operation: 18*43=774, Resulting Numbers: [774] 774,11 unequal: No Solution Exploring Operation: 18+43=61, Resulting Numbers: [61] 61,11 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: 11:[35, 18, 8], Operations: ['20-12=8'] Exploring Operation: 35-8=27, Resulting Numbers: [18, 27] Generated Node #0,3,0: 11:[18, 27] Operation: 35-8=27 Exploring Operation: 18-8=10, Resulting Numbers: [35, 10] Generated Node #0,3,1: 11:[35, 10] Operation: 18-8=10 Exploring Operation: 35+8=43, Resulting Numbers: [18, 43] Generated Node #0,3,2: 11:[18, 43] Operation: 35+8=43 Exploring Operation: 35-18=17, Resulting Numbers: [8, 17] Generated Node #0,3,3: 11:[8, 17] Operation: 35-18=17 Exploring Operation: 18+8=26, Resulting Numbers: [35, 26] Generated Node #0,3,4: 11:[35, 26] Operation: 18+8=26 Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 11:[8, 17], Operations: ['20-12=8', '35-18=17'] Exploring Operation: 8*17=136, Resulting Numbers: [136] 136,11 unequal: No Solution Exploring Operation: 17-8=9, Resulting Numbers: [9] 9,11 unequal: No Solution Exploring Operation: 8+17=25, Resulting Numbers: [25] 25,11 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: 11:[18, 27], Operations: ['20-12=8', '35-8=27'] Exploring Operation: 18+27=45, Resulting Numbers: [45] 45,11 unequal: No Solution Exploring Operation: 27-18=9, Resulting Numbers: [9] 9,11 unequal: No Solution Exploring Operation: 18*27=486, Resulting Numbers: [486] 486,11 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: 11:[35, 10], Operations: ['20-12=8', '18-8=10'] Exploring Operation: 35-10=25, Resulting Numbers: [25] 25,11 unequal: No Solution Exploring Operation: 35+10=45, Resulting Numbers: [45] 45,11 unequal: No Solution Exploring Operation: 35*10=350, Resulting Numbers: [350] 350,11 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: 11:[18, 43], Operations: ['20-12=8', '35+8=43'] Exploring Operation: 18+43=61, Resulting Numbers: [61] 61,11 unequal: No Solution Exploring Operation: 43-18=25, Resulting Numbers: [25] 25,11 unequal: No Solution Exploring Operation: 18*43=774, Resulting Numbers: [774] 774,11 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: 11:[35, 26], Operations: ['20-12=8', '18+8=26'] Exploring Operation: 35*26=910, Resulting Numbers: [910] 910,11 unequal: No Solution Exploring Operation: 35+26=61, Resulting Numbers: [61] 61,11 unequal: No Solution Exploring Operation: 35-26=9, Resulting Numbers: [9] 9,11 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: 11:[35, 12, 2], Operations: ['20-18=2'] Exploring Operation: 35+2=37, Resulting Numbers: [12, 37] Generated Node #0,4,0: 11:[12, 37] Operation: 35+2=37 Exploring Operation: 12+2=14, Resulting Numbers: [35, 14] Generated Node #0,4,1: 11:[35, 14] Operation: 12+2=14 Exploring Operation: 35-2=33, Resulting Numbers: [12, 33] Generated Node #0,4,2: 11:[12, 33] Operation: 35-2=33 Exploring Operation: 12-2=10, Resulting Numbers: [35, 10] Generated Node #0,4,3: 11:[35, 10] Operation: 12-2=10 Exploring Operation: 35-12=23, Resulting Numbers: [2, 23] Generated Node #0,4,4: 11:[2, 23] Operation: 35-12=23 Start Sub Search at level 1: Moving to Node #0,4,4 Current State: 11:[2, 23], Operations: ['20-18=2', '35-12=23'] Exploring Operation: 2*23=46, Resulting Numbers: [46] 46,11 unequal: No Solution Exploring Operation: 2+23=25, Resulting Numbers: [25] 25,11 unequal: No Solution Exploring Operation: 23-2=21, Resulting Numbers: [21] 21,11 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: 11:[12, 33], Operations: ['20-18=2', '35-2=33'] Exploring Operation: 12*33=396, Resulting Numbers: [396] 396,11 unequal: No Solution Exploring Operation: 33-12=21, Resulting Numbers: [21] 21,11 unequal: No Solution Exploring Operation: 12+33=45, Resulting Numbers: [45] 45,11 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: 11:[35, 10], Operations: ['20-18=2', '12-2=10'] Exploring Operation: 35-10=25, Resulting Numbers: [25] 25,11 unequal: No Solution Exploring Operation: 35*10=350, Resulting Numbers: [350] 350,11 unequal: No Solution Exploring Operation: 35+10=45, Resulting Numbers: [45] 45,11 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: 11:[12, 37], Operations: ['20-18=2', '35+2=37'] Exploring Operation: 37-12=25, Resulting Numbers: [25] 25,11 unequal: No Solution Exploring Operation: 12*37=444, Resulting Numbers: [444] 444,11 unequal: No Solution Exploring Operation: 12+37=49, Resulting Numbers: [49] 49,11 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: 11:[35, 14], Operations: ['20-18=2', '12+2=14'] Exploring Operation: 35-14=21, Resulting Numbers: [21] 21,11 unequal: No Solution Exploring Operation: 35*14=490, Resulting Numbers: [490] 490,11 unequal: No Solution Exploring Operation: 35+14=49, Resulting Numbers: [49] 49,11 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2,0 Current State: 11:[15, 6], Operations: ['35-20=15', '18-12=6'] Exploring Operation: 15+6=21, Resulting Numbers: [21] 21,11 unequal: No Solution Exploring Operation: 15*6=90, Resulting Numbers: [90] 90,11 unequal: No Solution Exploring Operation: 15-6=9, Resulting Numbers: [9] 9,11 unequal: No Solution Moving to Node #0,1,2 Current State: 11:[17, 8], Operations: ['35-18=17', '20-12=8'] Exploring Operation: 17+8=25, Resulting Numbers: [25] 25,11 unequal: No Solution Exploring Operation: 17*8=136, Resulting Numbers: [136] 136,11 unequal: No Solution Exploring Operation: 17-8=9, Resulting Numbers: [9] 9,11 unequal: No Solution Moving to Node #0,1,3 Current State: 11:[12, 3], Operations: ['35-18=17', '20-17=3'] Exploring Operation: 12*3=36, Resulting Numbers: [36] 36,11 unequal: No Solution Exploring Operation: 12-3=9, Resulting Numbers: [9] 9,11 unequal: No Solution Exploring Operation: 12/3=4, Resulting Numbers: [4] 4,11 unequal: No Solution Exploring Operation: 12+3=15, Resulting Numbers: [15] 15,11 unequal: No Solution Moving to Node #0,2,4 Current State: 11:[12, 3], Operations: ['35-20=15', '18-15=3'] Exploring Operation: 12-3=9, Resulting Numbers: [9] 9,11 unequal: No Solution Exploring Operation: 12/3=4, Resulting Numbers: [4] 4,11 unequal: No Solution Exploring Operation: 12+3=15, Resulting Numbers: [15] 15,11 unequal: No Solution Exploring Operation: 12*3=36, Resulting Numbers: [36] 36,11 unequal: No Solution Moving to Node #0,2,1 Current State: 11:[18, 3], Operations: ['35-20=15', '15-12=3'] Exploring Operation: 18*3=54, Resulting Numbers: [54] 54,11 unequal: No Solution Exploring Operation: 18+3=21, Resulting Numbers: [21] 21,11 unequal: No Solution Exploring Operation: 18-3=15, Resulting Numbers: [15] 15,11 unequal: No Solution Exploring Operation: 18/3=6, Resulting Numbers: [6] 6,11 unequal: No Solution Moving to Node #0,1,0 Current State: 11:[20, 5], Operations: ['35-18=17', '17-12=5'] Exploring Operation: 20+5=25, Resulting Numbers: [25] 25,11 unequal: No Solution Exploring Operation: 20-5=15, Resulting Numbers: [15] 15,11 unequal: No Solution Exploring Operation: 20/5=4, Resulting Numbers: [4] 4,11 unequal: No Solution Exploring Operation: 20*5=100, Resulting Numbers: [100] 100,11 unequal: No Solution Moving to Node #0,2,3 Current State: 11:[18, 27], Operations: ['35-20=15', '12+15=27'] Exploring Operation: 18*27=486, Resulting Numbers: [486] 486,11 unequal: No Solution Exploring Operation: 18+27=45, Resulting Numbers: [45] 45,11 unequal: No Solution Exploring Operation: 27-18=9, Resulting Numbers: [9] 9,11 unequal: No Solution Moving to Node #0,2,2 Current State: 11:[15, 30], Operations: ['35-20=15', '12+18=30'] Exploring Operation: 30-15=15, Resulting Numbers: [15] 15,11 unequal: No Solution Exploring Operation: 15*30=450, Resulting Numbers: [450] 450,11 unequal: No Solution Exploring Operation: 30/15=2, Resulting Numbers: [2] 2,11 unequal: No Solution Exploring Operation: 15+30=45, Resulting Numbers: [45] 45,11 unequal: No Solution Moving to Node #0,1,4 Current State: 11:[17, 32], Operations: ['35-18=17', '12+20=32'] Exploring Operation: 17+32=49, Resulting Numbers: [49] 49,11 unequal: No Solution Exploring Operation: 32-17=15, Resulting Numbers: [15] 15,11 unequal: No Solution Exploring Operation: 17*32=544, Resulting Numbers: [544] 544,11 unequal: No Solution Moving to Node #0,1,1 Current State: 11:[20, 29], Operations: ['35-18=17', '12+17=29'] Exploring Operation: 20+29=49, Resulting Numbers: [49] 49,11 unequal: No Solution Exploring Operation: 20*29=580, Resulting Numbers: [580] 580,11 unequal: No Solution Exploring Operation: 29-20=9, Resulting Numbers: [9] 9,11 unequal: No Solution No solution found.
0
hs_5
mult_heuristic
[ 56, 21, 61, 2 ]
63
[ "61-56=5", "5-2=3", "21*3=63" ]
Current State: 63:[56, 21, 61, 2], Operations: [] Exploring Operation: 61-56=5, Resulting Numbers: [21, 2, 5] Generated Node #2: [21, 2, 5] from Operation: 61-56=5 Current State: 63:[21, 2, 5], Operations: ['61-56=5'] Exploring Operation: 5-2=3, Resulting Numbers: [21, 3] Generated Node #3: [21, 3] from Operation: 5-2=3 Current State: 63:[21, 3], Operations: ['61-56=5', '5-2=3'] Exploring Operation: 21*3=63, Resulting Numbers: [63] 63,63 equal: Goal Reached
4
Current State: 63:[56, 21, 61, 2], Operations: [] Exploring Operation: 61-56=5, Resulting Numbers: [21, 2, 5] Generated Node #0,0: 63:[21, 2, 5] Operation: 61-56=5 Exploring Operation: 56+2=58, Resulting Numbers: [21, 61, 58] Generated Node #0,1: 63:[21, 61, 58] Operation: 56+2=58 Moving to Node #0,0 Current State: 63:[21, 2, 5], Operations: ['61-56=5'] Exploring Operation: 2+5=7, Resulting Numbers: [21, 7] Generated Node #0,0,0: 63:[21, 7] Operation: 2+5=7 Exploring Operation: 5-2=3, Resulting Numbers: [21, 3] Generated Node #0,0,1: 63:[21, 3] Operation: 5-2=3 Moving to Node #0,1 Current State: 63:[21, 61, 58], Operations: ['56+2=58'] Exploring Operation: 21+58=79, Resulting Numbers: [61, 79] Generated Node #0,1,0: 63:[61, 79] Operation: 21+58=79 Exploring Operation: 61-58=3, Resulting Numbers: [21, 3] Generated Node #0,1,1: 63:[21, 3] Operation: 61-58=3 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 63:[21, 3], Operations: ['56+2=58', '61-58=3'] Exploring Operation: 21/3=7, Resulting Numbers: [7] 7,63 unequal: No Solution Exploring Operation: 21*3=63, Resulting Numbers: [63] 63,63 equal: Goal Reached Moving to Node #0 Current State: 63:[56, 21, 61, 2], Operations: [] Exploring Operation: 56+2=58, Resulting Numbers: [21, 61, 58] Generated Node #0,1: 63:[21, 61, 58] Operation: 56+2=58 Moving to Node #0,1 Current State: 63:[21, 61, 58], Operations: ['56+2=58'] Exploring Operation: 61-58=3, Resulting Numbers: [21, 3] Generated Node #0,1,1: 63:[21, 3] Operation: 61-58=3 Moving to Node #0,1,1 Current State: 63:[21, 3], Operations: ['56+2=58', '61-58=3'] Exploring Operation: 21*3=63, Resulting Numbers: [63] 63,63 equal: Goal Reached Exit Sub Search at level 1
0.989583
hs_2
mult_heuristic
[ 56, 69, 55, 58 ]
11
[ "56-55=1", "69-58=11", "1*11=11" ]
Current State: 11:[56, 69, 55, 58], Operations: [] Exploring Operation: 56-55=1, Resulting Numbers: [69, 58, 1] Generated Node #2: [69, 58, 1] from Operation: 56-55=1 Current State: 11:[69, 58, 1], Operations: ['56-55=1'] Exploring Operation: 69-58=11, Resulting Numbers: [1, 11] Generated Node #3: [1, 11] from Operation: 69-58=11 Current State: 11:[1, 11], Operations: ['56-55=1', '69-58=11'] Exploring Operation: 1*11=11, Resulting Numbers: [11] 11,11 equal: Goal Reached
4
Current State: 11:[56, 69, 55, 58], Operations: [] Exploring Operation: 69-58=11, Resulting Numbers: [56, 55, 11] Generated Node #0,0: 11:[56, 55, 11] Operation: 69-58=11 Start Sub Search at level 1: Moving to Node #0,0 Current State: 11:[56, 55, 11], Operations: ['69-58=11'] Exploring Operation: 56-55=1, Resulting Numbers: [11, 1] Generated Node #0,0,0: 11:[11, 1] Operation: 56-55=1 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 11:[11, 1], Operations: ['69-58=11', '56-55=1'] Exploring Operation: 11*1=11, Resulting Numbers: [11] 11,11 equal: Goal Reached Moving to Node #0 Current State: 11:[56, 69, 55, 58], Operations: [] Exploring Operation: 69-58=11, Resulting Numbers: [56, 55, 11] Generated Node #0,0: 11:[56, 55, 11] Operation: 69-58=11 Moving to Node #0,0 Current State: 11:[56, 55, 11], Operations: ['69-58=11'] Exploring Operation: 56-55=1, Resulting Numbers: [11, 1] Generated Node #0,0,0: 11:[11, 1] Operation: 56-55=1 Moving to Node #0,0,0 Current State: 11:[11, 1], Operations: ['69-58=11', '56-55=1'] Exploring Operation: 11*1=11, Resulting Numbers: [11] 11,11 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.993924
hs_1
sum_heuristic
[ 28, 13, 32, 59 ]
35
[ "32+59=91", "91/13=7", "28+7=35" ]
Current State: 35:[28, 13, 32, 59], Operations: [] Exploring Operation: 32+59=91, Resulting Numbers: [28, 13, 91] Generated Node #2: [28, 13, 91] from Operation: 32+59=91 Current State: 35:[28, 13, 91], Operations: ['32+59=91'] Exploring Operation: 91/13=7, Resulting Numbers: [28, 7] Generated Node #3: [28, 7] from Operation: 91/13=7 Current State: 35:[28, 7], Operations: ['32+59=91', '91/13=7'] Exploring Operation: 28+7=35, Resulting Numbers: [35] 35,35 equal: Goal Reached
4
Current State: 35:[28, 13, 32, 59], Operations: [] Exploring Operation: 59-32=27, Resulting Numbers: [28, 13, 27] Generated Node #0,0: 35:[28, 13, 27] Operation: 59-32=27 Exploring Operation: 59-28=31, Resulting Numbers: [13, 32, 31] Generated Node #0,1: 35:[13, 32, 31] Operation: 59-28=31 Exploring Operation: 59-13=46, Resulting Numbers: [28, 32, 46] Generated Node #0,2: 35:[28, 32, 46] Operation: 59-13=46 Exploring Operation: 32-28=4, Resulting Numbers: [13, 59, 4] Generated Node #0,3: 35:[13, 59, 4] Operation: 32-28=4 Start Sub Search at level 1: Moving to Node #0,1 Current State: 35:[13, 32, 31], Operations: ['59-28=31'] Exploring Operation: 32-31=1, Resulting Numbers: [13, 1] Generated Node #0,1,0: 35:[13, 1] Operation: 32-31=1 Exploring Operation: 13+32=45, Resulting Numbers: [31, 45] Generated Node #0,1,1: 35:[31, 45] Operation: 13+32=45 Exploring Operation: 31-13=18, Resulting Numbers: [32, 18] Generated Node #0,1,2: 35:[32, 18] Operation: 31-13=18 Exploring Operation: 13+31=44, Resulting Numbers: [32, 44] Generated Node #0,1,3: 35:[32, 44] Operation: 13+31=44 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 35:[13, 1], Operations: ['59-28=31', '32-31=1'] Exploring Operation: 13*1=13, Resulting Numbers: [13] 13,35 unequal: No Solution Exploring Operation: 13+1=14, Resulting Numbers: [14] 14,35 unequal: No Solution Exploring Operation: 13/1=13, Resulting Numbers: [13] 13,35 unequal: No Solution Exploring Operation: 13-1=12, Resulting Numbers: [12] 12,35 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: 35:[32, 44], Operations: ['59-28=31', '13+31=44'] Exploring Operation: 44-32=12, Resulting Numbers: [12] 12,35 unequal: No Solution Exploring Operation: 32*44=1408, Resulting Numbers: [1408] 1408,35 unequal: No Solution Exploring Operation: 32+44=76, Resulting Numbers: [76] 76,35 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: 35:[31, 45], Operations: ['59-28=31', '13+32=45'] Exploring Operation: 45-31=14, Resulting Numbers: [14] 14,35 unequal: No Solution Exploring Operation: 31+45=76, Resulting Numbers: [76] 76,35 unequal: No Solution Exploring Operation: 31*45=1395, Resulting Numbers: [1395] 1395,35 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: 35:[32, 18], Operations: ['59-28=31', '31-13=18'] Exploring Operation: 32+18=50, Resulting Numbers: [50] 50,35 unequal: No Solution Exploring Operation: 32-18=14, Resulting Numbers: [14] 14,35 unequal: No Solution Exploring Operation: 32*18=576, Resulting Numbers: [576] 576,35 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: 35:[28, 13, 27], Operations: ['59-32=27'] Exploring Operation: 28+13=41, Resulting Numbers: [27, 41] Generated Node #0,0,0: 35:[27, 41] Operation: 28+13=41 Exploring Operation: 28-27=1, Resulting Numbers: [13, 1] Generated Node #0,0,1: 35:[13, 1] Operation: 28-27=1 Exploring Operation: 27-13=14, Resulting Numbers: [28, 14] Generated Node #0,0,2: 35:[28, 14] Operation: 27-13=14 Exploring Operation: 13+27=40, Resulting Numbers: [28, 40] Generated Node #0,0,3: 35:[28, 40] Operation: 13+27=40 Moving to Node #0,0,1 Current State: 35:[13, 1], Operations: ['59-32=27', '28-27=1'] Exploring Operation: 13-1=12, Resulting Numbers: [12] 12,35 unequal: No Solution Exploring Operation: 13+1=14, Resulting Numbers: [14] 14,35 unequal: No Solution Exploring Operation: 13*1=13, Resulting Numbers: [13] 13,35 unequal: No Solution Exploring Operation: 13/1=13, Resulting Numbers: [13] 13,35 unequal: No Solution Moving to Node #0,0,3 Current State: 35:[28, 40], Operations: ['59-32=27', '13+27=40'] Exploring Operation: 28+40=68, Resulting Numbers: [68] 68,35 unequal: No Solution Exploring Operation: 28*40=1120, Resulting Numbers: [1120] 1120,35 unequal: No Solution Exploring Operation: 40-28=12, Resulting Numbers: [12] 12,35 unequal: No Solution Moving to Node #0,0,2 Current State: 35:[28, 14], Operations: ['59-32=27', '27-13=14'] Exploring Operation: 28+14=42, Resulting Numbers: [42] 42,35 unequal: No Solution Exploring Operation: 28/14=2, Resulting Numbers: [2] 2,35 unequal: No Solution Exploring Operation: 28*14=392, Resulting Numbers: [392] 392,35 unequal: No Solution Exploring Operation: 28-14=14, Resulting Numbers: [14] 14,35 unequal: No Solution Moving to Node #0,0,0 Current State: 35:[27, 41], Operations: ['59-32=27', '28+13=41'] Exploring Operation: 27*41=1107, Resulting Numbers: [1107] 1107,35 unequal: No Solution Exploring Operation: 27+41=68, Resulting Numbers: [68] 68,35 unequal: No Solution Exploring Operation: 41-27=14, Resulting Numbers: [14] 14,35 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 Current State: 35:[28, 32, 46], Operations: ['59-13=46'] Exploring Operation: 46-28=18, Resulting Numbers: [32, 18] Generated Node #0,2,0: 35:[32, 18] Operation: 46-28=18 Exploring Operation: 46-32=14, Resulting Numbers: [28, 14] Generated Node #0,2,1: 35:[28, 14] Operation: 46-32=14 Exploring Operation: 28+32=60, Resulting Numbers: [46, 60] Generated Node #0,2,2: 35:[46, 60] Operation: 28+32=60 Exploring Operation: 32-28=4, Resulting Numbers: [46, 4] Generated Node #0,2,3: 35:[46, 4] Operation: 32-28=4 Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 35:[46, 4], Operations: ['59-13=46', '32-28=4'] Exploring Operation: 46+4=50, Resulting Numbers: [50] 50,35 unequal: No Solution Exploring Operation: 46*4=184, Resulting Numbers: [184] 184,35 unequal: No Solution Exploring Operation: 46-4=42, Resulting Numbers: [42] 42,35 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: 35:[32, 18], Operations: ['59-13=46', '46-28=18'] Exploring Operation: 32*18=576, Resulting Numbers: [576] 576,35 unequal: No Solution Exploring Operation: 32-18=14, Resulting Numbers: [14] 14,35 unequal: No Solution Exploring Operation: 32+18=50, Resulting Numbers: [50] 50,35 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: 35:[28, 14], Operations: ['59-13=46', '46-32=14'] Exploring Operation: 28+14=42, Resulting Numbers: [42] 42,35 unequal: No Solution Exploring Operation: 28/14=2, Resulting Numbers: [2] 2,35 unequal: No Solution Exploring Operation: 28-14=14, Resulting Numbers: [14] 14,35 unequal: No Solution Exploring Operation: 28*14=392, Resulting Numbers: [392] 392,35 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: 35:[46, 60], Operations: ['59-13=46', '28+32=60'] Exploring Operation: 46+60=106, Resulting Numbers: [106] 106,35 unequal: No Solution Exploring Operation: 46*60=2760, Resulting Numbers: [2760] 2760,35 unequal: No Solution Exploring Operation: 60-46=14, Resulting Numbers: [14] 14,35 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: 35:[13, 59, 4], Operations: ['32-28=4'] Exploring Operation: 13+4=17, Resulting Numbers: [59, 17] Generated Node #0,3,0: 35:[59, 17] Operation: 13+4=17 Exploring Operation: 59-13=46, Resulting Numbers: [4, 46] Generated Node #0,3,1: 35:[4, 46] Operation: 59-13=46 Exploring Operation: 59-4=55, Resulting Numbers: [13, 55] Generated Node #0,3,2: 35:[13, 55] Operation: 59-4=55 Exploring Operation: 13-4=9, Resulting Numbers: [59, 9] Generated Node #0,3,3: 35:[59, 9] Operation: 13-4=9 Moving to Node #0,3,1 Current State: 35:[4, 46], Operations: ['32-28=4', '59-13=46'] Exploring Operation: 46-4=42, Resulting Numbers: [42] 42,35 unequal: No Solution Exploring Operation: 4*46=184, Resulting Numbers: [184] 184,35 unequal: No Solution Exploring Operation: 4+46=50, Resulting Numbers: [50] 50,35 unequal: No Solution Moving to Node #0,3,3 Current State: 35:[59, 9], Operations: ['32-28=4', '13-4=9'] Exploring Operation: 59-9=50, Resulting Numbers: [50] 50,35 unequal: No Solution Exploring Operation: 59*9=531, Resulting Numbers: [531] 531,35 unequal: No Solution Exploring Operation: 59+9=68, Resulting Numbers: [68] 68,35 unequal: No Solution Moving to Node #0,3,2 Current State: 35:[13, 55], Operations: ['32-28=4', '59-4=55'] Exploring Operation: 13*55=715, Resulting Numbers: [715] 715,35 unequal: No Solution Exploring Operation: 55-13=42, Resulting Numbers: [42] 42,35 unequal: No Solution Exploring Operation: 13+55=68, Resulting Numbers: [68] 68,35 unequal: No Solution Moving to Node #0,3,0 Current State: 35:[59, 17], Operations: ['32-28=4', '13+4=17'] Exploring Operation: 59+17=76, Resulting Numbers: [76] 76,35 unequal: No Solution Exploring Operation: 59*17=1003, Resulting Numbers: [1003] 1003,35 unequal: No Solution Exploring Operation: 59-17=42, Resulting Numbers: [42] 42,35 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
[ 45, 59, 80, 70 ]
75
[ "59-45=14", "70/14=5", "80-5=75" ]
Current State: 75:[45, 59, 80, 70], Operations: [] Exploring Operation: 59-45=14, Resulting Numbers: [80, 70, 14] Generated Node #2: [80, 70, 14] from Operation: 59-45=14 Current State: 75:[80, 70, 14], Operations: ['59-45=14'] Exploring Operation: 70/14=5, Resulting Numbers: [80, 5] Generated Node #3: [80, 5] from Operation: 70/14=5 Current State: 75:[80, 5], Operations: ['59-45=14', '70/14=5'] Exploring Operation: 80-5=75, Resulting Numbers: [75] 75,75 equal: Goal Reached
4
Current State: 75:[45, 59, 80, 70], Operations: [] Exploring Operation: 59-45=14, Resulting Numbers: [80, 70, 14] Generated Node #0,0: 75:[80, 70, 14] Operation: 59-45=14 Start Sub Search at level 1: Moving to Node #0,0 Current State: 75:[80, 70, 14], Operations: ['59-45=14'] Exploring Operation: 70/14=5, Resulting Numbers: [80, 5] Generated Node #0,0,0: 75:[80, 5] Operation: 70/14=5 Moving to Node #0,0,0 Current State: 75:[80, 5], Operations: ['59-45=14', '70/14=5'] Exploring Operation: 80-5=75, Resulting Numbers: [75] 75,75 equal: Goal Reached Moving to Node #0 Current State: 75:[45, 59, 80, 70], Operations: [] Exploring Operation: 59-45=14, Resulting Numbers: [80, 70, 14] Generated Node #0,0: 75:[80, 70, 14] Operation: 59-45=14 Moving to Node #0,0 Current State: 75:[80, 70, 14], Operations: ['59-45=14'] Exploring Operation: 70/14=5, Resulting Numbers: [80, 5] Generated Node #0,0,0: 75:[80, 5] Operation: 70/14=5 Moving to Node #0,0,0 Current State: 75:[80, 5], Operations: ['59-45=14', '70/14=5'] Exploring Operation: 80-5=75, Resulting Numbers: [75] 75,75 equal: Goal Reached Exit Sub Search at level 1
0.993924
hs_1
mult_heuristic
[ 15, 10, 3, 29 ]
39
[ "29-3=26", "15*26=390", "390/10=39" ]
Current State: 39:[15, 10, 3, 29], Operations: [] Exploring Operation: 29-3=26, Resulting Numbers: [15, 10, 26] Generated Node #2: [15, 10, 26] from Operation: 29-3=26 Current State: 39:[15, 10, 26], Operations: ['29-3=26'] Exploring Operation: 15*26=390, Resulting Numbers: [10, 390] Generated Node #3: [10, 390] from Operation: 15*26=390 Current State: 39:[10, 390], Operations: ['29-3=26', '15*26=390'] Exploring Operation: 390/10=39, Resulting Numbers: [39] 39,39 equal: Goal Reached
4
Current State: 39:[15, 10, 3, 29], Operations: [] Exploring Operation: 15-10=5, Resulting Numbers: [3, 29, 5] Generated Node #0,0: 39:[3, 29, 5] Operation: 15-10=5 Exploring Operation: 10+29=39, Resulting Numbers: [15, 3, 39] Generated Node #0,1: 39:[15, 3, 39] Operation: 10+29=39 Exploring Operation: 29-15=14, Resulting Numbers: [10, 3, 14] Generated Node #0,2: 39:[10, 3, 14] Operation: 29-15=14 Exploring Operation: 15+29=44, Resulting Numbers: [10, 3, 44] Generated Node #0,3: 39:[10, 3, 44] Operation: 15+29=44 Exploring Operation: 29-10=19, Resulting Numbers: [15, 3, 19] Generated Node #0,4: 39:[15, 3, 19] Operation: 29-10=19 Moving to Node #0,1 Current State: 39:[15, 3, 39], Operations: ['10+29=39'] Exploring Operation: 39/3=13, Resulting Numbers: [15, 13] Generated Node #0,1,0: 39:[15, 13] Operation: 39/3=13 Exploring Operation: 15-3=12, Resulting Numbers: [39, 12] Generated Node #0,1,1: 39:[39, 12] Operation: 15-3=12 Exploring Operation: 15+3=18, Resulting Numbers: [39, 18] Generated Node #0,1,2: 39:[39, 18] Operation: 15+3=18 Exploring Operation: 15/3=5, Resulting Numbers: [39, 5] Generated Node #0,1,3: 39:[39, 5] Operation: 15/3=5 Exploring Operation: 3+39=42, Resulting Numbers: [15, 42] Generated Node #0,1,4: 39:[15, 42] Operation: 3+39=42 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 39:[39, 12], Operations: ['10+29=39', '15-3=12'] Exploring Operation: 39*12=468, Resulting Numbers: [468] 468,39 unequal: No Solution Exploring Operation: 39-12=27, Resulting Numbers: [27] 27,39 unequal: No Solution Exploring Operation: 39+12=51, Resulting Numbers: [51] 51,39 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: 39:[15, 13], Operations: ['10+29=39', '39/3=13'] Exploring Operation: 15+13=28, Resulting Numbers: [28] 28,39 unequal: No Solution Exploring Operation: 15-13=2, Resulting Numbers: [2] 2,39 unequal: No Solution Exploring Operation: 15*13=195, Resulting Numbers: [195] 195,39 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: 39:[39, 5], Operations: ['10+29=39', '15/3=5'] Exploring Operation: 39+5=44, Resulting Numbers: [44] 44,39 unequal: No Solution Exploring Operation: 39-5=34, Resulting Numbers: [34] 34,39 unequal: No Solution Exploring Operation: 39*5=195, Resulting Numbers: [195] 195,39 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: 39:[39, 18], Operations: ['10+29=39', '15+3=18'] Exploring Operation: 39-18=21, Resulting Numbers: [21] 21,39 unequal: No Solution Exploring Operation: 39*18=702, Resulting Numbers: [702] 702,39 unequal: No Solution Exploring Operation: 39+18=57, Resulting Numbers: [57] 57,39 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: 39:[15, 42], Operations: ['10+29=39', '3+39=42'] Exploring Operation: 15+42=57, Resulting Numbers: [57] 57,39 unequal: No Solution Exploring Operation: 15*42=630, Resulting Numbers: [630] 630,39 unequal: No Solution Exploring Operation: 42-15=27, Resulting Numbers: [27] 27,39 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: 39:[10, 3, 14], Operations: ['29-15=14'] Exploring Operation: 14-10=4, Resulting Numbers: [3, 4] Generated Node #0,2,0: 39:[3, 4] Operation: 14-10=4 Exploring Operation: 14-3=11, Resulting Numbers: [10, 11] Generated Node #0,2,1: 39:[10, 11] Operation: 14-3=11 Exploring Operation: 3*14=42, Resulting Numbers: [10, 42] Generated Node #0,2,2: 39:[10, 42] Operation: 3*14=42 Exploring Operation: 10-3=7, Resulting Numbers: [14, 7] Generated Node #0,2,3: 39:[14, 7] Operation: 10-3=7 Exploring Operation: 10+3=13, Resulting Numbers: [14, 13] Generated Node #0,2,4: 39:[14, 13] Operation: 10+3=13 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 39:[3, 4], Operations: ['29-15=14', '14-10=4'] Exploring Operation: 3*4=12, Resulting Numbers: [12] 12,39 unequal: No Solution Exploring Operation: 3+4=7, Resulting Numbers: [7] 7,39 unequal: No Solution Exploring Operation: 4-3=1, Resulting Numbers: [1] 1,39 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: 39:[14, 13], Operations: ['29-15=14', '10+3=13'] Exploring Operation: 14+13=27, Resulting Numbers: [27] 27,39 unequal: No Solution Exploring Operation: 14-13=1, Resulting Numbers: [1] 1,39 unequal: No Solution Exploring Operation: 14*13=182, Resulting Numbers: [182] 182,39 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: 39:[10, 11], Operations: ['29-15=14', '14-3=11'] Exploring Operation: 11-10=1, Resulting Numbers: [1] 1,39 unequal: No Solution Exploring Operation: 10*11=110, Resulting Numbers: [110] 110,39 unequal: No Solution Exploring Operation: 10+11=21, Resulting Numbers: [21] 21,39 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: 39:[14, 7], Operations: ['29-15=14', '10-3=7'] Exploring Operation: 14-7=7, Resulting Numbers: [7] 7,39 unequal: No Solution Exploring Operation: 14*7=98, Resulting Numbers: [98] 98,39 unequal: No Solution Exploring Operation: 14+7=21, Resulting Numbers: [21] 21,39 unequal: No Solution Exploring Operation: 14/7=2, Resulting Numbers: [2] 2,39 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: 39:[10, 42], Operations: ['29-15=14', '3*14=42'] Exploring Operation: 10*42=420, Resulting Numbers: [420] 420,39 unequal: No Solution Exploring Operation: 42-10=32, Resulting Numbers: [32] 32,39 unequal: No Solution Exploring Operation: 10+42=52, Resulting Numbers: [52] 52,39 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: 39:[10, 3, 44], Operations: ['15+29=44'] Exploring Operation: 10+3=13, Resulting Numbers: [44, 13] Generated Node #0,3,0: 39:[44, 13] Operation: 10+3=13 Exploring Operation: 44-3=41, Resulting Numbers: [10, 41] Generated Node #0,3,1: 39:[10, 41] Operation: 44-3=41 Exploring Operation: 10-3=7, Resulting Numbers: [44, 7] Generated Node #0,3,2: 39:[44, 7] Operation: 10-3=7 Exploring Operation: 44-10=34, Resulting Numbers: [3, 34] Generated Node #0,3,3: 39:[3, 34] Operation: 44-10=34 Exploring Operation: 3+44=47, Resulting Numbers: [10, 47] Generated Node #0,3,4: 39:[10, 47] Operation: 3+44=47 Moving to Node #0,4 Current State: 39:[15, 3, 19], Operations: ['29-10=19'] Exploring Operation: 15-3=12, Resulting Numbers: [19, 12] Generated Node #0,4,0: 39:[19, 12] Operation: 15-3=12 Exploring Operation: 19-3=16, Resulting Numbers: [15, 16] Generated Node #0,4,1: 39:[15, 16] Operation: 19-3=16 Exploring Operation: 15/3=5, Resulting Numbers: [19, 5] Generated Node #0,4,2: 39:[19, 5] Operation: 15/3=5 Exploring Operation: 15+19=34, Resulting Numbers: [3, 34] Generated Node #0,4,3: 39:[3, 34] Operation: 15+19=34 Exploring Operation: 19-15=4, Resulting Numbers: [3, 4] Generated Node #0,4,4: 39:[3, 4] Operation: 19-15=4 Moving to Node #0,0 Current State: 39:[3, 29, 5], Operations: ['15-10=5'] Exploring Operation: 29+5=34, Resulting Numbers: [3, 34] Generated Node #0,0,0: 39:[3, 34] Operation: 29+5=34 Exploring Operation: 29-5=24, Resulting Numbers: [3, 24] Generated Node #0,0,1: 39:[3, 24] Operation: 29-5=24 Exploring Operation: 3+29=32, Resulting Numbers: [5, 32] Generated Node #0,0,2: 39:[5, 32] Operation: 3+29=32 Exploring Operation: 5-3=2, Resulting Numbers: [29, 2] Generated Node #0,0,3: 39:[29, 2] Operation: 5-3=2 Exploring Operation: 3*5=15, Resulting Numbers: [29, 15] Generated Node #0,0,4: 39:[29, 15] Operation: 3*5=15 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 39:[3, 34], Operations: ['15-10=5', '29+5=34'] Exploring Operation: 3*34=102, Resulting Numbers: [102] 102,39 unequal: No Solution Exploring Operation: 34-3=31, Resulting Numbers: [31] 31,39 unequal: No Solution Exploring Operation: 3+34=37, Resulting Numbers: [37] 37,39 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: 39:[5, 32], Operations: ['15-10=5', '3+29=32'] Exploring Operation: 32-5=27, Resulting Numbers: [27] 27,39 unequal: No Solution Exploring Operation: 5+32=37, Resulting Numbers: [37] 37,39 unequal: No Solution Exploring Operation: 5*32=160, Resulting Numbers: [160] 160,39 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: 39:[3, 24], Operations: ['15-10=5', '29-5=24'] Exploring Operation: 24/3=8, Resulting Numbers: [8] 8,39 unequal: No Solution Exploring Operation: 3+24=27, Resulting Numbers: [27] 27,39 unequal: No Solution Exploring Operation: 24-3=21, Resulting Numbers: [21] 21,39 unequal: No Solution Exploring Operation: 3*24=72, Resulting Numbers: [72] 72,39 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: 39:[29, 2], Operations: ['15-10=5', '5-3=2'] Exploring Operation: 29+2=31, Resulting Numbers: [31] 31,39 unequal: No Solution Exploring Operation: 29-2=27, Resulting Numbers: [27] 27,39 unequal: No Solution Exploring Operation: 29*2=58, Resulting Numbers: [58] 58,39 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 #0,0,4 Current State: 39:[29, 15], Operations: ['15-10=5', '3*5=15'] Exploring Operation: 29*15=435, Resulting Numbers: [435] 435,39 unequal: No Solution Exploring Operation: 29-15=14, Resulting Numbers: [14] 14,39 unequal: No Solution Exploring Operation: 29+15=44, Resulting Numbers: [44] 44,39 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,4,4 Current State: 39:[3, 4], Operations: ['29-10=19', '19-15=4'] Exploring Operation: 3+4=7, Resulting Numbers: [7] 7,39 unequal: No Solution Exploring Operation: 3*4=12, Resulting Numbers: [12] 12,39 unequal: No Solution Exploring Operation: 4-3=1, Resulting Numbers: [1] 1,39 unequal: No Solution Moving to Node #0,3,0 Current State: 39:[44, 13], Operations: ['15+29=44', '10+3=13'] Exploring Operation: 44-13=31, Resulting Numbers: [31] 31,39 unequal: No Solution Exploring Operation: 44*13=572, Resulting Numbers: [572] 572,39 unequal: No Solution Exploring Operation: 44+13=57, Resulting Numbers: [57] 57,39 unequal: No Solution Moving to Node #0,4,1 Current State: 39:[15, 16], Operations: ['29-10=19', '19-3=16'] Exploring Operation: 16-15=1, Resulting Numbers: [1] 1,39 unequal: No Solution Exploring Operation: 15+16=31, Resulting Numbers: [31] 31,39 unequal: No Solution Exploring Operation: 15*16=240, Resulting Numbers: [240] 240,39 unequal: No Solution Moving to Node #0,3,3 Current State: 39:[3, 34], Operations: ['15+29=44', '44-10=34'] Exploring Operation: 34-3=31, Resulting Numbers: [31] 31,39 unequal: No Solution Exploring Operation: 3*34=102, Resulting Numbers: [102] 102,39 unequal: No Solution Exploring Operation: 3+34=37, Resulting Numbers: [37] 37,39 unequal: No Solution Moving to Node #0,3,1 Current State: 39:[10, 41], Operations: ['15+29=44', '44-3=41'] Exploring Operation: 10+41=51, Resulting Numbers: [51] 51,39 unequal: No Solution Exploring Operation: 41-10=31, Resulting Numbers: [31] 31,39 unequal: No Solution Exploring Operation: 10*41=410, Resulting Numbers: [410] 410,39 unequal: No Solution Moving to Node #0,4,3 Current State: 39:[3, 34], Operations: ['29-10=19', '15+19=34'] Exploring Operation: 3+34=37, Resulting Numbers: [37] 37,39 unequal: No Solution Exploring Operation: 3*34=102, Resulting Numbers: [102] 102,39 unequal: No Solution Exploring Operation: 34-3=31, Resulting Numbers: [31] 31,39 unequal: No Solution Moving to Node #0,4,0 Current State: 39:[19, 12], Operations: ['29-10=19', '15-3=12'] Exploring Operation: 19+12=31, Resulting Numbers: [31] 31,39 unequal: No Solution Exploring Operation: 19-12=7, Resulting Numbers: [7] 7,39 unequal: No Solution Exploring Operation: 19*12=228, Resulting Numbers: [228] 228,39 unequal: No Solution Moving to Node #0,4,2 Current State: 39:[19, 5], Operations: ['29-10=19', '15/3=5'] Exploring Operation: 19-5=14, Resulting Numbers: [14] 14,39 unequal: No Solution Exploring Operation: 19*5=95, Resulting Numbers: [95] 95,39 unequal: No Solution Exploring Operation: 19+5=24, Resulting Numbers: [24] 24,39 unequal: No Solution Moving to Node #0,3,2 Current State: 39:[44, 7], Operations: ['15+29=44', '10-3=7'] Exploring Operation: 44-7=37, Resulting Numbers: [37] 37,39 unequal: No Solution Exploring Operation: 44+7=51, Resulting Numbers: [51] 51,39 unequal: No Solution Exploring Operation: 44*7=308, Resulting Numbers: [308] 308,39 unequal: No Solution Moving to Node #0,3,4 Current State: 39:[10, 47], Operations: ['15+29=44', '3+44=47'] Exploring Operation: 47-10=37, Resulting Numbers: [37] 37,39 unequal: No Solution Exploring Operation: 10*47=470, Resulting Numbers: [470] 470,39 unequal: No Solution Exploring Operation: 10+47=57, Resulting Numbers: [57] 57,39 unequal: No Solution No solution found.
0
hs_5
mult_heuristic
[ 38, 25, 43, 16 ]
21
[ "43-38=5", "25/5=5", "16+5=21" ]
Current State: 21:[38, 25, 43, 16], Operations: [] Exploring Operation: 43-38=5, Resulting Numbers: [25, 16, 5] Generated Node #2: [25, 16, 5] from Operation: 43-38=5 Current State: 21:[25, 16, 5], Operations: ['43-38=5'] Exploring Operation: 25/5=5, Resulting Numbers: [16, 5] Generated Node #3: [16, 5] from Operation: 25/5=5 Current State: 21:[16, 5], Operations: ['43-38=5', '25/5=5'] Exploring Operation: 16+5=21, Resulting Numbers: [21] 21,21 equal: Goal Reached
4
Current State: 21:[38, 25, 43, 16], Operations: [] Exploring Operation: 43-38=5, Resulting Numbers: [25, 16, 5] Generated Node #0,0: 21:[25, 16, 5] Operation: 43-38=5 Exploring Operation: 43-25=18, Resulting Numbers: [38, 16, 18] Generated Node #0,1: 21:[38, 16, 18] Operation: 43-25=18 Moving to Node #0,0 Current State: 21:[25, 16, 5], Operations: ['43-38=5'] Exploring Operation: 25-16=9, Resulting Numbers: [5, 9] Generated Node #0,0,0: 21:[5, 9] Operation: 25-16=9 Exploring Operation: 16+5=21, Resulting Numbers: [25, 21] Generated Node #0,0,1: 21:[25, 21] Operation: 16+5=21 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 21:[5, 9], Operations: ['43-38=5', '25-16=9'] Exploring Operation: 9-5=4, Resulting Numbers: [4] 4,21 unequal: No Solution Exploring Operation: 5+9=14, Resulting Numbers: [14] 14,21 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: 21:[25, 21], Operations: ['43-38=5', '16+5=21'] Exploring Operation: 25+21=46, Resulting Numbers: [46] 46,21 unequal: No Solution Exploring Operation: 25-21=4, Resulting Numbers: [4] 4,21 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: 21:[38, 16, 18], Operations: ['43-25=18'] Exploring Operation: 38-18=20, Resulting Numbers: [16, 20] Generated Node #0,1,0: 21:[16, 20] Operation: 38-18=20 Exploring Operation: 38-16=22, Resulting Numbers: [18, 22] Generated Node #0,1,1: 21:[18, 22] Operation: 38-16=22 Moving to Node #0,1,1 Current State: 21:[18, 22], Operations: ['43-25=18', '38-16=22'] Exploring Operation: 22-18=4, Resulting Numbers: [4] 4,21 unequal: No Solution Exploring Operation: 18+22=40, Resulting Numbers: [40] 40,21 unequal: No Solution Moving to Node #0,1,0 Current State: 21:[16, 20], Operations: ['43-25=18', '38-18=20'] Exploring Operation: 20-16=4, Resulting Numbers: [4] 4,21 unequal: No Solution Exploring Operation: 16+20=36, Resulting Numbers: [36] 36,21 unequal: No Solution No solution found.
0
hs_2
mult_heuristic
[ 66, 3, 82, 11 ]
85
[ "66/11=6", "82-3=79", "6+79=85" ]
Current State: 85:[66, 3, 82, 11], Operations: [] Exploring Operation: 66/11=6, Resulting Numbers: [3, 82, 6] Generated Node #2: [3, 82, 6] from Operation: 66/11=6 Current State: 85:[3, 82, 6], Operations: ['66/11=6'] Exploring Operation: 82-3=79, Resulting Numbers: [6, 79] Generated Node #3: [6, 79] from Operation: 82-3=79 Current State: 85:[6, 79], Operations: ['66/11=6', '82-3=79'] Exploring Operation: 6+79=85, Resulting Numbers: [85] 85,85 equal: Goal Reached
4
Current State: 85:[66, 3, 82, 11], Operations: [] Exploring Operation: 66/11=6, Resulting Numbers: [3, 82, 6] Generated Node #0,0: 85:[3, 82, 6] Operation: 66/11=6 Moving to Node #0,0 Current State: 85:[3, 82, 6], Operations: ['66/11=6'] Exploring Operation: 3+82=85, Resulting Numbers: [6, 85] Generated Node #0,0,0: 85:[6, 85] Operation: 3+82=85 Moving to Node #0,0,0 Current State: 85:[6, 85], Operations: ['66/11=6', '3+82=85'] Exploring Operation: 6+85=91, Resulting Numbers: [91] 91,85 unequal: No Solution No solution found.
0
hs_1
mult_heuristic
[ 5, 90, 6, 81 ]
93
[ "90/5=18", "81-6=75", "18+75=93" ]
Current State: 93:[5, 90, 6, 81], Operations: [] Exploring Operation: 90/5=18, Resulting Numbers: [6, 81, 18] Generated Node #2: [6, 81, 18] from Operation: 90/5=18 Current State: 93:[6, 81, 18], Operations: ['90/5=18'] Exploring Operation: 81-6=75, Resulting Numbers: [18, 75] Generated Node #3: [18, 75] from Operation: 81-6=75 Current State: 93:[18, 75], Operations: ['90/5=18', '81-6=75'] Exploring Operation: 18+75=93, Resulting Numbers: [93] 93,93 equal: Goal Reached
4
Current State: 93:[5, 90, 6, 81], Operations: [] Exploring Operation: 6+81=87, Resulting Numbers: [5, 90, 87] Generated Node #0,0: 93:[5, 90, 87] Operation: 6+81=87 Exploring Operation: 90-81=9, Resulting Numbers: [5, 6, 9] Generated Node #0,1: 93:[5, 6, 9] Operation: 90-81=9 Start Sub Search at level 1: Moving to Node #0,0 Current State: 93:[5, 90, 87], Operations: ['6+81=87'] Exploring Operation: 5+87=92, Resulting Numbers: [90, 92] Generated Node #0,0,0: 93:[90, 92] Operation: 5+87=92 Exploring Operation: 90-87=3, Resulting Numbers: [5, 3] Generated Node #0,0,1: 93:[5, 3] Operation: 90-87=3 Moving to Node #0,0,1 Current State: 93:[5, 3], Operations: ['6+81=87', '90-87=3'] Exploring Operation: 5-3=2, Resulting Numbers: [2] 2,93 unequal: No Solution Exploring Operation: 5+3=8, Resulting Numbers: [8] 8,93 unequal: No Solution Moving to Node #0,0,0 Current State: 93:[90, 92], Operations: ['6+81=87', '5+87=92'] Exploring Operation: 92-90=2, Resulting Numbers: [2] 2,93 unequal: No Solution Exploring Operation: 90+92=182, Resulting Numbers: [182] 182,93 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 Current State: 93:[5, 6, 9], Operations: ['90-81=9'] Exploring Operation: 9-6=3, Resulting Numbers: [5, 3] Generated Node #0,1,0: 93:[5, 3] Operation: 9-6=3 Exploring Operation: 9-5=4, Resulting Numbers: [6, 4] Generated Node #0,1,1: 93:[6, 4] Operation: 9-5=4 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 93:[5, 3], Operations: ['90-81=9', '9-6=3'] Exploring Operation: 5+3=8, Resulting Numbers: [8] 8,93 unequal: No Solution Exploring Operation: 5-3=2, Resulting Numbers: [2] 2,93 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: 93:[6, 4], Operations: ['90-81=9', '9-5=4'] Exploring Operation: 6-4=2, Resulting Numbers: [2] 2,93 unequal: No Solution Exploring Operation: 6+4=10, Resulting Numbers: [10] 10,93 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
[ 56, 8, 28, 6 ]
15
[ "56/8=7", "28-6=22", "22-7=15" ]
Current State: 15:[56, 8, 28, 6], Operations: [] Exploring Operation: 56/8=7, Resulting Numbers: [28, 6, 7] Generated Node #2: [28, 6, 7] from Operation: 56/8=7 Current State: 15:[28, 6, 7], Operations: ['56/8=7'] Exploring Operation: 28-6=22, Resulting Numbers: [7, 22] Generated Node #3: [7, 22] from Operation: 28-6=22 Current State: 15:[7, 22], Operations: ['56/8=7', '28-6=22'] Exploring Operation: 22-7=15, Resulting Numbers: [15] 15,15 equal: Goal Reached
4
Current State: 15:[56, 8, 28, 6], Operations: [] Exploring Operation: 56/8=7, Resulting Numbers: [28, 6, 7] Generated Node #0,0: 15:[28, 6, 7] Operation: 56/8=7 Exploring Operation: 56/28=2, Resulting Numbers: [8, 6, 2] Generated Node #0,1: 15:[8, 6, 2] Operation: 56/28=2 Exploring Operation: 56-8=48, Resulting Numbers: [28, 6, 48] Generated Node #0,2: 15:[28, 6, 48] Operation: 56-8=48 Exploring Operation: 56-28=28, Resulting Numbers: [8, 6, 28] Generated Node #0,3: 15:[8, 6, 28] Operation: 56-28=28 Start Sub Search at level 1: Moving to Node #0,1 Current State: 15:[8, 6, 2], Operations: ['56/28=2'] Exploring Operation: 8-6=2, Resulting Numbers: [2, 2] Generated Node #0,1,0: 15:[2, 2] Operation: 8-6=2 Exploring Operation: 8-2=6, Resulting Numbers: [6, 6] Generated Node #0,1,1: 15:[6, 6] Operation: 8-2=6 Exploring Operation: 8*2=16, Resulting Numbers: [6, 16] Generated Node #0,1,2: 15:[6, 16] Operation: 8*2=16 Exploring Operation: 8+6=14, Resulting Numbers: [2, 14] Generated Node #0,1,3: 15:[2, 14] Operation: 8+6=14 Moving to Node #0,1,0 Current State: 15:[2, 2], Operations: ['56/28=2', '8-6=2'] Exploring Operation: 2+2=4, Resulting Numbers: [4] 4,15 unequal: No Solution Exploring Operation: 2-2=0, Resulting Numbers: [0] 0,15 unequal: No Solution Exploring Operation: 2*2=4, Resulting Numbers: [4] 4,15 unequal: No Solution Exploring Operation: 2/2=1, Resulting Numbers: [1] 1,15 unequal: No Solution Moving to Node #0,1,2 Current State: 15:[6, 16], Operations: ['56/28=2', '8*2=16'] Exploring Operation: 6*16=96, Resulting Numbers: [96] 96,15 unequal: No Solution Exploring Operation: 16-6=10, Resulting Numbers: [10] 10,15 unequal: No Solution Exploring Operation: 6+16=22, Resulting Numbers: [22] 22,15 unequal: No Solution Moving to Node #0,1,1 Current State: 15:[6, 6], Operations: ['56/28=2', '8-2=6'] Exploring Operation: 6+6=12, Resulting Numbers: [12] 12,15 unequal: No Solution Exploring Operation: 6-6=0, Resulting Numbers: [0] 0,15 unequal: No Solution Exploring Operation: 6*6=36, Resulting Numbers: [36] 36,15 unequal: No Solution Exploring Operation: 6/6=1, Resulting Numbers: [1] 1,15 unequal: No Solution Moving to Node #0,1,3 Current State: 15:[2, 14], Operations: ['56/28=2', '8+6=14'] Exploring Operation: 14/2=7, Resulting Numbers: [7] 7,15 unequal: No Solution Exploring Operation: 14-2=12, Resulting Numbers: [12] 12,15 unequal: No Solution Exploring Operation: 2*14=28, Resulting Numbers: [28] 28,15 unequal: No Solution Exploring Operation: 2+14=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 #0,0 Current State: 15:[28, 6, 7], Operations: ['56/8=7'] Exploring Operation: 6+7=13, Resulting Numbers: [28, 13] Generated Node #0,0,0: 15:[28, 13] Operation: 6+7=13 Exploring Operation: 28-7=21, Resulting Numbers: [6, 21] Generated Node #0,0,1: 15:[6, 21] Operation: 28-7=21 Exploring Operation: 28-6=22, Resulting Numbers: [7, 22] Generated Node #0,0,2: 15:[7, 22] Operation: 28-6=22 Exploring Operation: 28/7=4, Resulting Numbers: [6, 4] Generated Node #0,0,3: 15:[6, 4] Operation: 28/7=4 Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 15:[6, 4], Operations: ['56/8=7', '28/7=4'] Exploring Operation: 6-4=2, Resulting Numbers: [2] 2,15 unequal: No Solution Exploring Operation: 6+4=10, Resulting Numbers: [10] 10,15 unequal: No Solution Exploring Operation: 6*4=24, Resulting Numbers: [24] 24,15 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: 15:[6, 21], Operations: ['56/8=7', '28-7=21'] Exploring Operation: 6+21=27, Resulting Numbers: [27] 27,15 unequal: No Solution Exploring Operation: 6*21=126, Resulting Numbers: [126] 126,15 unequal: No Solution Exploring Operation: 21-6=15, Resulting Numbers: [15] 15,15 equal: Goal Reached Moving to Node #0 Current State: 15:[56, 8, 28, 6], Operations: [] Exploring Operation: 56/8=7, Resulting Numbers: [28, 6, 7] Generated Node #0,0: 15:[28, 6, 7] Operation: 56/8=7 Moving to Node #0,0 Current State: 15:[28, 6, 7], Operations: ['56/8=7'] Exploring Operation: 28-7=21, Resulting Numbers: [6, 21] Generated Node #0,0,1: 15:[6, 21] Operation: 28-7=21 Moving to Node #0,0,1 Current State: 15:[6, 21], Operations: ['56/8=7', '28-7=21'] Exploring Operation: 21-6=15, Resulting Numbers: [15] 15,15 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.967882
hs_4
mult_heuristic
[ 66, 87, 2, 26 ]
31
[ "87-66=21", "2*26=52", "52-21=31" ]
Current State: 31:[66, 87, 2, 26], Operations: [] Exploring Operation: 87-66=21, Resulting Numbers: [2, 26, 21] Generated Node #2: [2, 26, 21] from Operation: 87-66=21 Current State: 31:[2, 26, 21], Operations: ['87-66=21'] Exploring Operation: 2*26=52, Resulting Numbers: [21, 52] Generated Node #3: [21, 52] from Operation: 2*26=52 Current State: 31:[21, 52], Operations: ['87-66=21', '2*26=52'] Exploring Operation: 52-21=31, Resulting Numbers: [31] 31,31 equal: Goal Reached
4
Current State: 31:[66, 87, 2, 26], Operations: [] Exploring Operation: 87-66=21, Resulting Numbers: [2, 26, 21] Generated Node #0,0: 31:[2, 26, 21] Operation: 87-66=21 Exploring Operation: 87-2=85, Resulting Numbers: [66, 26, 85] Generated Node #0,1: 31:[66, 26, 85] Operation: 87-2=85 Exploring Operation: 66-26=40, Resulting Numbers: [87, 2, 40] Generated Node #0,2: 31:[87, 2, 40] Operation: 66-26=40 Exploring Operation: 66-2=64, Resulting Numbers: [87, 26, 64] Generated Node #0,3: 31:[87, 26, 64] Operation: 66-2=64 Exploring Operation: 66/2=33, Resulting Numbers: [87, 26, 33] Generated Node #0,4: 31:[87, 26, 33] Operation: 66/2=33 Start Sub Search at level 1: Moving to Node #0,0 Current State: 31:[2, 26, 21], Operations: ['87-66=21'] Exploring Operation: 21-2=19, Resulting Numbers: [26, 19] Generated Node #0,0,0: 31:[26, 19] Operation: 21-2=19 Exploring Operation: 2+26=28, Resulting Numbers: [21, 28] Generated Node #0,0,1: 31:[21, 28] Operation: 2+26=28 Exploring Operation: 2*21=42, Resulting Numbers: [26, 42] Generated Node #0,0,2: 31:[26, 42] Operation: 2*21=42 Exploring Operation: 26-2=24, Resulting Numbers: [21, 24] Generated Node #0,0,3: 31:[21, 24] Operation: 26-2=24 Exploring Operation: 2+21=23, Resulting Numbers: [26, 23] Generated Node #0,0,4: 31:[26, 23] Operation: 2+21=23 Moving to Node #0,0,1 Current State: 31:[21, 28], Operations: ['87-66=21', '2+26=28'] Exploring Operation: 28-21=7, Resulting Numbers: [7] 7,31 unequal: No Solution Exploring Operation: 21+28=49, Resulting Numbers: [49] 49,31 unequal: No Solution Exploring Operation: 21*28=588, Resulting Numbers: [588] 588,31 unequal: No Solution Moving to Node #0,0,4 Current State: 31:[26, 23], Operations: ['87-66=21', '2+21=23'] Exploring Operation: 26*23=598, Resulting Numbers: [598] 598,31 unequal: No Solution Exploring Operation: 26-23=3, Resulting Numbers: [3] 3,31 unequal: No Solution Exploring Operation: 26+23=49, Resulting Numbers: [49] 49,31 unequal: No Solution Moving to Node #0,0,2 Current State: 31:[26, 42], Operations: ['87-66=21', '2*21=42'] Exploring Operation: 26*42=1092, Resulting Numbers: [1092] 1092,31 unequal: No Solution Exploring Operation: 42-26=16, Resulting Numbers: [16] 16,31 unequal: No Solution Exploring Operation: 26+42=68, Resulting Numbers: [68] 68,31 unequal: No Solution Moving to Node #0,0,0 Current State: 31:[26, 19], Operations: ['87-66=21', '21-2=19'] Exploring Operation: 26-19=7, Resulting Numbers: [7] 7,31 unequal: No Solution Exploring Operation: 26+19=45, Resulting Numbers: [45] 45,31 unequal: No Solution Exploring Operation: 26*19=494, Resulting Numbers: [494] 494,31 unequal: No Solution Moving to Node #0,0,3 Current State: 31:[21, 24], Operations: ['87-66=21', '26-2=24'] Exploring Operation: 21+24=45, Resulting Numbers: [45] 45,31 unequal: No Solution Exploring Operation: 21*24=504, Resulting Numbers: [504] 504,31 unequal: No Solution Exploring Operation: 24-21=3, Resulting Numbers: [3] 3,31 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: 31:[87, 26, 33], Operations: ['66/2=33'] Exploring Operation: 33-26=7, Resulting Numbers: [87, 7] Generated Node #0,4,0: 31:[87, 7] Operation: 33-26=7 Exploring Operation: 87+26=113, Resulting Numbers: [33, 113] Generated Node #0,4,1: 31:[33, 113] Operation: 87+26=113 Exploring Operation: 26+33=59, Resulting Numbers: [87, 59] Generated Node #0,4,2: 31:[87, 59] Operation: 26+33=59 Exploring Operation: 87-26=61, Resulting Numbers: [33, 61] Generated Node #0,4,3: 31:[33, 61] Operation: 87-26=61 Exploring Operation: 87-33=54, Resulting Numbers: [26, 54] Generated Node #0,4,4: 31:[26, 54] Operation: 87-33=54 Moving to Node #0,4,4 Current State: 31:[26, 54], Operations: ['66/2=33', '87-33=54'] Exploring Operation: 26*54=1404, Resulting Numbers: [1404] 1404,31 unequal: No Solution Exploring Operation: 54-26=28, Resulting Numbers: [28] 28,31 unequal: No Solution Exploring Operation: 26+54=80, Resulting Numbers: [80] 80,31 unequal: No Solution Moving to Node #0,4,3 Current State: 31:[33, 61], Operations: ['66/2=33', '87-26=61'] Exploring Operation: 61-33=28, Resulting Numbers: [28] 28,31 unequal: No Solution Exploring Operation: 33+61=94, Resulting Numbers: [94] 94,31 unequal: No Solution Exploring Operation: 33*61=2013, Resulting Numbers: [2013] 2013,31 unequal: No Solution Moving to Node #0,4,0 Current State: 31:[87, 7], Operations: ['66/2=33', '33-26=7'] Exploring Operation: 87+7=94, Resulting Numbers: [94] 94,31 unequal: No Solution Exploring Operation: 87*7=609, Resulting Numbers: [609] 609,31 unequal: No Solution Exploring Operation: 87-7=80, Resulting Numbers: [80] 80,31 unequal: No Solution Moving to Node #0,4,1 Current State: 31:[33, 113], Operations: ['66/2=33', '87+26=113'] Exploring Operation: 33+113=146, Resulting Numbers: [146] 146,31 unequal: No Solution Exploring Operation: 113-33=80, Resulting Numbers: [80] 80,31 unequal: No Solution Exploring Operation: 33*113=3729, Resulting Numbers: [3729] 3729,31 unequal: No Solution Moving to Node #0,4,2 Current State: 31:[87, 59], Operations: ['66/2=33', '26+33=59'] Exploring Operation: 87+59=146, Resulting Numbers: [146] 146,31 unequal: No Solution Exploring Operation: 87*59=5133, Resulting Numbers: [5133] 5133,31 unequal: No Solution Exploring Operation: 87-59=28, Resulting Numbers: [28] 28,31 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: 31:[66, 26, 85], Operations: ['87-2=85'] Exploring Operation: 66+26=92, Resulting Numbers: [85, 92] Generated Node #0,1,0: 31:[85, 92] Operation: 66+26=92 Exploring Operation: 26+85=111, Resulting Numbers: [66, 111] Generated Node #0,1,1: 31:[66, 111] Operation: 26+85=111 Exploring Operation: 85-26=59, Resulting Numbers: [66, 59] Generated Node #0,1,2: 31:[66, 59] Operation: 85-26=59 Exploring Operation: 85-66=19, Resulting Numbers: [26, 19] Generated Node #0,1,3: 31:[26, 19] Operation: 85-66=19 Exploring Operation: 66-26=40, Resulting Numbers: [85, 40] Generated Node #0,1,4: 31:[85, 40] Operation: 66-26=40 Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 31:[26, 19], Operations: ['87-2=85', '85-66=19'] Exploring Operation: 26+19=45, Resulting Numbers: [45] 45,31 unequal: No Solution Exploring Operation: 26-19=7, Resulting Numbers: [7] 7,31 unequal: No Solution Exploring Operation: 26*19=494, Resulting Numbers: [494] 494,31 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: 31:[66, 59], Operations: ['87-2=85', '85-26=59'] Exploring Operation: 66*59=3894, Resulting Numbers: [3894] 3894,31 unequal: No Solution Exploring Operation: 66-59=7, Resulting Numbers: [7] 7,31 unequal: No Solution Exploring Operation: 66+59=125, Resulting Numbers: [125] 125,31 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: 31:[85, 40], Operations: ['87-2=85', '66-26=40'] Exploring Operation: 85*40=3400, Resulting Numbers: [3400] 3400,31 unequal: No Solution Exploring Operation: 85-40=45, Resulting Numbers: [45] 45,31 unequal: No Solution Exploring Operation: 85+40=125, Resulting Numbers: [125] 125,31 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: 31:[85, 92], Operations: ['87-2=85', '66+26=92'] Exploring Operation: 92-85=7, Resulting Numbers: [7] 7,31 unequal: No Solution Exploring Operation: 85+92=177, Resulting Numbers: [177] 177,31 unequal: No Solution Exploring Operation: 85*92=7820, Resulting Numbers: [7820] 7820,31 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: 31:[66, 111], Operations: ['87-2=85', '26+85=111'] Exploring Operation: 111-66=45, Resulting Numbers: [45] 45,31 unequal: No Solution Exploring Operation: 66+111=177, Resulting Numbers: [177] 177,31 unequal: No Solution Exploring Operation: 66*111=7326, Resulting Numbers: [7326] 7326,31 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: 31:[87, 2, 40], Operations: ['66-26=40'] Exploring Operation: 87-40=47, Resulting Numbers: [2, 47] Generated Node #0,2,0: 31:[2, 47] Operation: 87-40=47 Exploring Operation: 40-2=38, Resulting Numbers: [87, 38] Generated Node #0,2,1: 31:[87, 38] Operation: 40-2=38 Exploring Operation: 2+40=42, Resulting Numbers: [87, 42] Generated Node #0,2,2: 31:[87, 42] Operation: 2+40=42 Exploring Operation: 87+2=89, Resulting Numbers: [40, 89] Generated Node #0,2,3: 31:[40, 89] Operation: 87+2=89 Exploring Operation: 87-2=85, Resulting Numbers: [40, 85] Generated Node #0,2,4: 31:[40, 85] Operation: 87-2=85 Moving to Node #0,2,0 Current State: 31:[2, 47], Operations: ['66-26=40', '87-40=47'] Exploring Operation: 2*47=94, Resulting Numbers: [94] 94,31 unequal: No Solution Exploring Operation: 47-2=45, Resulting Numbers: [45] 45,31 unequal: No Solution Exploring Operation: 2+47=49, Resulting Numbers: [49] 49,31 unequal: No Solution Moving to Node #0,2,4 Current State: 31:[40, 85], Operations: ['66-26=40', '87-2=85'] Exploring Operation: 85-40=45, Resulting Numbers: [45] 45,31 unequal: No Solution Exploring Operation: 40+85=125, Resulting Numbers: [125] 125,31 unequal: No Solution Exploring Operation: 40*85=3400, Resulting Numbers: [3400] 3400,31 unequal: No Solution Moving to Node #0,2,1 Current State: 31:[87, 38], Operations: ['66-26=40', '40-2=38'] Exploring Operation: 87+38=125, Resulting Numbers: [125] 125,31 unequal: No Solution Exploring Operation: 87*38=3306, Resulting Numbers: [3306] 3306,31 unequal: No Solution Exploring Operation: 87-38=49, Resulting Numbers: [49] 49,31 unequal: No Solution Moving to Node #0,2,2 Current State: 31:[87, 42], Operations: ['66-26=40', '2+40=42'] Exploring Operation: 87-42=45, Resulting Numbers: [45] 45,31 unequal: No Solution Exploring Operation: 87*42=3654, Resulting Numbers: [3654] 3654,31 unequal: No Solution Exploring Operation: 87+42=129, Resulting Numbers: [129] 129,31 unequal: No Solution Moving to Node #0,2,3 Current State: 31:[40, 89], Operations: ['66-26=40', '87+2=89'] Exploring Operation: 40+89=129, Resulting Numbers: [129] 129,31 unequal: No Solution Exploring Operation: 40*89=3560, Resulting Numbers: [3560] 3560,31 unequal: No Solution Exploring Operation: 89-40=49, Resulting Numbers: [49] 49,31 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: 31:[87, 26, 64], Operations: ['66-2=64'] Exploring Operation: 26+64=90, Resulting Numbers: [87, 90] Generated Node #0,3,0: 31:[87, 90] Operation: 26+64=90 Exploring Operation: 64-26=38, Resulting Numbers: [87, 38] Generated Node #0,3,1: 31:[87, 38] Operation: 64-26=38 Exploring Operation: 87-64=23, Resulting Numbers: [26, 23] Generated Node #0,3,2: 31:[26, 23] Operation: 87-64=23 Exploring Operation: 87-26=61, Resulting Numbers: [64, 61] Generated Node #0,3,3: 31:[64, 61] Operation: 87-26=61 Exploring Operation: 87+26=113, Resulting Numbers: [64, 113] Generated Node #0,3,4: 31:[64, 113] Operation: 87+26=113 Moving to Node #0,3,2 Current State: 31:[26, 23], Operations: ['66-2=64', '87-64=23'] Exploring Operation: 26*23=598, Resulting Numbers: [598] 598,31 unequal: No Solution Exploring Operation: 26-23=3, Resulting Numbers: [3] 3,31 unequal: No Solution Exploring Operation: 26+23=49, Resulting Numbers: [49] 49,31 unequal: No Solution Moving to Node #0,3,3 Current State: 31:[64, 61], Operations: ['66-2=64', '87-26=61'] Exploring Operation: 64-61=3, Resulting Numbers: [3] 3,31 unequal: No Solution Exploring Operation: 64*61=3904, Resulting Numbers: [3904] 3904,31 unequal: No Solution Exploring Operation: 64+61=125, Resulting Numbers: [125] 125,31 unequal: No Solution Moving to Node #0,3,1 Current State: 31:[87, 38], Operations: ['66-2=64', '64-26=38'] Exploring Operation: 87-38=49, Resulting Numbers: [49] 49,31 unequal: No Solution Exploring Operation: 87*38=3306, Resulting Numbers: [3306] 3306,31 unequal: No Solution Exploring Operation: 87+38=125, Resulting Numbers: [125] 125,31 unequal: No Solution Moving to Node #0,3,0 Current State: 31:[87, 90], Operations: ['66-2=64', '26+64=90'] Exploring Operation: 90-87=3, Resulting Numbers: [3] 3,31 unequal: No Solution Exploring Operation: 87+90=177, Resulting Numbers: [177] 177,31 unequal: No Solution Exploring Operation: 87*90=7830, Resulting Numbers: [7830] 7830,31 unequal: No Solution Moving to Node #0,3,4 Current State: 31:[64, 113], Operations: ['66-2=64', '87+26=113'] Exploring Operation: 113-64=49, Resulting Numbers: [49] 49,31 unequal: No Solution Exploring Operation: 64*113=7232, Resulting Numbers: [7232] 7232,31 unequal: No Solution Exploring Operation: 64+113=177, Resulting Numbers: [177] 177,31 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
[ 87, 68, 6, 77 ]
58
[ "87*6=522", "77-68=9", "522/9=58" ]
Current State: 58:[87, 68, 6, 77], Operations: [] Exploring Operation: 87*6=522, Resulting Numbers: [68, 77, 522] Generated Node #2: [68, 77, 522] from Operation: 87*6=522 Current State: 58:[68, 77, 522], Operations: ['87*6=522'] Exploring Operation: 77-68=9, Resulting Numbers: [522, 9] Generated Node #3: [522, 9] from Operation: 77-68=9 Current State: 58:[522, 9], Operations: ['87*6=522', '77-68=9'] Exploring Operation: 522/9=58, Resulting Numbers: [58] 58,58 equal: Goal Reached
4
Current State: 58:[87, 68, 6, 77], Operations: [] Exploring Operation: 87-68=19, Resulting Numbers: [6, 77, 19] Generated Node #0,0: 58:[6, 77, 19] Operation: 87-68=19 Exploring Operation: 87-77=10, Resulting Numbers: [68, 6, 10] Generated Node #0,1: 58:[68, 6, 10] Operation: 87-77=10 Start Sub Search at level 1: Moving to Node #0,1 Current State: 58:[68, 6, 10], Operations: ['87-77=10'] Exploring Operation: 68-10=58, Resulting Numbers: [6, 58] Generated Node #0,1,0: 58:[6, 58] Operation: 68-10=58 Exploring Operation: 68-6=62, Resulting Numbers: [10, 62] Generated Node #0,1,1: 58:[10, 62] Operation: 68-6=62 Moving to Node #0,1,0 Current State: 58:[6, 58], Operations: ['87-77=10', '68-10=58'] Exploring Operation: 6+58=64, Resulting Numbers: [64] 64,58 unequal: No Solution Exploring Operation: 58-6=52, Resulting Numbers: [52] 52,58 unequal: No Solution Moving to Node #0,1,1 Current State: 58:[10, 62], Operations: ['87-77=10', '68-6=62'] Exploring Operation: 62-10=52, Resulting Numbers: [52] 52,58 unequal: No Solution Exploring Operation: 10+62=72, Resulting Numbers: [72] 72,58 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 #0,0 Current State: 58:[6, 77, 19], Operations: ['87-68=19'] Exploring Operation: 77-19=58, Resulting Numbers: [6, 58] Generated Node #0,0,0: 58:[6, 58] Operation: 77-19=58 Exploring Operation: 77-6=71, Resulting Numbers: [19, 71] Generated Node #0,0,1: 58:[19, 71] Operation: 77-6=71 Moving to Node #0,0,0 Current State: 58:[6, 58], Operations: ['87-68=19', '77-19=58'] Exploring Operation: 58-6=52, Resulting Numbers: [52] 52,58 unequal: No Solution Exploring Operation: 6+58=64, Resulting Numbers: [64] 64,58 unequal: No Solution Moving to Node #0,0,1 Current State: 58:[19, 71], Operations: ['87-68=19', '77-6=71'] Exploring Operation: 71-19=52, Resulting Numbers: [52] 52,58 unequal: No Solution Exploring Operation: 19+71=90, Resulting Numbers: [90] 90,58 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
[ 22, 25, 93, 28 ]
91
[ "22+28=50", "50/25=2", "93-2=91" ]
Current State: 91:[22, 25, 93, 28], Operations: [] Exploring Operation: 22+28=50, Resulting Numbers: [25, 93, 50] Generated Node #2: [25, 93, 50] from Operation: 22+28=50 Current State: 91:[25, 93, 50], Operations: ['22+28=50'] Exploring Operation: 50/25=2, Resulting Numbers: [93, 2] Generated Node #3: [93, 2] from Operation: 50/25=2 Current State: 91:[93, 2], Operations: ['22+28=50', '50/25=2'] Exploring Operation: 93-2=91, Resulting Numbers: [91] 91,91 equal: Goal Reached
4
Current State: 91:[22, 25, 93, 28], Operations: [] Exploring Operation: 28-22=6, Resulting Numbers: [25, 93, 6] Generated Node #0,0: 91:[25, 93, 6] Operation: 28-22=6 Start Sub Search at level 1: Moving to Node #0,0 Current State: 91:[25, 93, 6], Operations: ['28-22=6'] Exploring Operation: 25-6=19, Resulting Numbers: [93, 19] Generated Node #0,0,0: 91:[93, 19] Operation: 25-6=19 Moving to Node #0,0,0 Current State: 91:[93, 19], Operations: ['28-22=6', '25-6=19'] Exploring Operation: 93-19=74, Resulting Numbers: [74] 74,91 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
[ 7, 18, 6, 29 ]
94
[ "18/6=3", "29*3=87", "7+87=94" ]
Current State: 94:[7, 18, 6, 29], Operations: [] Exploring Operation: 18/6=3, Resulting Numbers: [7, 29, 3] Generated Node #2: [7, 29, 3] from Operation: 18/6=3 Current State: 94:[7, 29, 3], Operations: ['18/6=3'] Exploring Operation: 29*3=87, Resulting Numbers: [7, 87] Generated Node #3: [7, 87] from Operation: 29*3=87 Current State: 94:[7, 87], Operations: ['18/6=3', '29*3=87'] Exploring Operation: 7+87=94, Resulting Numbers: [94] 94,94 equal: Goal Reached
4
Current State: 94:[7, 18, 6, 29], Operations: [] Exploring Operation: 18+29=47, Resulting Numbers: [7, 6, 47] Generated Node #0,0: 94:[7, 6, 47] Operation: 18+29=47 Moving to Node #0,0 Current State: 94:[7, 6, 47], Operations: ['18+29=47'] Exploring Operation: 7-6=1, Resulting Numbers: [47, 1] Generated Node #0,0,0: 94:[47, 1] Operation: 7-6=1 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 94:[47, 1], Operations: ['18+29=47', '7-6=1'] Exploring Operation: 47*1=47, Resulting Numbers: [47] 47,94 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
[ 89, 25, 78, 95 ]
72
[ "95-89=6", "25*6=150", "150-78=72" ]
Current State: 72:[89, 25, 78, 95], Operations: [] Exploring Operation: 95-89=6, Resulting Numbers: [25, 78, 6] Generated Node #2: [25, 78, 6] from Operation: 95-89=6 Current State: 72:[25, 78, 6], Operations: ['95-89=6'] Exploring Operation: 25*6=150, Resulting Numbers: [78, 150] Generated Node #3: [78, 150] from Operation: 25*6=150 Current State: 72:[78, 150], Operations: ['95-89=6', '25*6=150'] Exploring Operation: 150-78=72, Resulting Numbers: [72] 72,72 equal: Goal Reached
4
Current State: 72:[89, 25, 78, 95], Operations: [] Exploring Operation: 95-89=6, Resulting Numbers: [25, 78, 6] Generated Node #0,0: 72:[25, 78, 6] Operation: 95-89=6 Exploring Operation: 95-78=17, Resulting Numbers: [89, 25, 17] Generated Node #0,1: 72:[89, 25, 17] Operation: 95-78=17 Exploring Operation: 89-78=11, Resulting Numbers: [25, 95, 11] Generated Node #0,2: 72:[25, 95, 11] Operation: 89-78=11 Exploring Operation: 89-25=64, Resulting Numbers: [78, 95, 64] Generated Node #0,3: 72:[78, 95, 64] Operation: 89-25=64 Exploring Operation: 95-25=70, Resulting Numbers: [89, 78, 70] Generated Node #0,4: 72:[89, 78, 70] Operation: 95-25=70 Start Sub Search at level 1: Moving to Node #0,0 Current State: 72:[25, 78, 6], Operations: ['95-89=6'] Exploring Operation: 78-6=72, Resulting Numbers: [25, 72] Generated Node #0,0,0: 72:[25, 72] Operation: 78-6=72 Exploring Operation: 25+6=31, Resulting Numbers: [78, 31] Generated Node #0,0,1: 72:[78, 31] Operation: 25+6=31 Exploring Operation: 25-6=19, Resulting Numbers: [78, 19] Generated Node #0,0,2: 72:[78, 19] Operation: 25-6=19 Exploring Operation: 78/6=13, Resulting Numbers: [25, 13] Generated Node #0,0,3: 72:[25, 13] Operation: 78/6=13 Exploring Operation: 78+6=84, Resulting Numbers: [25, 84] Generated Node #0,0,4: 72:[25, 84] Operation: 78+6=84 Moving to Node #0,0,0 Current State: 72:[25, 72], Operations: ['95-89=6', '78-6=72'] Exploring Operation: 25*72=1800, Resulting Numbers: [1800] 1800,72 unequal: No Solution Exploring Operation: 25+72=97, Resulting Numbers: [97] 97,72 unequal: No Solution Exploring Operation: 72-25=47, Resulting Numbers: [47] 47,72 unequal: No Solution Moving to Node #0,0,3 Current State: 72:[25, 13], Operations: ['95-89=6', '78/6=13'] Exploring Operation: 25*13=325, Resulting Numbers: [325] 325,72 unequal: No Solution Exploring Operation: 25+13=38, Resulting Numbers: [38] 38,72 unequal: No Solution Exploring Operation: 25-13=12, Resulting Numbers: [12] 12,72 unequal: No Solution Moving to Node #0,0,2 Current State: 72:[78, 19], Operations: ['95-89=6', '25-6=19'] Exploring Operation: 78+19=97, Resulting Numbers: [97] 97,72 unequal: No Solution Exploring Operation: 78-19=59, Resulting Numbers: [59] 59,72 unequal: No Solution Exploring Operation: 78*19=1482, Resulting Numbers: [1482] 1482,72 unequal: No Solution Moving to Node #0,0,1 Current State: 72:[78, 31], Operations: ['95-89=6', '25+6=31'] Exploring Operation: 78-31=47, Resulting Numbers: [47] 47,72 unequal: No Solution Exploring Operation: 78*31=2418, Resulting Numbers: [2418] 2418,72 unequal: No Solution Exploring Operation: 78+31=109, Resulting Numbers: [109] 109,72 unequal: No Solution Moving to Node #0,0,4 Current State: 72:[25, 84], Operations: ['95-89=6', '78+6=84'] Exploring Operation: 84-25=59, Resulting Numbers: [59] 59,72 unequal: No Solution Exploring Operation: 25*84=2100, Resulting Numbers: [2100] 2100,72 unequal: No Solution Exploring Operation: 25+84=109, Resulting Numbers: [109] 109,72 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:[89, 25, 17], Operations: ['95-78=17'] Exploring Operation: 89+17=106, Resulting Numbers: [25, 106] Generated Node #0,1,0: 72:[25, 106] Operation: 89+17=106 Exploring Operation: 89-25=64, Resulting Numbers: [17, 64] Generated Node #0,1,1: 72:[17, 64] Operation: 89-25=64 Exploring Operation: 25-17=8, Resulting Numbers: [89, 8] Generated Node #0,1,2: 72:[89, 8] Operation: 25-17=8 Exploring Operation: 89-17=72, Resulting Numbers: [25, 72] Generated Node #0,1,3: 72:[25, 72] Operation: 89-17=72 Exploring Operation: 25+17=42, Resulting Numbers: [89, 42] Generated Node #0,1,4: 72:[89, 42] Operation: 25+17=42 Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 72:[25, 72], Operations: ['95-78=17', '89-17=72'] Exploring Operation: 25*72=1800, Resulting Numbers: [1800] 1800,72 unequal: No Solution Exploring Operation: 25+72=97, Resulting Numbers: [97] 97,72 unequal: No Solution Exploring Operation: 72-25=47, Resulting Numbers: [47] 47,72 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 #0,1,1 Current State: 72:[17, 64], Operations: ['95-78=17', '89-25=64'] Exploring Operation: 64-17=47, Resulting Numbers: [47] 47,72 unequal: No Solution Exploring Operation: 17*64=1088, Resulting Numbers: [1088] 1088,72 unequal: No Solution Exploring Operation: 17+64=81, Resulting Numbers: [81] 81,72 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 #0,1,2 Current State: 72:[89, 8], Operations: ['95-78=17', '25-17=8'] Exploring Operation: 89-8=81, Resulting Numbers: [81] 81,72 unequal: No Solution Exploring Operation: 89*8=712, Resulting Numbers: [712] 712,72 unequal: No Solution Exploring Operation: 89+8=97, Resulting Numbers: [97] 97,72 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 #0,1,4 Current State: 72:[89, 42], Operations: ['95-78=17', '25+17=42'] Exploring Operation: 89-42=47, Resulting Numbers: [47] 47,72 unequal: No Solution Exploring Operation: 89+42=131, Resulting Numbers: [131] 131,72 unequal: No Solution Exploring Operation: 89*42=3738, Resulting Numbers: [3738] 3738,72 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 #0,1,0 Current State: 72:[25, 106], Operations: ['95-78=17', '89+17=106'] Exploring Operation: 25+106=131, Resulting Numbers: [131] 131,72 unequal: No Solution Exploring Operation: 106-25=81, Resulting Numbers: [81] 81,72 unequal: No Solution Exploring Operation: 25*106=2650, Resulting Numbers: [2650] 2650,72 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 #0,2 Current State: 72:[25, 95, 11], Operations: ['89-78=11'] Exploring Operation: 95-11=84, Resulting Numbers: [25, 84] Generated Node #0,2,0: 72:[25, 84] Operation: 95-11=84 Exploring Operation: 25+11=36, Resulting Numbers: [95, 36] Generated Node #0,2,1: 72:[95, 36] Operation: 25+11=36 Exploring Operation: 95-25=70, Resulting Numbers: [11, 70] Generated Node #0,2,2: 72:[11, 70] Operation: 95-25=70 Exploring Operation: 95+11=106, Resulting Numbers: [25, 106] Generated Node #0,2,3: 72:[25, 106] Operation: 95+11=106 Exploring Operation: 25-11=14, Resulting Numbers: [95, 14] Generated Node #0,2,4: 72:[95, 14] Operation: 25-11=14 Moving to Node #0,2,2 Current State: 72:[11, 70], Operations: ['89-78=11', '95-25=70'] Exploring Operation: 70-11=59, Resulting Numbers: [59] 59,72 unequal: No Solution Exploring Operation: 11+70=81, Resulting Numbers: [81] 81,72 unequal: No Solution Exploring Operation: 11*70=770, Resulting Numbers: [770] 770,72 unequal: No Solution Moving to Node #0,2,0 Current State: 72:[25, 84], Operations: ['89-78=11', '95-11=84'] Exploring Operation: 25+84=109, Resulting Numbers: [109] 109,72 unequal: No Solution Exploring Operation: 84-25=59, Resulting Numbers: [59] 59,72 unequal: No Solution Exploring Operation: 25*84=2100, Resulting Numbers: [2100] 2100,72 unequal: No Solution Moving to Node #0,2,1 Current State: 72:[95, 36], Operations: ['89-78=11', '25+11=36'] Exploring Operation: 95+36=131, Resulting Numbers: [131] 131,72 unequal: No Solution Exploring Operation: 95-36=59, Resulting Numbers: [59] 59,72 unequal: No Solution Exploring Operation: 95*36=3420, Resulting Numbers: [3420] 3420,72 unequal: No Solution Moving to Node #0,2,4 Current State: 72:[95, 14], Operations: ['89-78=11', '25-11=14'] Exploring Operation: 95+14=109, Resulting Numbers: [109] 109,72 unequal: No Solution Exploring Operation: 95-14=81, Resulting Numbers: [81] 81,72 unequal: No Solution Exploring Operation: 95*14=1330, Resulting Numbers: [1330] 1330,72 unequal: No Solution Moving to Node #0,2,3 Current State: 72:[25, 106], Operations: ['89-78=11', '95+11=106'] Exploring Operation: 25*106=2650, Resulting Numbers: [2650] 2650,72 unequal: No Solution Exploring Operation: 25+106=131, Resulting Numbers: [131] 131,72 unequal: No Solution Exploring Operation: 106-25=81, Resulting Numbers: [81] 81,72 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 #0,4 Current State: 72:[89, 78, 70], Operations: ['95-25=70'] Exploring Operation: 89-70=19, Resulting Numbers: [78, 19] Generated Node #0,4,0: 72:[78, 19] Operation: 89-70=19 Exploring Operation: 89+70=159, Resulting Numbers: [78, 159] Generated Node #0,4,1: 72:[78, 159] Operation: 89+70=159 Exploring Operation: 89-78=11, Resulting Numbers: [70, 11] Generated Node #0,4,2: 72:[70, 11] Operation: 89-78=11 Exploring Operation: 78+70=148, Resulting Numbers: [89, 148] Generated Node #0,4,3: 72:[89, 148] Operation: 78+70=148 Exploring Operation: 78-70=8, Resulting Numbers: [89, 8] Generated Node #0,4,4: 72:[89, 8] Operation: 78-70=8 Moving to Node #0,4,2 Current State: 72:[70, 11], Operations: ['95-25=70', '89-78=11'] Exploring Operation: 70+11=81, Resulting Numbers: [81] 81,72 unequal: No Solution Exploring Operation: 70-11=59, Resulting Numbers: [59] 59,72 unequal: No Solution Exploring Operation: 70*11=770, Resulting Numbers: [770] 770,72 unequal: No Solution Moving to Node #0,4,0 Current State: 72:[78, 19], Operations: ['95-25=70', '89-70=19'] Exploring Operation: 78+19=97, Resulting Numbers: [97] 97,72 unequal: No Solution Exploring Operation: 78-19=59, Resulting Numbers: [59] 59,72 unequal: No Solution Exploring Operation: 78*19=1482, Resulting Numbers: [1482] 1482,72 unequal: No Solution Moving to Node #0,4,4 Current State: 72:[89, 8], Operations: ['95-25=70', '78-70=8'] Exploring Operation: 89-8=81, Resulting Numbers: [81] 81,72 unequal: No Solution Exploring Operation: 89*8=712, Resulting Numbers: [712] 712,72 unequal: No Solution Exploring Operation: 89+8=97, Resulting Numbers: [97] 97,72 unequal: No Solution Moving to Node #0,4,1 Current State: 72:[78, 159], Operations: ['95-25=70', '89+70=159'] Exploring Operation: 78+159=237, Resulting Numbers: [237] 237,72 unequal: No Solution Exploring Operation: 78*159=12402, Resulting Numbers: [12402] 12402,72 unequal: No Solution Exploring Operation: 159-78=81, Resulting Numbers: [81] 81,72 unequal: No Solution Moving to Node #0,4,3 Current State: 72:[89, 148], Operations: ['95-25=70', '78+70=148'] Exploring Operation: 89*148=13172, Resulting Numbers: [13172] 13172,72 unequal: No Solution Exploring Operation: 148-89=59, Resulting Numbers: [59] 59,72 unequal: No Solution Exploring Operation: 89+148=237, Resulting Numbers: [237] 237,72 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:[78, 95, 64], Operations: ['89-25=64'] Exploring Operation: 95-78=17, Resulting Numbers: [64, 17] Generated Node #0,3,0: 72:[64, 17] Operation: 95-78=17 Exploring Operation: 95+64=159, Resulting Numbers: [78, 159] Generated Node #0,3,1: 72:[78, 159] Operation: 95+64=159 Exploring Operation: 78-64=14, Resulting Numbers: [95, 14] Generated Node #0,3,2: 72:[95, 14] Operation: 78-64=14 Exploring Operation: 78+64=142, Resulting Numbers: [95, 142] Generated Node #0,3,3: 72:[95, 142] Operation: 78+64=142 Exploring Operation: 95-64=31, Resulting Numbers: [78, 31] Generated Node #0,3,4: 72:[78, 31] Operation: 95-64=31 Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 72:[64, 17], Operations: ['89-25=64', '95-78=17'] Exploring Operation: 64*17=1088, Resulting Numbers: [1088] 1088,72 unequal: No Solution Exploring Operation: 64+17=81, Resulting Numbers: [81] 81,72 unequal: No Solution Exploring Operation: 64-17=47, Resulting Numbers: [47] 47,72 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:[78, 31], Operations: ['89-25=64', '95-64=31'] Exploring Operation: 78-31=47, Resulting Numbers: [47] 47,72 unequal: No Solution Exploring Operation: 78*31=2418, Resulting Numbers: [2418] 2418,72 unequal: No Solution Exploring Operation: 78+31=109, Resulting Numbers: [109] 109,72 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:[95, 14], Operations: ['89-25=64', '78-64=14'] Exploring Operation: 95-14=81, Resulting Numbers: [81] 81,72 unequal: No Solution Exploring Operation: 95*14=1330, Resulting Numbers: [1330] 1330,72 unequal: No Solution Exploring Operation: 95+14=109, Resulting Numbers: [109] 109,72 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 #0,3,1 Current State: 72:[78, 159], Operations: ['89-25=64', '95+64=159'] Exploring Operation: 159-78=81, Resulting Numbers: [81] 81,72 unequal: No Solution Exploring Operation: 78*159=12402, Resulting Numbers: [12402] 12402,72 unequal: No Solution Exploring Operation: 78+159=237, Resulting Numbers: [237] 237,72 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:[95, 142], Operations: ['89-25=64', '78+64=142'] Exploring Operation: 142-95=47, Resulting Numbers: [47] 47,72 unequal: No Solution Exploring Operation: 95*142=13490, Resulting Numbers: [13490] 13490,72 unequal: No Solution Exploring Operation: 95+142=237, Resulting Numbers: [237] 237,72 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 No solution found.
0
hs_5
mult_heuristic
[ 64, 44, 3, 47 ]
63
[ "44+3=47", "47/47=1", "64-1=63" ]
Current State: 63:[64, 44, 3, 47], Operations: [] Exploring Operation: 44+3=47, Resulting Numbers: [64, 47, 47] Generated Node #2: [64, 47, 47] from Operation: 44+3=47 Current State: 63:[64, 47, 47], Operations: ['44+3=47'] Exploring Operation: 47/47=1, Resulting Numbers: [64, 1] Generated Node #3: [64, 1] from Operation: 47/47=1 Current State: 63:[64, 1], Operations: ['44+3=47', '47/47=1'] Exploring Operation: 64-1=63, Resulting Numbers: [63] 63,63 equal: Goal Reached
4
Current State: 63:[64, 44, 3, 47], Operations: [] Exploring Operation: 64-47=17, Resulting Numbers: [44, 3, 17] Generated Node #0,0: 63:[44, 3, 17] Operation: 64-47=17 Exploring Operation: 47-44=3, Resulting Numbers: [64, 3, 3] Generated Node #0,1: 63:[64, 3, 3] Operation: 47-44=3 Exploring Operation: 64-44=20, Resulting Numbers: [3, 47, 20] Generated Node #0,2: 63:[3, 47, 20] Operation: 64-44=20 Moving to Node #0,1 Current State: 63:[64, 3, 3], Operations: ['47-44=3'] Exploring Operation: 64-3=61, Resulting Numbers: [3, 61] Generated Node #0,1,0: 63:[3, 61] Operation: 64-3=61 Exploring Operation: 64-3=61, Resulting Numbers: [3, 61] Generated Node #0,1,1: 63:[3, 61] Operation: 64-3=61 Exploring Operation: 3*3=9, Resulting Numbers: [64, 9] Generated Node #0,1,2: 63:[64, 9] Operation: 3*3=9 Moving to Node #0,2 Current State: 63:[3, 47, 20], Operations: ['64-44=20'] Exploring Operation: 47-20=27, Resulting Numbers: [3, 27] Generated Node #0,2,0: 63:[3, 27] Operation: 47-20=27 Exploring Operation: 47+20=67, Resulting Numbers: [3, 67] Generated Node #0,2,1: 63:[3, 67] Operation: 47+20=67 Exploring Operation: 3+47=50, Resulting Numbers: [20, 50] Generated Node #0,2,2: 63:[20, 50] Operation: 3+47=50 Moving to Node #0,0 Current State: 63:[44, 3, 17], Operations: ['64-47=17'] Exploring Operation: 44+3=47, Resulting Numbers: [17, 47] Generated Node #0,0,0: 63:[17, 47] Operation: 44+3=47 Exploring Operation: 44-17=27, Resulting Numbers: [3, 27] Generated Node #0,0,1: 63:[3, 27] Operation: 44-17=27 Exploring Operation: 44+17=61, Resulting Numbers: [3, 61] Generated Node #0,0,2: 63:[3, 61] Operation: 44+17=61 Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 63:[3, 61], Operations: ['64-47=17', '44+17=61'] Exploring Operation: 3+61=64, Resulting Numbers: [64] 64,63 unequal: No Solution Exploring Operation: 3*61=183, Resulting Numbers: [183] 183,63 unequal: No Solution Exploring Operation: 61-3=58, Resulting Numbers: [58] 58,63 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:[3, 27], Operations: ['64-47=17', '44-17=27'] Exploring Operation: 27-3=24, Resulting Numbers: [24] 24,63 unequal: No Solution Exploring Operation: 3+27=30, Resulting Numbers: [30] 30,63 unequal: No Solution Exploring Operation: 27/3=9, Resulting Numbers: [9] 9,63 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 #0,0,0 Current State: 63:[17, 47], Operations: ['64-47=17', '44+3=47'] Exploring Operation: 47-17=30, Resulting Numbers: [30] 30,63 unequal: No Solution Exploring Operation: 17*47=799, Resulting Numbers: [799] 799,63 unequal: No Solution Exploring Operation: 17+47=64, Resulting Numbers: [64] 64,63 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1,2 Current State: 63:[64, 9], Operations: ['47-44=3', '3*3=9'] Exploring Operation: 64-9=55, Resulting Numbers: [55] 55,63 unequal: No Solution Exploring Operation: 64*9=576, Resulting Numbers: [576] 576,63 unequal: No Solution Exploring Operation: 64+9=73, Resulting Numbers: [73] 73,63 unequal: No Solution Moving to Node #0,1,1 Current State: 63:[3, 61], Operations: ['47-44=3', '64-3=61'] Exploring Operation: 3+61=64, Resulting Numbers: [64] 64,63 unequal: No Solution Exploring Operation: 3*61=183, Resulting Numbers: [183] 183,63 unequal: No Solution Exploring Operation: 61-3=58, Resulting Numbers: [58] 58,63 unequal: No Solution Moving to Node #0,1,0 Current State: 63:[3, 61], Operations: ['47-44=3', '64-3=61'] Exploring Operation: 3+61=64, Resulting Numbers: [64] 64,63 unequal: No Solution Exploring Operation: 61-3=58, Resulting Numbers: [58] 58,63 unequal: No Solution Exploring Operation: 3*61=183, Resulting Numbers: [183] 183,63 unequal: No Solution Moving to Node #0,2,1 Current State: 63:[3, 67], Operations: ['64-44=20', '47+20=67'] Exploring Operation: 3*67=201, Resulting Numbers: [201] 201,63 unequal: No Solution Exploring Operation: 3+67=70, Resulting Numbers: [70] 70,63 unequal: No Solution Exploring Operation: 67-3=64, Resulting Numbers: [64] 64,63 unequal: No Solution Moving to Node #0,2,0 Current State: 63:[3, 27], Operations: ['64-44=20', '47-20=27'] Exploring Operation: 27/3=9, Resulting Numbers: [9] 9,63 unequal: No Solution Exploring Operation: 3+27=30, Resulting Numbers: [30] 30,63 unequal: No Solution Exploring Operation: 27-3=24, Resulting Numbers: [24] 24,63 unequal: No Solution Moving to Node #0,2,2 Current State: 63:[20, 50], Operations: ['64-44=20', '3+47=50'] Exploring Operation: 50-20=30, Resulting Numbers: [30] 30,63 unequal: No Solution Exploring Operation: 20+50=70, Resulting Numbers: [70] 70,63 unequal: No Solution Exploring Operation: 20*50=1000, Resulting Numbers: [1000] 1000,63 unequal: No Solution No solution found.
0
hs_3
sum_heuristic
[ 8, 16, 96, 62 ]
42
[ "16-8=8", "96-62=34", "8+34=42" ]
Current State: 42:[8, 16, 96, 62], Operations: [] Exploring Operation: 16-8=8, Resulting Numbers: [96, 62, 8] Generated Node #2: [96, 62, 8] from Operation: 16-8=8 Current State: 42:[96, 62, 8], Operations: ['16-8=8'] Exploring Operation: 96-62=34, Resulting Numbers: [8, 34] Generated Node #3: [8, 34] from Operation: 96-62=34 Current State: 42:[8, 34], Operations: ['16-8=8', '96-62=34'] Exploring Operation: 8+34=42, Resulting Numbers: [42] 42,42 equal: Goal Reached
4
Current State: 42:[8, 16, 96, 62], Operations: [] Exploring Operation: 96-62=34, Resulting Numbers: [8, 16, 34] Generated Node #0,0: 42:[8, 16, 34] Operation: 96-62=34 Exploring Operation: 96-16=80, Resulting Numbers: [8, 62, 80] Generated Node #0,1: 42:[8, 62, 80] Operation: 96-16=80 Exploring Operation: 62-16=46, Resulting Numbers: [8, 96, 46] Generated Node #0,2: 42:[8, 96, 46] Operation: 62-16=46 Exploring Operation: 96/16=6, Resulting Numbers: [8, 62, 6] Generated Node #0,3: 42:[8, 62, 6] Operation: 96/16=6 Exploring Operation: 96/8=12, Resulting Numbers: [16, 62, 12] Generated Node #0,4: 42:[16, 62, 12] Operation: 96/8=12 Moving to Node #0,0 Current State: 42:[8, 16, 34], Operations: ['96-62=34'] Exploring Operation: 16/8=2, Resulting Numbers: [34, 2] Generated Node #0,0,0: 42:[34, 2] Operation: 16/8=2 Exploring Operation: 8+34=42, Resulting Numbers: [16, 42] Generated Node #0,0,1: 42:[16, 42] Operation: 8+34=42 Exploring Operation: 34-16=18, Resulting Numbers: [8, 18] Generated Node #0,0,2: 42:[8, 18] Operation: 34-16=18 Exploring Operation: 16-8=8, Resulting Numbers: [34, 8] Generated Node #0,0,3: 42:[34, 8] Operation: 16-8=8 Exploring Operation: 34-8=26, Resulting Numbers: [16, 26] Generated Node #0,0,4: 42:[16, 26] Operation: 34-8=26 Moving to Node #0,3 Current State: 42:[8, 62, 6], Operations: ['96/16=6'] Exploring Operation: 62-8=54, Resulting Numbers: [6, 54] Generated Node #0,3,0: 42:[6, 54] Operation: 62-8=54 Exploring Operation: 8-6=2, Resulting Numbers: [62, 2] Generated Node #0,3,1: 42:[62, 2] Operation: 8-6=2 Exploring Operation: 8*6=48, Resulting Numbers: [62, 48] Generated Node #0,3,2: 42:[62, 48] Operation: 8*6=48 Exploring Operation: 8+6=14, Resulting Numbers: [62, 14] Generated Node #0,3,3: 42:[62, 14] Operation: 8+6=14 Exploring Operation: 62-6=56, Resulting Numbers: [8, 56] Generated Node #0,3,4: 42:[8, 56] Operation: 62-6=56 Moving to Node #0,4 Current State: 42:[16, 62, 12], Operations: ['96/8=12'] Exploring Operation: 62+12=74, Resulting Numbers: [16, 74] Generated Node #0,4,0: 42:[16, 74] Operation: 62+12=74 Exploring Operation: 62-16=46, Resulting Numbers: [12, 46] Generated Node #0,4,1: 42:[12, 46] Operation: 62-16=46 Exploring Operation: 16-12=4, Resulting Numbers: [62, 4] Generated Node #0,4,2: 42:[62, 4] Operation: 16-12=4 Exploring Operation: 16+12=28, Resulting Numbers: [62, 28] Generated Node #0,4,3: 42:[62, 28] Operation: 16+12=28 Exploring Operation: 62-12=50, Resulting Numbers: [16, 50] Generated Node #0,4,4: 42:[16, 50] Operation: 62-12=50 Start Sub Search at level 1: Moving to Node #0,4,1 Current State: 42:[12, 46], Operations: ['96/8=12', '62-16=46'] Exploring Operation: 12+46=58, Resulting Numbers: [58] 58,42 unequal: No Solution Exploring Operation: 46-12=34, Resulting Numbers: [34] 34,42 unequal: No Solution Exploring Operation: 12*46=552, Resulting Numbers: [552] 552,42 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: 42:[16, 50], Operations: ['96/8=12', '62-12=50'] Exploring Operation: 16*50=800, Resulting Numbers: [800] 800,42 unequal: No Solution Exploring Operation: 50-16=34, Resulting Numbers: [34] 34,42 unequal: No Solution Exploring Operation: 16+50=66, Resulting Numbers: [66] 66,42 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: 42:[62, 4], Operations: ['96/8=12', '16-12=4'] Exploring Operation: 62-4=58, Resulting Numbers: [58] 58,42 unequal: No Solution Exploring Operation: 62*4=248, Resulting Numbers: [248] 248,42 unequal: No Solution Exploring Operation: 62+4=66, Resulting Numbers: [66] 66,42 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: 42:[62, 28], Operations: ['96/8=12', '16+12=28'] Exploring Operation: 62*28=1736, Resulting Numbers: [1736] 1736,42 unequal: No Solution Exploring Operation: 62-28=34, Resulting Numbers: [34] 34,42 unequal: No Solution Exploring Operation: 62+28=90, Resulting Numbers: [90] 90,42 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: 42:[16, 74], Operations: ['96/8=12', '62+12=74'] Exploring Operation: 16+74=90, Resulting Numbers: [90] 90,42 unequal: No Solution Exploring Operation: 74-16=58, Resulting Numbers: [58] 58,42 unequal: No Solution Exploring Operation: 16*74=1184, Resulting Numbers: [1184] 1184,42 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: 42:[8, 62, 80], Operations: ['96-16=80'] Exploring Operation: 62-8=54, Resulting Numbers: [80, 54] Generated Node #0,1,0: 42:[80, 54] Operation: 62-8=54 Exploring Operation: 80-62=18, Resulting Numbers: [8, 18] Generated Node #0,1,1: 42:[8, 18] Operation: 80-62=18 Exploring Operation: 80-8=72, Resulting Numbers: [62, 72] Generated Node #0,1,2: 42:[62, 72] Operation: 80-8=72 Exploring Operation: 80/8=10, Resulting Numbers: [62, 10] Generated Node #0,1,3: 42:[62, 10] Operation: 80/8=10 Exploring Operation: 8+62=70, Resulting Numbers: [80, 70] Generated Node #0,1,4: 42:[80, 70] Operation: 8+62=70 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 42:[8, 18], Operations: ['96-16=80', '80-62=18'] Exploring Operation: 8*18=144, Resulting Numbers: [144] 144,42 unequal: No Solution Exploring Operation: 8+18=26, Resulting Numbers: [26] 26,42 unequal: No Solution Exploring Operation: 18-8=10, Resulting Numbers: [10] 10,42 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: 42:[62, 10], Operations: ['96-16=80', '80/8=10'] Exploring Operation: 62-10=52, Resulting Numbers: [52] 52,42 unequal: No Solution Exploring Operation: 62+10=72, Resulting Numbers: [72] 72,42 unequal: No Solution Exploring Operation: 62*10=620, Resulting Numbers: [620] 620,42 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: 42:[80, 54], Operations: ['96-16=80', '62-8=54'] Exploring Operation: 80-54=26, Resulting Numbers: [26] 26,42 unequal: No Solution Exploring Operation: 80*54=4320, Resulting Numbers: [4320] 4320,42 unequal: No Solution Exploring Operation: 80+54=134, Resulting Numbers: [134] 134,42 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: 42:[62, 72], Operations: ['96-16=80', '80-8=72'] Exploring Operation: 72-62=10, Resulting Numbers: [10] 10,42 unequal: No Solution Exploring Operation: 62+72=134, Resulting Numbers: [134] 134,42 unequal: No Solution Exploring Operation: 62*72=4464, Resulting Numbers: [4464] 4464,42 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: 42:[80, 70], Operations: ['96-16=80', '8+62=70'] Exploring Operation: 80*70=5600, Resulting Numbers: [5600] 5600,42 unequal: No Solution Exploring Operation: 80-70=10, Resulting Numbers: [10] 10,42 unequal: No Solution Exploring Operation: 80+70=150, Resulting Numbers: [150] 150,42 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: 42:[8, 96, 46], Operations: ['62-16=46'] Exploring Operation: 96-46=50, Resulting Numbers: [8, 50] Generated Node #0,2,0: 42:[8, 50] Operation: 96-46=50 Exploring Operation: 96/8=12, Resulting Numbers: [46, 12] Generated Node #0,2,1: 42:[46, 12] Operation: 96/8=12 Exploring Operation: 46-8=38, Resulting Numbers: [96, 38] Generated Node #0,2,2: 42:[96, 38] Operation: 46-8=38 Exploring Operation: 96-8=88, Resulting Numbers: [46, 88] Generated Node #0,2,3: 42:[46, 88] Operation: 96-8=88 Exploring Operation: 8+96=104, Resulting Numbers: [46, 104] Generated Node #0,2,4: 42:[46, 104] Operation: 8+96=104 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 42:[46, 12], Operations: ['62-16=46', '96/8=12'] Exploring Operation: 46+12=58, Resulting Numbers: [58] 58,42 unequal: No Solution Exploring Operation: 46-12=34, Resulting Numbers: [34] 34,42 unequal: No Solution Exploring Operation: 46*12=552, Resulting Numbers: [552] 552,42 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: 42:[8, 50], Operations: ['62-16=46', '96-46=50'] Exploring Operation: 8*50=400, Resulting Numbers: [400] 400,42 unequal: No Solution Exploring Operation: 50-8=42, Resulting Numbers: [42] 42,42 equal: Goal Reached Moving to Node #0 Current State: 42:[8, 16, 96, 62], Operations: [] Exploring Operation: 62-16=46, Resulting Numbers: [8, 96, 46] Generated Node #0,2: 42:[8, 96, 46] Operation: 62-16=46 Moving to Node #0,2 Current State: 42:[8, 96, 46], Operations: ['62-16=46'] Exploring Operation: 96-46=50, Resulting Numbers: [8, 50] Generated Node #0,2,0: 42:[8, 50] Operation: 96-46=50 Moving to Node #0,2,0 Current State: 42:[8, 50], Operations: ['62-16=46', '96-46=50'] Exploring Operation: 50-8=42, Resulting Numbers: [42] 42,42 equal: Goal Reached Exit Sub Search at level 1
0.940104
hs_5
sum_heuristic
[ 30, 27, 8, 60 ]
71
[ "30-27=3", "8+60=68", "3+68=71" ]
Current State: 71:[30, 27, 8, 60], Operations: [] Exploring Operation: 30-27=3, Resulting Numbers: [8, 60, 3] Generated Node #2: [8, 60, 3] from Operation: 30-27=3 Current State: 71:[8, 60, 3], Operations: ['30-27=3'] Exploring Operation: 8+60=68, Resulting Numbers: [3, 68] Generated Node #3: [3, 68] from Operation: 8+60=68 Current State: 71:[3, 68], Operations: ['30-27=3', '8+60=68'] Exploring Operation: 3+68=71, Resulting Numbers: [71] 71,71 equal: Goal Reached
4
Current State: 71:[30, 27, 8, 60], Operations: [] Exploring Operation: 30+8=38, Resulting Numbers: [27, 60, 38] Generated Node #0,0: 71:[27, 60, 38] Operation: 30+8=38 Exploring Operation: 30+27=57, Resulting Numbers: [8, 60, 57] Generated Node #0,1: 71:[8, 60, 57] Operation: 30+27=57 Exploring Operation: 8+60=68, Resulting Numbers: [30, 27, 68] Generated Node #0,2: 71:[30, 27, 68] Operation: 8+60=68 Exploring Operation: 27+8=35, Resulting Numbers: [30, 60, 35] Generated Node #0,3: 71:[30, 60, 35] Operation: 27+8=35 Start Sub Search at level 1: Moving to Node #0,0 Current State: 71:[27, 60, 38], Operations: ['30+8=38'] Exploring Operation: 38-27=11, Resulting Numbers: [60, 11] Generated Node #0,0,0: 71:[60, 11] Operation: 38-27=11 Exploring Operation: 60-27=33, Resulting Numbers: [38, 33] Generated Node #0,0,1: 71:[38, 33] Operation: 60-27=33 Exploring Operation: 27+60=87, Resulting Numbers: [38, 87] Generated Node #0,0,2: 71:[38, 87] Operation: 27+60=87 Exploring Operation: 27+38=65, Resulting Numbers: [60, 65] Generated Node #0,0,3: 71:[60, 65] Operation: 27+38=65 Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 71:[60, 65], Operations: ['30+8=38', '27+38=65'] Exploring Operation: 65-60=5, Resulting Numbers: [5] 5,71 unequal: No Solution Exploring Operation: 60+65=125, Resulting Numbers: [125] 125,71 unequal: No Solution Exploring Operation: 60*65=3900, Resulting Numbers: [3900] 3900,71 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: 71:[38, 87], Operations: ['30+8=38', '27+60=87'] Exploring Operation: 38+87=125, Resulting Numbers: [125] 125,71 unequal: No Solution Exploring Operation: 38*87=3306, Resulting Numbers: [3306] 3306,71 unequal: No Solution Exploring Operation: 87-38=49, Resulting Numbers: [49] 49,71 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: 71:[60, 11], Operations: ['30+8=38', '38-27=11'] Exploring Operation: 60*11=660, Resulting Numbers: [660] 660,71 unequal: No Solution Exploring Operation: 60+11=71, Resulting Numbers: [71] 71,71 equal: Goal Reached Moving to Node #0 Current State: 71:[30, 27, 8, 60], Operations: [] Exploring Operation: 30+8=38, Resulting Numbers: [27, 60, 38] Generated Node #0,0: 71:[27, 60, 38] Operation: 30+8=38 Moving to Node #0,0 Current State: 71:[27, 60, 38], Operations: ['30+8=38'] Exploring Operation: 38-27=11, Resulting Numbers: [60, 11] Generated Node #0,0,0: 71:[60, 11] Operation: 38-27=11 Moving to Node #0,0,0 Current State: 71:[60, 11], Operations: ['30+8=38', '38-27=11'] Exploring Operation: 60+11=71, Resulting Numbers: [71] 71,71 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.982639
hs_4
mult_heuristic
[ 84, 79, 73, 7 ]
91
[ "84*79=6636", "7+6636=6643", "6643/73=91" ]
Current State: 91:[84, 79, 73, 7], Operations: [] Exploring Operation: 84*79=6636, Resulting Numbers: [73, 7, 6636] Generated Node #2: [73, 7, 6636] from Operation: 84*79=6636 Current State: 91:[73, 7, 6636], Operations: ['84*79=6636'] Exploring Operation: 7+6636=6643, Resulting Numbers: [73, 6643] Generated Node #3: [73, 6643] from Operation: 7+6636=6643 Current State: 91:[73, 6643], Operations: ['84*79=6636', '7+6636=6643'] Exploring Operation: 6643/73=91, Resulting Numbers: [91] 91,91 equal: Goal Reached
4
Current State: 91:[84, 79, 73, 7], Operations: [] Exploring Operation: 84-79=5, Resulting Numbers: [73, 7, 5] Generated Node #0,0: 91:[73, 7, 5] Operation: 84-79=5 Exploring Operation: 84-73=11, Resulting Numbers: [79, 7, 11] Generated Node #0,1: 91:[79, 7, 11] Operation: 84-73=11 Exploring Operation: 79-73=6, Resulting Numbers: [84, 7, 6] Generated Node #0,2: 91:[84, 7, 6] Operation: 79-73=6 Start Sub Search at level 1: Moving to Node #0,2 Current State: 91:[84, 7, 6], Operations: ['79-73=6'] Exploring Operation: 84/6=14, Resulting Numbers: [7, 14] Generated Node #0,2,0: 91:[7, 14] Operation: 84/6=14 Exploring Operation: 84+6=90, Resulting Numbers: [7, 90] Generated Node #0,2,1: 91:[7, 90] Operation: 84+6=90 Exploring Operation: 84+7=91, Resulting Numbers: [6, 91] Generated Node #0,2,2: 91:[6, 91] Operation: 84+7=91 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 91:[7, 14], Operations: ['79-73=6', '84/6=14'] Exploring Operation: 14/7=2, Resulting Numbers: [2] 2,91 unequal: No Solution Exploring Operation: 14-7=7, Resulting Numbers: [7] 7,91 unequal: No Solution Exploring Operation: 7*14=98, Resulting Numbers: [98] 98,91 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 #0,2,1 Current State: 91:[7, 90], Operations: ['79-73=6', '84+6=90'] Exploring Operation: 90-7=83, Resulting Numbers: [83] 83,91 unequal: No Solution Exploring Operation: 7*90=630, Resulting Numbers: [630] 630,91 unequal: No Solution Exploring Operation: 7+90=97, Resulting Numbers: [97] 97,91 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 #0,2,2 Current State: 91:[6, 91], Operations: ['79-73=6', '84+7=91'] Exploring Operation: 6*91=546, Resulting Numbers: [546] 546,91 unequal: No Solution Exploring Operation: 6+91=97, Resulting Numbers: [97] 97,91 unequal: No Solution Exploring Operation: 91-6=85, Resulting Numbers: [85] 85,91 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:[79, 7, 11], Operations: ['84-73=11'] Exploring Operation: 11-7=4, Resulting Numbers: [79, 4] Generated Node #0,1,0: 91:[79, 4] Operation: 11-7=4 Exploring Operation: 79+7=86, Resulting Numbers: [11, 86] Generated Node #0,1,1: 91:[11, 86] Operation: 79+7=86 Exploring Operation: 79+11=90, Resulting Numbers: [7, 90] Generated Node #0,1,2: 91:[7, 90] Operation: 79+11=90 Moving to Node #0,1,2 Current State: 91:[7, 90], Operations: ['84-73=11', '79+11=90'] Exploring Operation: 90-7=83, Resulting Numbers: [83] 83,91 unequal: No Solution Exploring Operation: 7+90=97, Resulting Numbers: [97] 97,91 unequal: No Solution Exploring Operation: 7*90=630, Resulting Numbers: [630] 630,91 unequal: No Solution Moving to Node #0,1,1 Current State: 91:[11, 86], Operations: ['84-73=11', '79+7=86'] Exploring Operation: 11+86=97, Resulting Numbers: [97] 97,91 unequal: No Solution Exploring Operation: 11*86=946, Resulting Numbers: [946] 946,91 unequal: No Solution Exploring Operation: 86-11=75, Resulting Numbers: [75] 75,91 unequal: No Solution Moving to Node #0,1,0 Current State: 91:[79, 4], Operations: ['84-73=11', '11-7=4'] Exploring Operation: 79*4=316, Resulting Numbers: [316] 316,91 unequal: No Solution Exploring Operation: 79-4=75, Resulting Numbers: [75] 75,91 unequal: No Solution Exploring Operation: 79+4=83, Resulting Numbers: [83] 83,91 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 #0,0 Current State: 91:[73, 7, 5], Operations: ['84-79=5'] Exploring Operation: 7+5=12, Resulting Numbers: [73, 12] Generated Node #0,0,0: 91:[73, 12] Operation: 7+5=12 Exploring Operation: 73+5=78, Resulting Numbers: [7, 78] Generated Node #0,0,1: 91:[7, 78] Operation: 73+5=78 Exploring Operation: 73+7=80, Resulting Numbers: [5, 80] Generated Node #0,0,2: 91:[5, 80] Operation: 73+7=80 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 91:[7, 78], Operations: ['84-79=5', '73+5=78'] Exploring Operation: 7*78=546, Resulting Numbers: [546] 546,91 unequal: No Solution Exploring Operation: 7+78=85, Resulting Numbers: [85] 85,91 unequal: No Solution Exploring Operation: 78-7=71, Resulting Numbers: [71] 71,91 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:[5, 80], Operations: ['84-79=5', '73+7=80'] Exploring Operation: 80/5=16, Resulting Numbers: [16] 16,91 unequal: No Solution Exploring Operation: 80-5=75, Resulting Numbers: [75] 75,91 unequal: No Solution Exploring Operation: 5+80=85, Resulting Numbers: [85] 85,91 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:[73, 12], Operations: ['84-79=5', '7+5=12'] Exploring Operation: 73*12=876, Resulting Numbers: [876] 876,91 unequal: No Solution Exploring Operation: 73+12=85, Resulting Numbers: [85] 85,91 unequal: No Solution Exploring Operation: 73-12=61, Resulting Numbers: [61] 61,91 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 No solution found.
0
hs_3
sum_heuristic
[ 83, 39, 51, 10 ]
74
[ "39+51=90", "90/10=9", "83-9=74" ]
Current State: 74:[83, 39, 51, 10], Operations: [] Exploring Operation: 39+51=90, Resulting Numbers: [83, 10, 90] Generated Node #2: [83, 10, 90] from Operation: 39+51=90 Current State: 74:[83, 10, 90], Operations: ['39+51=90'] Exploring Operation: 90/10=9, Resulting Numbers: [83, 9] Generated Node #3: [83, 9] from Operation: 90/10=9 Current State: 74:[83, 9], Operations: ['39+51=90', '90/10=9'] Exploring Operation: 83-9=74, Resulting Numbers: [74] 74,74 equal: Goal Reached
4
Current State: 74:[83, 39, 51, 10], Operations: [] Exploring Operation: 51-10=41, Resulting Numbers: [83, 39, 41] Generated Node #0,0: 74:[83, 39, 41] Operation: 51-10=41 Exploring Operation: 83-51=32, Resulting Numbers: [39, 10, 32] Generated Node #0,1: 74:[39, 10, 32] Operation: 83-51=32 Start Sub Search at level 1: Moving to Node #0,0 Current State: 74:[83, 39, 41], Operations: ['51-10=41'] Exploring Operation: 83-41=42, Resulting Numbers: [39, 42] Generated Node #0,0,0: 74:[39, 42] Operation: 83-41=42 Exploring Operation: 41-39=2, Resulting Numbers: [83, 2] Generated Node #0,0,1: 74:[83, 2] Operation: 41-39=2 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 74:[39, 42], Operations: ['51-10=41', '83-41=42'] Exploring Operation: 39+42=81, Resulting Numbers: [81] 81,74 unequal: No Solution Exploring Operation: 42-39=3, Resulting Numbers: [3] 3,74 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:[83, 2], Operations: ['51-10=41', '41-39=2'] Exploring Operation: 83+2=85, Resulting Numbers: [85] 85,74 unequal: No Solution Exploring Operation: 83-2=81, Resulting Numbers: [81] 81,74 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:[39, 10, 32], Operations: ['83-51=32'] Exploring Operation: 10+32=42, Resulting Numbers: [39, 42] Generated Node #0,1,0: 74:[39, 42] Operation: 10+32=42 Exploring Operation: 39+32=71, Resulting Numbers: [10, 71] Generated Node #0,1,1: 74:[10, 71] Operation: 39+32=71 Moving to Node #0,1,0 Current State: 74:[39, 42], Operations: ['83-51=32', '10+32=42'] Exploring Operation: 39+42=81, Resulting Numbers: [81] 81,74 unequal: No Solution Exploring Operation: 42-39=3, Resulting Numbers: [3] 3,74 unequal: No Solution Moving to Node #0,1,1 Current State: 74:[10, 71], Operations: ['83-51=32', '39+32=71'] Exploring Operation: 10+71=81, Resulting Numbers: [81] 81,74 unequal: No Solution Exploring Operation: 71-10=61, Resulting Numbers: [61] 61,74 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
[ 93, 45, 68, 36 ]
80
[ "93-45=48", "68-36=32", "48+32=80" ]
Current State: 80:[93, 45, 68, 36], Operations: [] Exploring Operation: 93-45=48, Resulting Numbers: [68, 36, 48] Generated Node #2: [68, 36, 48] from Operation: 93-45=48 Current State: 80:[68, 36, 48], Operations: ['93-45=48'] Exploring Operation: 68-36=32, Resulting Numbers: [48, 32] Generated Node #3: [48, 32] from Operation: 68-36=32 Current State: 80:[48, 32], Operations: ['93-45=48', '68-36=32'] Exploring Operation: 48+32=80, Resulting Numbers: [80] 80,80 equal: Goal Reached
4
Current State: 80:[93, 45, 68, 36], Operations: [] Exploring Operation: 93-68=25, Resulting Numbers: [45, 36, 25] Generated Node #0,0: 80:[45, 36, 25] Operation: 93-68=25 Exploring Operation: 45+36=81, Resulting Numbers: [93, 68, 81] Generated Node #0,1: 80:[93, 68, 81] Operation: 45+36=81 Exploring Operation: 93-45=48, Resulting Numbers: [68, 36, 48] Generated Node #0,2: 80:[68, 36, 48] Operation: 93-45=48 Exploring Operation: 68-45=23, Resulting Numbers: [93, 36, 23] Generated Node #0,3: 80:[93, 36, 23] Operation: 68-45=23 Start Sub Search at level 1: Moving to Node #0,0 Current State: 80:[45, 36, 25], Operations: ['93-68=25'] Exploring Operation: 45-36=9, Resulting Numbers: [25, 9] Generated Node #0,0,0: 80:[25, 9] Operation: 45-36=9 Exploring Operation: 36-25=11, Resulting Numbers: [45, 11] Generated Node #0,0,1: 80:[45, 11] Operation: 36-25=11 Exploring Operation: 45-25=20, Resulting Numbers: [36, 20] Generated Node #0,0,2: 80:[36, 20] Operation: 45-25=20 Exploring Operation: 45+36=81, Resulting Numbers: [25, 81] Generated Node #0,0,3: 80:[25, 81] Operation: 45+36=81 Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 80:[36, 20], Operations: ['93-68=25', '45-25=20'] Exploring Operation: 36+20=56, Resulting Numbers: [56] 56,80 unequal: No Solution Exploring Operation: 36*20=720, Resulting Numbers: [720] 720,80 unequal: No Solution Exploring Operation: 36-20=16, Resulting Numbers: [16] 16,80 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: 80:[25, 9], Operations: ['93-68=25', '45-36=9'] Exploring Operation: 25-9=16, Resulting Numbers: [16] 16,80 unequal: No Solution Exploring Operation: 25*9=225, Resulting Numbers: [225] 225,80 unequal: No Solution Exploring Operation: 25+9=34, Resulting Numbers: [34] 34,80 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: 80:[45, 11], Operations: ['93-68=25', '36-25=11'] Exploring Operation: 45-11=34, Resulting Numbers: [34] 34,80 unequal: No Solution Exploring Operation: 45*11=495, Resulting Numbers: [495] 495,80 unequal: No Solution Exploring Operation: 45+11=56, Resulting Numbers: [56] 56,80 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: 80:[25, 81], Operations: ['93-68=25', '45+36=81'] Exploring Operation: 81-25=56, Resulting Numbers: [56] 56,80 unequal: No Solution Exploring Operation: 25*81=2025, Resulting Numbers: [2025] 2025,80 unequal: No Solution Exploring Operation: 25+81=106, Resulting Numbers: [106] 106,80 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: 80:[93, 36, 23], Operations: ['68-45=23'] Exploring Operation: 36+23=59, Resulting Numbers: [93, 59] Generated Node #0,3,0: 80:[93, 59] Operation: 36+23=59 Exploring Operation: 36-23=13, Resulting Numbers: [93, 13] Generated Node #0,3,1: 80:[93, 13] Operation: 36-23=13 Exploring Operation: 93-36=57, Resulting Numbers: [23, 57] Generated Node #0,3,2: 80:[23, 57] Operation: 93-36=57 Exploring Operation: 93-23=70, Resulting Numbers: [36, 70] Generated Node #0,3,3: 80:[36, 70] Operation: 93-23=70 Moving to Node #0,3,3 Current State: 80:[36, 70], Operations: ['68-45=23', '93-23=70'] Exploring Operation: 70-36=34, Resulting Numbers: [34] 34,80 unequal: No Solution Exploring Operation: 36+70=106, Resulting Numbers: [106] 106,80 unequal: No Solution Exploring Operation: 36*70=2520, Resulting Numbers: [2520] 2520,80 unequal: No Solution Moving to Node #0,3,1 Current State: 80:[93, 13], Operations: ['68-45=23', '36-23=13'] Exploring Operation: 93+13=106, Resulting Numbers: [106] 106,80 unequal: No Solution Exploring Operation: 93*13=1209, Resulting Numbers: [1209] 1209,80 unequal: No Solution Exploring Operation: 93-13=80, Resulting Numbers: [80] 80,80 equal: Goal Reached Moving to Node #0 Current State: 80:[93, 45, 68, 36], Operations: [] Exploring Operation: 68-45=23, Resulting Numbers: [93, 36, 23] Generated Node #0,3: 80:[93, 36, 23] Operation: 68-45=23 Moving to Node #0,3 Current State: 80:[93, 36, 23], Operations: ['68-45=23'] Exploring Operation: 36-23=13, Resulting Numbers: [93, 13] Generated Node #0,3,1: 80:[93, 13] Operation: 36-23=13 Moving to Node #0,3,1 Current State: 80:[93, 13], Operations: ['68-45=23', '36-23=13'] Exploring Operation: 93-13=80, Resulting Numbers: [80] 80,80 equal: Goal Reached Exit Sub Search at level 1
0.970486
hs_4
sum_heuristic
[ 49, 11, 35, 7 ]
22
[ "49-35=14", "11*14=154", "154/7=22" ]
Current State: 22:[49, 11, 35, 7], Operations: [] Exploring Operation: 49-35=14, Resulting Numbers: [11, 7, 14] Generated Node #2: [11, 7, 14] from Operation: 49-35=14 Current State: 22:[11, 7, 14], Operations: ['49-35=14'] Exploring Operation: 11*14=154, Resulting Numbers: [7, 154] Generated Node #3: [7, 154] from Operation: 11*14=154 Current State: 22:[7, 154], Operations: ['49-35=14', '11*14=154'] Exploring Operation: 154/7=22, Resulting Numbers: [22] 22,22 equal: Goal Reached
4
Current State: 22:[49, 11, 35, 7], Operations: [] Exploring Operation: 49-35=14, Resulting Numbers: [11, 7, 14] Generated Node #0,0: 22:[11, 7, 14] Operation: 49-35=14 Moving to Node #0,0 Current State: 22:[11, 7, 14], Operations: ['49-35=14'] Exploring Operation: 14/7=2, Resulting Numbers: [11, 2] Generated Node #0,0,0: 22:[11, 2] Operation: 14/7=2 Moving to Node #0,0,0 Current State: 22:[11, 2], Operations: ['49-35=14', '14/7=2'] Exploring Operation: 11*2=22, Resulting Numbers: [22] 22,22 equal: Goal Reached Moving to Node #0 Current State: 22:[49, 11, 35, 7], Operations: [] Exploring Operation: 49-35=14, Resulting Numbers: [11, 7, 14] Generated Node #0,0: 22:[11, 7, 14] Operation: 49-35=14 Moving to Node #0,0 Current State: 22:[11, 7, 14], Operations: ['49-35=14'] Exploring Operation: 14/7=2, Resulting Numbers: [11, 2] Generated Node #0,0,0: 22:[11, 2] Operation: 14/7=2 Moving to Node #0,0,0 Current State: 22:[11, 2], Operations: ['49-35=14', '14/7=2'] Exploring Operation: 11*2=22, Resulting Numbers: [22] 22,22 equal: Goal Reached
0.993924
hs_1
sum_heuristic
[ 19, 42, 84, 55 ]
93
[ "19*84=1596", "1596/42=38", "55+38=93" ]
Current State: 93:[19, 42, 84, 55], Operations: [] Exploring Operation: 19*84=1596, Resulting Numbers: [42, 55, 1596] Generated Node #2: [42, 55, 1596] from Operation: 19*84=1596 Current State: 93:[42, 55, 1596], Operations: ['19*84=1596'] Exploring Operation: 1596/42=38, Resulting Numbers: [55, 38] Generated Node #3: [55, 38] from Operation: 1596/42=38 Current State: 93:[55, 38], Operations: ['19*84=1596', '1596/42=38'] Exploring Operation: 55+38=93, Resulting Numbers: [93] 93,93 equal: Goal Reached
4
Current State: 93:[19, 42, 84, 55], Operations: [] Exploring Operation: 55-19=36, Resulting Numbers: [42, 84, 36] Generated Node #0,0: 93:[42, 84, 36] Operation: 55-19=36 Moving to Node #0,0 Current State: 93:[42, 84, 36], Operations: ['55-19=36'] Exploring Operation: 84/42=2, Resulting Numbers: [36, 2] Generated Node #0,0,0: 93:[36, 2] Operation: 84/42=2 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 93:[36, 2], Operations: ['55-19=36', '84/42=2'] Exploring Operation: 36-2=34, Resulting Numbers: [34] 34,93 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
[ 43, 22, 51, 64 ]
52
[ "43+22=65", "64-51=13", "65-13=52" ]
Current State: 52:[43, 22, 51, 64], Operations: [] Exploring Operation: 43+22=65, Resulting Numbers: [51, 64, 65] Generated Node #2: [51, 64, 65] from Operation: 43+22=65 Current State: 52:[51, 64, 65], Operations: ['43+22=65'] Exploring Operation: 64-51=13, Resulting Numbers: [65, 13] Generated Node #3: [65, 13] from Operation: 64-51=13 Current State: 52:[65, 13], Operations: ['43+22=65', '64-51=13'] Exploring Operation: 65-13=52, Resulting Numbers: [52] 52,52 equal: Goal Reached
4
Current State: 52:[43, 22, 51, 64], Operations: [] Exploring Operation: 64-43=21, Resulting Numbers: [22, 51, 21] Generated Node #0,0: 52:[22, 51, 21] Operation: 64-43=21 Exploring Operation: 64-51=13, Resulting Numbers: [43, 22, 13] Generated Node #0,1: 52:[43, 22, 13] Operation: 64-51=13 Exploring Operation: 43-22=21, Resulting Numbers: [51, 64, 21] Generated Node #0,2: 52:[51, 64, 21] Operation: 43-22=21 Exploring Operation: 51-43=8, Resulting Numbers: [22, 64, 8] Generated Node #0,3: 52:[22, 64, 8] Operation: 51-43=8 Start Sub Search at level 1: Moving to Node #0,0 Current State: 52:[22, 51, 21], Operations: ['64-43=21'] Exploring Operation: 51-22=29, Resulting Numbers: [21, 29] Generated Node #0,0,0: 52:[21, 29] Operation: 51-22=29 Exploring Operation: 22-21=1, Resulting Numbers: [51, 1] Generated Node #0,0,1: 52:[51, 1] Operation: 22-21=1 Exploring Operation: 51-21=30, Resulting Numbers: [22, 30] Generated Node #0,0,2: 52:[22, 30] Operation: 51-21=30 Exploring Operation: 22+21=43, Resulting Numbers: [51, 43] Generated Node #0,0,3: 52:[51, 43] Operation: 22+21=43 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 52:[51, 1], Operations: ['64-43=21', '22-21=1'] Exploring Operation: 51/1=51, Resulting Numbers: [51] 51,52 unequal: No Solution Exploring Operation: 51+1=52, Resulting Numbers: [52] 52,52 equal: Goal Reached Moving to Node #0 Current State: 52:[43, 22, 51, 64], Operations: [] Exploring Operation: 64-43=21, Resulting Numbers: [22, 51, 21] Generated Node #0,0: 52:[22, 51, 21] Operation: 64-43=21 Moving to Node #0,0 Current State: 52:[22, 51, 21], Operations: ['64-43=21'] Exploring Operation: 22-21=1, Resulting Numbers: [51, 1] Generated Node #0,0,1: 52:[51, 1] Operation: 22-21=1 Moving to Node #0,0,1 Current State: 52:[51, 1], Operations: ['64-43=21', '22-21=1'] Exploring Operation: 51+1=52, Resulting Numbers: [52] 52,52 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.987847
hs_4
sum_heuristic
[ 41, 89, 21, 55 ]
54
[ "41+89=130", "21+55=76", "130-76=54" ]
Current State: 54:[41, 89, 21, 55], Operations: [] Exploring Operation: 41+89=130, Resulting Numbers: [21, 55, 130] Generated Node #2: [21, 55, 130] from Operation: 41+89=130 Current State: 54:[21, 55, 130], Operations: ['41+89=130'] Exploring Operation: 21+55=76, Resulting Numbers: [130, 76] Generated Node #3: [130, 76] from Operation: 21+55=76 Current State: 54:[130, 76], Operations: ['41+89=130', '21+55=76'] Exploring Operation: 130-76=54, Resulting Numbers: [54] 54,54 equal: Goal Reached
4
Current State: 54:[41, 89, 21, 55], Operations: [] Exploring Operation: 89-41=48, Resulting Numbers: [21, 55, 48] Generated Node #0,0: 54:[21, 55, 48] Operation: 89-41=48 Exploring Operation: 89-55=34, Resulting Numbers: [41, 21, 34] Generated Node #0,1: 54:[41, 21, 34] Operation: 89-55=34 Exploring Operation: 89-21=68, Resulting Numbers: [41, 55, 68] Generated Node #0,2: 54:[41, 55, 68] Operation: 89-21=68 Moving to Node #0,0 Current State: 54:[21, 55, 48], Operations: ['89-41=48'] Exploring Operation: 48-21=27, Resulting Numbers: [55, 27] Generated Node #0,0,0: 54:[55, 27] Operation: 48-21=27 Exploring Operation: 55-21=34, Resulting Numbers: [48, 34] Generated Node #0,0,1: 54:[48, 34] Operation: 55-21=34 Exploring Operation: 55-48=7, Resulting Numbers: [21, 7] Generated Node #0,0,2: 54:[21, 7] Operation: 55-48=7 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 54:[55, 27], Operations: ['89-41=48', '48-21=27'] Exploring Operation: 55*27=1485, Resulting Numbers: [1485] 1485,54 unequal: No Solution Exploring Operation: 55+27=82, Resulting Numbers: [82] 82,54 unequal: No Solution Exploring Operation: 55-27=28, Resulting Numbers: [28] 28,54 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 #0,0,2 Current State: 54:[21, 7], Operations: ['89-41=48', '55-48=7'] Exploring Operation: 21/7=3, Resulting Numbers: [3] 3,54 unequal: No Solution Exploring Operation: 21-7=14, Resulting Numbers: [14] 14,54 unequal: No Solution Exploring Operation: 21+7=28, Resulting Numbers: [28] 28,54 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 #0,0,1 Current State: 54:[48, 34], Operations: ['89-41=48', '55-21=34'] Exploring Operation: 48-34=14, Resulting Numbers: [14] 14,54 unequal: No Solution Exploring Operation: 48+34=82, Resulting Numbers: [82] 82,54 unequal: No Solution Exploring Operation: 48*34=1632, Resulting Numbers: [1632] 1632,54 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: 54:[41, 21, 34], Operations: ['89-55=34'] Exploring Operation: 21+34=55, Resulting Numbers: [41, 55] Generated Node #0,1,0: 54:[41, 55] Operation: 21+34=55 Exploring Operation: 41-21=20, Resulting Numbers: [34, 20] Generated Node #0,1,1: 54:[34, 20] Operation: 41-21=20 Exploring Operation: 41-34=7, Resulting Numbers: [21, 7] Generated Node #0,1,2: 54:[21, 7] Operation: 41-34=7 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 54:[21, 7], Operations: ['89-55=34', '41-34=7'] Exploring Operation: 21/7=3, Resulting Numbers: [3] 3,54 unequal: No Solution Exploring Operation: 21+7=28, Resulting Numbers: [28] 28,54 unequal: No Solution Exploring Operation: 21-7=14, Resulting Numbers: [14] 14,54 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 #0,1,1 Current State: 54:[34, 20], Operations: ['89-55=34', '41-21=20'] Exploring Operation: 34*20=680, Resulting Numbers: [680] 680,54 unequal: No Solution Exploring Operation: 34+20=54, Resulting Numbers: [54] 54,54 equal: Goal Reached Moving to Node #0 Current State: 54:[41, 89, 21, 55], Operations: [] Exploring Operation: 89-55=34, Resulting Numbers: [41, 21, 34] Generated Node #0,1: 54:[41, 21, 34] Operation: 89-55=34 Moving to Node #0,1 Current State: 54:[41, 21, 34], Operations: ['89-55=34'] Exploring Operation: 41-21=20, Resulting Numbers: [34, 20] Generated Node #0,1,1: 54:[34, 20] Operation: 41-21=20 Moving to Node #0,1,1 Current State: 54:[34, 20], Operations: ['89-55=34', '41-21=20'] Exploring Operation: 34+20=54, Resulting Numbers: [54] 54,54 equal: Goal Reached Exit Sub Search at level 1
0.976563
hs_3
mult_heuristic
[ 45, 81, 65, 55 ]
84
[ "81-45=36", "65+55=120", "120-36=84" ]
Current State: 84:[45, 81, 65, 55], Operations: [] Exploring Operation: 81-45=36, Resulting Numbers: [65, 55, 36] Generated Node #2: [65, 55, 36] from Operation: 81-45=36 Current State: 84:[65, 55, 36], Operations: ['81-45=36'] Exploring Operation: 65+55=120, Resulting Numbers: [36, 120] Generated Node #3: [36, 120] from Operation: 65+55=120 Current State: 84:[36, 120], Operations: ['81-45=36', '65+55=120'] Exploring Operation: 120-36=84, Resulting Numbers: [84] 84,84 equal: Goal Reached
4
Current State: 84:[45, 81, 65, 55], Operations: [] Exploring Operation: 81-65=16, Resulting Numbers: [45, 55, 16] Generated Node #0,0: 84:[45, 55, 16] Operation: 81-65=16 Exploring Operation: 55-45=10, Resulting Numbers: [81, 65, 10] Generated Node #0,1: 84:[81, 65, 10] Operation: 55-45=10 Exploring Operation: 65-45=20, Resulting Numbers: [81, 55, 20] Generated Node #0,2: 84:[81, 55, 20] Operation: 65-45=20 Exploring Operation: 65-55=10, Resulting Numbers: [45, 81, 10] Generated Node #0,3: 84:[45, 81, 10] Operation: 65-55=10 Moving to Node #0,3 Current State: 84:[45, 81, 10], Operations: ['65-55=10'] Exploring Operation: 81+10=91, Resulting Numbers: [45, 91] Generated Node #0,3,0: 84:[45, 91] Operation: 81+10=91 Exploring Operation: 45+10=55, Resulting Numbers: [81, 55] Generated Node #0,3,1: 84:[81, 55] Operation: 45+10=55 Exploring Operation: 45-10=35, Resulting Numbers: [81, 35] Generated Node #0,3,2: 84:[81, 35] Operation: 45-10=35 Exploring Operation: 81-45=36, Resulting Numbers: [10, 36] Generated Node #0,3,3: 84:[10, 36] Operation: 81-45=36 Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 84:[10, 36], Operations: ['65-55=10', '81-45=36'] Exploring Operation: 36-10=26, Resulting Numbers: [26] 26,84 unequal: No Solution Exploring Operation: 10+36=46, Resulting Numbers: [46] 46,84 unequal: No Solution Exploring Operation: 10*36=360, Resulting Numbers: [360] 360,84 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 #0,3,0 Current State: 84:[45, 91], Operations: ['65-55=10', '81+10=91'] Exploring Operation: 91-45=46, Resulting Numbers: [46] 46,84 unequal: No Solution Exploring Operation: 45*91=4095, Resulting Numbers: [4095] 4095,84 unequal: No Solution Exploring Operation: 45+91=136, Resulting Numbers: [136] 136,84 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 #0,3,2 Current State: 84:[81, 35], Operations: ['65-55=10', '45-10=35'] Exploring Operation: 81+35=116, Resulting Numbers: [116] 116,84 unequal: No Solution Exploring Operation: 81-35=46, Resulting Numbers: [46] 46,84 unequal: No Solution Exploring Operation: 81*35=2835, Resulting Numbers: [2835] 2835,84 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 #0,3,1 Current State: 84:[81, 55], Operations: ['65-55=10', '45+10=55'] Exploring Operation: 81+55=136, Resulting Numbers: [136] 136,84 unequal: No Solution Exploring Operation: 81-55=26, Resulting Numbers: [26] 26,84 unequal: No Solution Exploring Operation: 81*55=4455, Resulting Numbers: [4455] 4455,84 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: 84:[81, 55, 20], Operations: ['65-45=20'] Exploring Operation: 55+20=75, Resulting Numbers: [81, 75] Generated Node #0,2,0: 84:[81, 75] Operation: 55+20=75 Exploring Operation: 55-20=35, Resulting Numbers: [81, 35] Generated Node #0,2,1: 84:[81, 35] Operation: 55-20=35 Exploring Operation: 81-55=26, Resulting Numbers: [20, 26] Generated Node #0,2,2: 84:[20, 26] Operation: 81-55=26 Exploring Operation: 81+20=101, Resulting Numbers: [55, 101] Generated Node #0,2,3: 84:[55, 101] Operation: 81+20=101 Moving to Node #0,0 Current State: 84:[45, 55, 16], Operations: ['81-65=16'] Exploring Operation: 55-45=10, Resulting Numbers: [16, 10] Generated Node #0,0,0: 84:[16, 10] Operation: 55-45=10 Exploring Operation: 55-16=39, Resulting Numbers: [45, 39] Generated Node #0,0,1: 84:[45, 39] Operation: 55-16=39 Exploring Operation: 55+16=71, Resulting Numbers: [45, 71] Generated Node #0,0,2: 84:[45, 71] Operation: 55+16=71 Exploring Operation: 45-16=29, Resulting Numbers: [55, 29] Generated Node #0,0,3: 84:[55, 29] Operation: 45-16=29 Moving to Node #0,1 Current State: 84:[81, 65, 10], Operations: ['55-45=10'] Exploring Operation: 65-10=55, Resulting Numbers: [81, 55] Generated Node #0,1,0: 84:[81, 55] Operation: 65-10=55 Exploring Operation: 65+10=75, Resulting Numbers: [81, 75] Generated Node #0,1,1: 84:[81, 75] Operation: 65+10=75 Exploring Operation: 81-65=16, Resulting Numbers: [10, 16] Generated Node #0,1,2: 84:[10, 16] Operation: 81-65=16 Exploring Operation: 81+10=91, Resulting Numbers: [65, 91] Generated Node #0,1,3: 84:[65, 91] Operation: 81+10=91 Moving to Node #0,2,2 Current State: 84:[20, 26], Operations: ['65-45=20', '81-55=26'] Exploring Operation: 26-20=6, Resulting Numbers: [6] 6,84 unequal: No Solution Exploring Operation: 20+26=46, Resulting Numbers: [46] 46,84 unequal: No Solution Exploring Operation: 20*26=520, Resulting Numbers: [520] 520,84 unequal: No Solution Moving to Node #0,0,0 Current State: 84:[16, 10], Operations: ['81-65=16', '55-45=10'] Exploring Operation: 16+10=26, Resulting Numbers: [26] 26,84 unequal: No Solution Exploring Operation: 16-10=6, Resulting Numbers: [6] 6,84 unequal: No Solution Exploring Operation: 16*10=160, Resulting Numbers: [160] 160,84 unequal: No Solution Moving to Node #0,1,2 Current State: 84:[10, 16], Operations: ['55-45=10', '81-65=16'] Exploring Operation: 10*16=160, Resulting Numbers: [160] 160,84 unequal: No Solution Exploring Operation: 10+16=26, Resulting Numbers: [26] 26,84 unequal: No Solution Exploring Operation: 16-10=6, Resulting Numbers: [6] 6,84 unequal: No Solution Moving to Node #0,0,1 Current State: 84:[45, 39], Operations: ['81-65=16', '55-16=39'] Exploring Operation: 45-39=6, Resulting Numbers: [6] 6,84 unequal: No Solution Exploring Operation: 45*39=1755, Resulting Numbers: [1755] 1755,84 unequal: No Solution Exploring Operation: 45+39=84, Resulting Numbers: [84] 84,84 equal: Goal Reached Moving to Node #0 Current State: 84:[45, 81, 65, 55], Operations: [] Exploring Operation: 81-65=16, Resulting Numbers: [45, 55, 16] Generated Node #0,0: 84:[45, 55, 16] Operation: 81-65=16 Moving to Node #0,0 Current State: 84:[45, 55, 16], Operations: ['81-65=16'] Exploring Operation: 55-16=39, Resulting Numbers: [45, 39] Generated Node #0,0,1: 84:[45, 39] Operation: 55-16=39 Moving to Node #0,0,1 Current State: 84:[45, 39], Operations: ['81-65=16', '55-16=39'] Exploring Operation: 45+39=84, Resulting Numbers: [84] 84,84 equal: Goal Reached
0.958333
hs_4
mult_heuristic
[ 42, 71, 6, 78 ]
65
[ "78-42=36", "36/6=6", "71-6=65" ]
Current State: 65:[42, 71, 6, 78], Operations: [] Exploring Operation: 78-42=36, Resulting Numbers: [71, 6, 36] Generated Node #2: [71, 6, 36] from Operation: 78-42=36 Current State: 65:[71, 6, 36], Operations: ['78-42=36'] Exploring Operation: 36/6=6, Resulting Numbers: [71, 6] Generated Node #3: [71, 6] from Operation: 36/6=6 Current State: 65:[71, 6], Operations: ['78-42=36', '36/6=6'] Exploring Operation: 71-6=65, Resulting Numbers: [65] 65,65 equal: Goal Reached
4
Current State: 65:[42, 71, 6, 78], Operations: [] Exploring Operation: 71-42=29, Resulting Numbers: [6, 78, 29] Generated Node #0,0: 65:[6, 78, 29] Operation: 71-42=29 Exploring Operation: 78-71=7, Resulting Numbers: [42, 6, 7] Generated Node #0,1: 65:[42, 6, 7] Operation: 78-71=7 Exploring Operation: 42/6=7, Resulting Numbers: [71, 78, 7] Generated Node #0,2: 65:[71, 78, 7] Operation: 42/6=7 Exploring Operation: 78/6=13, Resulting Numbers: [42, 71, 13] Generated Node #0,3: 65:[42, 71, 13] Operation: 78/6=13 Moving to Node #0,2 Current State: 65:[71, 78, 7], Operations: ['42/6=7'] Exploring Operation: 71+7=78, Resulting Numbers: [78, 78] Generated Node #0,2,0: 65:[78, 78] Operation: 71+7=78 Exploring Operation: 78-7=71, Resulting Numbers: [71, 71] Generated Node #0,2,1: 65:[71, 71] Operation: 78-7=71 Exploring Operation: 78-71=7, Resulting Numbers: [7, 7] Generated Node #0,2,2: 65:[7, 7] Operation: 78-71=7 Exploring Operation: 71-7=64, Resulting Numbers: [78, 64] Generated Node #0,2,3: 65:[78, 64] Operation: 71-7=64 Moving to Node #0,1 Current State: 65:[42, 6, 7], Operations: ['78-71=7'] Exploring Operation: 42+6=48, Resulting Numbers: [7, 48] Generated Node #0,1,0: 65:[7, 48] Operation: 42+6=48 Exploring Operation: 42+7=49, Resulting Numbers: [6, 49] Generated Node #0,1,1: 65:[6, 49] Operation: 42+7=49 Exploring Operation: 42/7=6, Resulting Numbers: [6, 6] Generated Node #0,1,2: 65:[6, 6] Operation: 42/7=6 Exploring Operation: 42/6=7, Resulting Numbers: [7, 7] Generated Node #0,1,3: 65:[7, 7] Operation: 42/6=7 Moving to Node #0,3 Current State: 65:[42, 71, 13], Operations: ['78/6=13'] Exploring Operation: 71-13=58, Resulting Numbers: [42, 58] Generated Node #0,3,0: 65:[42, 58] Operation: 71-13=58 Exploring Operation: 42-13=29, Resulting Numbers: [71, 29] Generated Node #0,3,1: 65:[71, 29] Operation: 42-13=29 Exploring Operation: 42+13=55, Resulting Numbers: [71, 55] Generated Node #0,3,2: 65:[71, 55] Operation: 42+13=55 Exploring Operation: 71-42=29, Resulting Numbers: [13, 29] Generated Node #0,3,3: 65:[13, 29] Operation: 71-42=29 Moving to Node #0,0 Current State: 65:[6, 78, 29], Operations: ['71-42=29'] Exploring Operation: 78-6=72, Resulting Numbers: [29, 72] Generated Node #0,0,0: 65:[29, 72] Operation: 78-6=72 Exploring Operation: 78/6=13, Resulting Numbers: [29, 13] Generated Node #0,0,1: 65:[29, 13] Operation: 78/6=13 Exploring Operation: 29-6=23, Resulting Numbers: [78, 23] Generated Node #0,0,2: 65:[78, 23] Operation: 29-6=23 Exploring Operation: 78-29=49, Resulting Numbers: [6, 49] Generated Node #0,0,3: 65:[6, 49] Operation: 78-29=49 Moving to Node #0,1,2 Current State: 65:[6, 6], Operations: ['78-71=7', '42/7=6'] Exploring Operation: 6/6=1, Resulting Numbers: [1] 1,65 unequal: No Solution Exploring Operation: 6-6=0, Resulting Numbers: [0] 0,65 unequal: No Solution Exploring Operation: 6*6=36, Resulting Numbers: [36] 36,65 unequal: No Solution Exploring Operation: 6+6=12, Resulting Numbers: [12] 12,65 unequal: No Solution Moving to Node #0,1,3 Current State: 65:[7, 7], Operations: ['78-71=7', '42/6=7'] Exploring Operation: 7+7=14, Resulting Numbers: [14] 14,65 unequal: No Solution Exploring Operation: 7-7=0, Resulting Numbers: [0] 0,65 unequal: No Solution Exploring Operation: 7/7=1, Resulting Numbers: [1] 1,65 unequal: No Solution Exploring Operation: 7*7=49, Resulting Numbers: [49] 49,65 unequal: No Solution Moving to Node #0,2,2 Current State: 65:[7, 7], Operations: ['42/6=7', '78-71=7'] Exploring Operation: 7/7=1, Resulting Numbers: [1] 1,65 unequal: No Solution Exploring Operation: 7+7=14, Resulting Numbers: [14] 14,65 unequal: No Solution Exploring Operation: 7*7=49, Resulting Numbers: [49] 49,65 unequal: No Solution Exploring Operation: 7-7=0, Resulting Numbers: [0] 0,65 unequal: No Solution Moving to Node #0,2,1 Current State: 65:[71, 71], Operations: ['42/6=7', '78-7=71'] Exploring Operation: 71+71=142, Resulting Numbers: [142] 142,65 unequal: No Solution Exploring Operation: 71*71=5041, Resulting Numbers: [5041] 5041,65 unequal: No Solution Exploring Operation: 71/71=1, Resulting Numbers: [1] 1,65 unequal: No Solution Exploring Operation: 71-71=0, Resulting Numbers: [0] 0,65 unequal: No Solution Moving to Node #0,2,3 Current State: 65:[78, 64], Operations: ['42/6=7', '71-7=64'] Exploring Operation: 78+64=142, Resulting Numbers: [142] 142,65 unequal: No Solution Exploring Operation: 78*64=4992, Resulting Numbers: [4992] 4992,65 unequal: No Solution Exploring Operation: 78-64=14, Resulting Numbers: [14] 14,65 unequal: No Solution Moving to Node #0,0,1 Current State: 65:[29, 13], Operations: ['71-42=29', '78/6=13'] Exploring Operation: 29*13=377, Resulting Numbers: [377] 377,65 unequal: No Solution Exploring Operation: 29-13=16, Resulting Numbers: [16] 16,65 unequal: No Solution Exploring Operation: 29+13=42, Resulting Numbers: [42] 42,65 unequal: No Solution Moving to Node #0,3,3 Current State: 65:[13, 29], Operations: ['78/6=13', '71-42=29'] Exploring Operation: 13*29=377, Resulting Numbers: [377] 377,65 unequal: No Solution Exploring Operation: 29-13=16, Resulting Numbers: [16] 16,65 unequal: No Solution Exploring Operation: 13+29=42, Resulting Numbers: [42] 42,65 unequal: No Solution Moving to Node #0,3,2 Current State: 65:[71, 55], Operations: ['78/6=13', '42+13=55'] Exploring Operation: 71*55=3905, Resulting Numbers: [3905] 3905,65 unequal: No Solution Exploring Operation: 71-55=16, Resulting Numbers: [16] 16,65 unequal: No Solution Exploring Operation: 71+55=126, Resulting Numbers: [126] 126,65 unequal: No Solution Moving to Node #0,1,1 Current State: 65:[6, 49], Operations: ['78-71=7', '42+7=49'] Exploring Operation: 6*49=294, Resulting Numbers: [294] 294,65 unequal: No Solution Exploring Operation: 49-6=43, Resulting Numbers: [43] 43,65 unequal: No Solution Exploring Operation: 6+49=55, Resulting Numbers: [55] 55,65 unequal: No Solution Moving to Node #0,0,3 Current State: 65:[6, 49], Operations: ['71-42=29', '78-29=49'] Exploring Operation: 6*49=294, Resulting Numbers: [294] 294,65 unequal: No Solution Exploring Operation: 6+49=55, Resulting Numbers: [55] 55,65 unequal: No Solution Exploring Operation: 49-6=43, Resulting Numbers: [43] 43,65 unequal: No Solution Moving to Node #0,1,0 Current State: 65:[7, 48], Operations: ['78-71=7', '42+6=48'] Exploring Operation: 7+48=55, Resulting Numbers: [55] 55,65 unequal: No Solution Exploring Operation: 48-7=41, Resulting Numbers: [41] 41,65 unequal: No Solution Exploring Operation: 7*48=336, Resulting Numbers: [336] 336,65 unequal: No Solution Moving to Node #0,3,1 Current State: 65:[71, 29], Operations: ['78/6=13', '42-13=29'] Exploring Operation: 71+29=100, Resulting Numbers: [100] 100,65 unequal: No Solution Exploring Operation: 71-29=42, Resulting Numbers: [42] 42,65 unequal: No Solution Exploring Operation: 71*29=2059, Resulting Numbers: [2059] 2059,65 unequal: No Solution Moving to Node #0,0,0 Current State: 65:[29, 72], Operations: ['71-42=29', '78-6=72'] Exploring Operation: 72-29=43, Resulting Numbers: [43] 43,65 unequal: No Solution Exploring Operation: 29+72=101, Resulting Numbers: [101] 101,65 unequal: No Solution Exploring Operation: 29*72=2088, Resulting Numbers: [2088] 2088,65 unequal: No Solution Moving to Node #0,0,2 Current State: 65:[78, 23], Operations: ['71-42=29', '29-6=23'] Exploring Operation: 78+23=101, Resulting Numbers: [101] 101,65 unequal: No Solution Exploring Operation: 78-23=55, Resulting Numbers: [55] 55,65 unequal: No Solution Exploring Operation: 78*23=1794, Resulting Numbers: [1794] 1794,65 unequal: No Solution Moving to Node #0,2,0 Current State: 65:[78, 78], Operations: ['42/6=7', '71+7=78'] Exploring Operation: 78/78=1, Resulting Numbers: [1] 1,65 unequal: No Solution Exploring Operation: 78-78=0, Resulting Numbers: [0] 0,65 unequal: No Solution Exploring Operation: 78+78=156, Resulting Numbers: [156] 156,65 unequal: No Solution Exploring Operation: 78*78=6084, Resulting Numbers: [6084] 6084,65 unequal: No Solution Moving to Node #0,3,0 Current State: 65:[42, 58], Operations: ['78/6=13', '71-13=58'] Exploring Operation: 58-42=16, Resulting Numbers: [16] 16,65 unequal: No Solution Exploring Operation: 42+58=100, Resulting Numbers: [100] 100,65 unequal: No Solution Exploring Operation: 42*58=2436, Resulting Numbers: [2436] 2436,65 unequal: No Solution No solution found.
0
hs_4
sum_heuristic
[ 52, 52, 9, 88 ]
79
[ "52-52=0", "88-9=79", "0+79=79" ]
Current State: 79:[52, 52, 9, 88], Operations: [] Exploring Operation: 52-52=0, Resulting Numbers: [9, 88, 0] Generated Node #2: [9, 88, 0] from Operation: 52-52=0 Current State: 79:[9, 88, 0], Operations: ['52-52=0'] Exploring Operation: 88-9=79, Resulting Numbers: [0, 79] Generated Node #3: [0, 79] from Operation: 88-9=79 Current State: 79:[0, 79], Operations: ['52-52=0', '88-9=79'] Exploring Operation: 0+79=79, Resulting Numbers: [79] 79,79 equal: Goal Reached
4
Current State: 79:[52, 52, 9, 88], Operations: [] Exploring Operation: 52-9=43, Resulting Numbers: [52, 88, 43] Generated Node #0,0: 79:[52, 88, 43] Operation: 52-9=43 Exploring Operation: 52+9=61, Resulting Numbers: [52, 88, 61] Generated Node #0,1: 79:[52, 88, 61] Operation: 52+9=61 Exploring Operation: 52-9=43, Resulting Numbers: [52, 88, 43] Generated Node #0,2: 79:[52, 88, 43] Operation: 52-9=43 Exploring Operation: 88-9=79, Resulting Numbers: [52, 52, 79] Generated Node #0,3: 79:[52, 52, 79] Operation: 88-9=79 Exploring Operation: 52+9=61, Resulting Numbers: [52, 88, 61] Generated Node #0,4: 79:[52, 88, 61] Operation: 52+9=61 Moving to Node #0,1 Current State: 79:[52, 88, 61], Operations: ['52+9=61'] Exploring Operation: 88-52=36, Resulting Numbers: [61, 36] Generated Node #0,1,0: 79:[61, 36] Operation: 88-52=36 Exploring Operation: 88-61=27, Resulting Numbers: [52, 27] Generated Node #0,1,1: 79:[52, 27] Operation: 88-61=27 Exploring Operation: 52+61=113, Resulting Numbers: [88, 113] Generated Node #0,1,2: 79:[88, 113] Operation: 52+61=113 Exploring Operation: 61-52=9, Resulting Numbers: [88, 9] Generated Node #0,1,3: 79:[88, 9] Operation: 61-52=9 Exploring Operation: 52+88=140, Resulting Numbers: [61, 140] Generated Node #0,1,4: 79:[61, 140] Operation: 52+88=140 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 79:[88, 113], Operations: ['52+9=61', '52+61=113'] Exploring Operation: 88*113=9944, Resulting Numbers: [9944] 9944,79 unequal: No Solution Exploring Operation: 88+113=201, Resulting Numbers: [201] 201,79 unequal: No Solution Exploring Operation: 113-88=25, Resulting Numbers: [25] 25,79 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 #0,1,0 Current State: 79:[61, 36], Operations: ['52+9=61', '88-52=36'] Exploring Operation: 61+36=97, Resulting Numbers: [97] 97,79 unequal: No Solution Exploring Operation: 61*36=2196, Resulting Numbers: [2196] 2196,79 unequal: No Solution Exploring Operation: 61-36=25, Resulting Numbers: [25] 25,79 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:[52, 27], Operations: ['52+9=61', '88-61=27'] Exploring Operation: 52-27=25, Resulting Numbers: [25] 25,79 unequal: No Solution Exploring Operation: 52*27=1404, Resulting Numbers: [1404] 1404,79 unequal: No Solution Exploring Operation: 52+27=79, Resulting Numbers: [79] 79,79 equal: Goal Reached Moving to Node #0 Current State: 79:[52, 52, 9, 88], Operations: [] Exploring Operation: 52+9=61, Resulting Numbers: [52, 88, 61] Generated Node #0,1: 79:[52, 88, 61] Operation: 52+9=61 Moving to Node #0,1 Current State: 79:[52, 88, 61], Operations: ['52+9=61'] Exploring Operation: 88-61=27, Resulting Numbers: [52, 27] Generated Node #0,1,1: 79:[52, 27] Operation: 88-61=27 Moving to Node #0,1,1 Current State: 79:[52, 27], Operations: ['52+9=61', '88-61=27'] Exploring Operation: 52+27=79, Resulting Numbers: [79] 79,79 equal: Goal Reached Exit Sub Search at level 1
0.980035
hs_5
mult_heuristic
[ 91, 77, 4, 44 ]
12
[ "91-77=14", "4*14=56", "56-44=12" ]
Current State: 12:[91, 77, 4, 44], Operations: [] Exploring Operation: 91-77=14, Resulting Numbers: [4, 44, 14] Generated Node #2: [4, 44, 14] from Operation: 91-77=14 Current State: 12:[4, 44, 14], Operations: ['91-77=14'] Exploring Operation: 4*14=56, Resulting Numbers: [44, 56] Generated Node #3: [44, 56] from Operation: 4*14=56 Current State: 12:[44, 56], Operations: ['91-77=14', '4*14=56'] Exploring Operation: 56-44=12, Resulting Numbers: [12] 12,12 equal: Goal Reached
4
Current State: 12:[91, 77, 4, 44], Operations: [] Exploring Operation: 44/4=11, Resulting Numbers: [91, 77, 11] Generated Node #0,0: 12:[91, 77, 11] Operation: 44/4=11 Exploring Operation: 91-44=47, Resulting Numbers: [77, 4, 47] Generated Node #0,1: 12:[77, 4, 47] Operation: 91-44=47 Exploring Operation: 77-44=33, Resulting Numbers: [91, 4, 33] Generated Node #0,2: 12:[91, 4, 33] Operation: 77-44=33 Exploring Operation: 91-77=14, Resulting Numbers: [4, 44, 14] Generated Node #0,3: 12:[4, 44, 14] Operation: 91-77=14 Start Sub Search at level 1: Moving to Node #0,3 Current State: 12:[4, 44, 14], Operations: ['91-77=14'] Exploring Operation: 44-14=30, Resulting Numbers: [4, 30] Generated Node #0,3,0: 12:[4, 30] Operation: 44-14=30 Exploring Operation: 44-4=40, Resulting Numbers: [14, 40] Generated Node #0,3,1: 12:[14, 40] Operation: 44-4=40 Exploring Operation: 14-4=10, Resulting Numbers: [44, 10] Generated Node #0,3,2: 12:[44, 10] Operation: 14-4=10 Exploring Operation: 44/4=11, Resulting Numbers: [14, 11] Generated Node #0,3,3: 12:[14, 11] Operation: 44/4=11 Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 12:[14, 11], Operations: ['91-77=14', '44/4=11'] Exploring Operation: 14-11=3, Resulting Numbers: [3] 3,12 unequal: No Solution Exploring Operation: 14+11=25, Resulting Numbers: [25] 25,12 unequal: No Solution Exploring Operation: 14*11=154, Resulting Numbers: [154] 154,12 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: 12:[4, 30], Operations: ['91-77=14', '44-14=30'] Exploring Operation: 4+30=34, Resulting Numbers: [34] 34,12 unequal: No Solution Exploring Operation: 4*30=120, Resulting Numbers: [120] 120,12 unequal: No Solution Exploring Operation: 30-4=26, Resulting Numbers: [26] 26,12 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: 12:[14, 40], Operations: ['91-77=14', '44-4=40'] Exploring Operation: 40-14=26, Resulting Numbers: [26] 26,12 unequal: No Solution Exploring Operation: 14*40=560, Resulting Numbers: [560] 560,12 unequal: No Solution Exploring Operation: 14+40=54, Resulting Numbers: [54] 54,12 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: 12:[44, 10], Operations: ['91-77=14', '14-4=10'] Exploring Operation: 44+10=54, Resulting Numbers: [54] 54,12 unequal: No Solution Exploring Operation: 44*10=440, Resulting Numbers: [440] 440,12 unequal: No Solution Exploring Operation: 44-10=34, Resulting Numbers: [34] 34,12 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: 12:[77, 4, 47], Operations: ['91-44=47'] Exploring Operation: 77-4=73, Resulting Numbers: [47, 73] Generated Node #0,1,0: 12:[47, 73] Operation: 77-4=73 Exploring Operation: 47-4=43, Resulting Numbers: [77, 43] Generated Node #0,1,1: 12:[77, 43] Operation: 47-4=43 Exploring Operation: 77+4=81, Resulting Numbers: [47, 81] Generated Node #0,1,2: 12:[47, 81] Operation: 77+4=81 Exploring Operation: 77-47=30, Resulting Numbers: [4, 30] Generated Node #0,1,3: 12:[4, 30] Operation: 77-47=30 Moving to Node #0,1,3 Current State: 12:[4, 30], Operations: ['91-44=47', '77-47=30'] Exploring Operation: 4*30=120, Resulting Numbers: [120] 120,12 unequal: No Solution Exploring Operation: 4+30=34, Resulting Numbers: [34] 34,12 unequal: No Solution Exploring Operation: 30-4=26, Resulting Numbers: [26] 26,12 unequal: No Solution Moving to Node #0,1,1 Current State: 12:[77, 43], Operations: ['91-44=47', '47-4=43'] Exploring Operation: 77-43=34, Resulting Numbers: [34] 34,12 unequal: No Solution Exploring Operation: 77*43=3311, Resulting Numbers: [3311] 3311,12 unequal: No Solution Exploring Operation: 77+43=120, Resulting Numbers: [120] 120,12 unequal: No Solution Moving to Node #0,1,0 Current State: 12:[47, 73], Operations: ['91-44=47', '77-4=73'] Exploring Operation: 47+73=120, Resulting Numbers: [120] 120,12 unequal: No Solution Exploring Operation: 47*73=3431, Resulting Numbers: [3431] 3431,12 unequal: No Solution Exploring Operation: 73-47=26, Resulting Numbers: [26] 26,12 unequal: No Solution Moving to Node #0,1,2 Current State: 12:[47, 81], Operations: ['91-44=47', '77+4=81'] Exploring Operation: 47*81=3807, Resulting Numbers: [3807] 3807,12 unequal: No Solution Exploring Operation: 47+81=128, Resulting Numbers: [128] 128,12 unequal: No Solution Exploring Operation: 81-47=34, Resulting Numbers: [34] 34,12 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: 12:[91, 4, 33], Operations: ['77-44=33'] Exploring Operation: 91-4=87, Resulting Numbers: [33, 87] Generated Node #0,2,0: 12:[33, 87] Operation: 91-4=87 Exploring Operation: 33-4=29, Resulting Numbers: [91, 29] Generated Node #0,2,1: 12:[91, 29] Operation: 33-4=29 Exploring Operation: 91-33=58, Resulting Numbers: [4, 58] Generated Node #0,2,2: 12:[4, 58] Operation: 91-33=58 Exploring Operation: 91+4=95, Resulting Numbers: [33, 95] Generated Node #0,2,3: 12:[33, 95] Operation: 91+4=95 Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 12:[4, 58], Operations: ['77-44=33', '91-33=58'] Exploring Operation: 4+58=62, Resulting Numbers: [62] 62,12 unequal: No Solution Exploring Operation: 58-4=54, Resulting Numbers: [54] 54,12 unequal: No Solution Exploring Operation: 4*58=232, Resulting Numbers: [232] 232,12 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: 12:[33, 87], Operations: ['77-44=33', '91-4=87'] Exploring Operation: 87-33=54, Resulting Numbers: [54] 54,12 unequal: No Solution Exploring Operation: 33*87=2871, Resulting Numbers: [2871] 2871,12 unequal: No Solution Exploring Operation: 33+87=120, Resulting Numbers: [120] 120,12 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: 12:[91, 29], Operations: ['77-44=33', '33-4=29'] Exploring Operation: 91*29=2639, Resulting Numbers: [2639] 2639,12 unequal: No Solution Exploring Operation: 91+29=120, Resulting Numbers: [120] 120,12 unequal: No Solution Exploring Operation: 91-29=62, Resulting Numbers: [62] 62,12 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: 12:[33, 95], Operations: ['77-44=33', '91+4=95'] Exploring Operation: 33*95=3135, Resulting Numbers: [3135] 3135,12 unequal: No Solution Exploring Operation: 95-33=62, Resulting Numbers: [62] 62,12 unequal: No Solution Exploring Operation: 33+95=128, Resulting Numbers: [128] 128,12 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: 12:[91, 77, 11], Operations: ['44/4=11'] Exploring Operation: 77-11=66, Resulting Numbers: [91, 66] Generated Node #0,0,0: 12:[91, 66] Operation: 77-11=66 Exploring Operation: 91-77=14, Resulting Numbers: [11, 14] Generated Node #0,0,1: 12:[11, 14] Operation: 91-77=14 Exploring Operation: 91-11=80, Resulting Numbers: [77, 80] Generated Node #0,0,2: 12:[77, 80] Operation: 91-11=80 Exploring Operation: 77/11=7, Resulting Numbers: [91, 7] Generated Node #0,0,3: 12:[91, 7] Operation: 77/11=7 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 12:[11, 14], Operations: ['44/4=11', '91-77=14'] Exploring Operation: 14-11=3, Resulting Numbers: [3] 3,12 unequal: No Solution Exploring Operation: 11+14=25, Resulting Numbers: [25] 25,12 unequal: No Solution Exploring Operation: 11*14=154, Resulting Numbers: [154] 154,12 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: 12:[91, 7], Operations: ['44/4=11', '77/11=7'] Exploring Operation: 91-7=84, Resulting Numbers: [84] 84,12 unequal: No Solution Exploring Operation: 91*7=637, Resulting Numbers: [637] 637,12 unequal: No Solution Exploring Operation: 91/7=13, Resulting Numbers: [13] 13,12 unequal: No Solution Exploring Operation: 91+7=98, Resulting Numbers: [98] 98,12 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: 12:[91, 66], Operations: ['44/4=11', '77-11=66'] Exploring Operation: 91*66=6006, Resulting Numbers: [6006] 6006,12 unequal: No Solution Exploring Operation: 91-66=25, Resulting Numbers: [25] 25,12 unequal: No Solution Exploring Operation: 91+66=157, Resulting Numbers: [157] 157,12 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: 12:[77, 80], Operations: ['44/4=11', '91-11=80'] Exploring Operation: 77+80=157, Resulting Numbers: [157] 157,12 unequal: No Solution Exploring Operation: 80-77=3, Resulting Numbers: [3] 3,12 unequal: No Solution Exploring Operation: 77*80=6160, Resulting Numbers: [6160] 6160,12 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
[ 33, 21, 18, 49 ]
13
[ "33+21=54", "18+49=67", "67-54=13" ]
Current State: 13:[33, 21, 18, 49], Operations: [] Exploring Operation: 33+21=54, Resulting Numbers: [18, 49, 54] Generated Node #2: [18, 49, 54] from Operation: 33+21=54 Current State: 13:[18, 49, 54], Operations: ['33+21=54'] Exploring Operation: 18+49=67, Resulting Numbers: [54, 67] Generated Node #3: [54, 67] from Operation: 18+49=67 Current State: 13:[54, 67], Operations: ['33+21=54', '18+49=67'] Exploring Operation: 67-54=13, Resulting Numbers: [13] 13,13 equal: Goal Reached
4
Current State: 13:[33, 21, 18, 49], Operations: [] Exploring Operation: 49-33=16, Resulting Numbers: [21, 18, 16] Generated Node #0,0: 13:[21, 18, 16] Operation: 49-33=16 Start Sub Search at level 1: Moving to Node #0,0 Current State: 13:[21, 18, 16], Operations: ['49-33=16'] Exploring Operation: 21-18=3, Resulting Numbers: [16, 3] Generated Node #0,0,0: 13:[16, 3] Operation: 21-18=3 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 13:[16, 3], Operations: ['49-33=16', '21-18=3'] Exploring Operation: 16-3=13, Resulting Numbers: [13] 13,13 equal: Goal Reached Moving to Node #0 Current State: 13:[33, 21, 18, 49], Operations: [] Exploring Operation: 49-33=16, Resulting Numbers: [21, 18, 16] Generated Node #0,0: 13:[21, 18, 16] Operation: 49-33=16 Moving to Node #0,0 Current State: 13:[21, 18, 16], Operations: ['49-33=16'] Exploring Operation: 21-18=3, Resulting Numbers: [16, 3] Generated Node #0,0,0: 13:[16, 3] Operation: 21-18=3 Moving to Node #0,0,0 Current State: 13:[16, 3], Operations: ['49-33=16', '21-18=3'] Exploring Operation: 16-3=13, Resulting Numbers: [13] 13,13 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.993924
hs_1
sum_heuristic
[ 83, 6, 95, 92 ]
81
[ "95-92=3", "6/3=2", "83-2=81" ]
Current State: 81:[83, 6, 95, 92], Operations: [] Exploring Operation: 95-92=3, Resulting Numbers: [83, 6, 3] Generated Node #2: [83, 6, 3] from Operation: 95-92=3 Current State: 81:[83, 6, 3], Operations: ['95-92=3'] Exploring Operation: 6/3=2, Resulting Numbers: [83, 2] Generated Node #3: [83, 2] from Operation: 6/3=2 Current State: 81:[83, 2], Operations: ['95-92=3', '6/3=2'] Exploring Operation: 83-2=81, Resulting Numbers: [81] 81,81 equal: Goal Reached
4
Current State: 81:[83, 6, 95, 92], Operations: [] Exploring Operation: 92-83=9, Resulting Numbers: [6, 95, 9] Generated Node #0,0: 81:[6, 95, 9] Operation: 92-83=9 Exploring Operation: 95-92=3, Resulting Numbers: [83, 6, 3] Generated Node #0,1: 81:[83, 6, 3] Operation: 95-92=3 Exploring Operation: 95-83=12, Resulting Numbers: [6, 92, 12] Generated Node #0,2: 81:[6, 92, 12] Operation: 95-83=12 Exploring Operation: 95-6=89, Resulting Numbers: [83, 92, 89] Generated Node #0,3: 81:[83, 92, 89] Operation: 95-6=89 Exploring Operation: 92-6=86, Resulting Numbers: [83, 95, 86] Generated Node #0,4: 81:[83, 95, 86] Operation: 92-6=86 Moving to Node #0,1 Current State: 81:[83, 6, 3], Operations: ['95-92=3'] Exploring Operation: 6-3=3, Resulting Numbers: [83, 3] Generated Node #0,1,0: 81:[83, 3] Operation: 6-3=3 Exploring Operation: 6+3=9, Resulting Numbers: [83, 9] Generated Node #0,1,1: 81:[83, 9] Operation: 6+3=9 Exploring Operation: 83-3=80, Resulting Numbers: [6, 80] Generated Node #0,1,2: 81:[6, 80] Operation: 83-3=80 Exploring Operation: 83-6=77, Resulting Numbers: [3, 77] Generated Node #0,1,3: 81:[3, 77] Operation: 83-6=77 Exploring Operation: 6/3=2, Resulting Numbers: [83, 2] Generated Node #0,1,4: 81:[83, 2] Operation: 6/3=2 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 81:[83, 3], Operations: ['95-92=3', '6-3=3'] Exploring Operation: 83+3=86, Resulting Numbers: [86] 86,81 unequal: No Solution Exploring Operation: 83-3=80, Resulting Numbers: [80] 80,81 unequal: No Solution Exploring Operation: 83*3=249, Resulting Numbers: [249] 249,81 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: 81:[83, 9], Operations: ['95-92=3', '6+3=9'] Exploring Operation: 83*9=747, Resulting Numbers: [747] 747,81 unequal: No Solution Exploring Operation: 83+9=92, Resulting Numbers: [92] 92,81 unequal: No Solution Exploring Operation: 83-9=74, Resulting Numbers: [74] 74,81 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: 81:[83, 2], Operations: ['95-92=3', '6/3=2'] Exploring Operation: 83+2=85, Resulting Numbers: [85] 85,81 unequal: No Solution Exploring Operation: 83*2=166, Resulting Numbers: [166] 166,81 unequal: No Solution Exploring Operation: 83-2=81, Resulting Numbers: [81] 81,81 equal: Goal Reached Moving to Node #0 Current State: 81:[83, 6, 95, 92], Operations: [] Exploring Operation: 95-92=3, Resulting Numbers: [83, 6, 3] Generated Node #0,1: 81:[83, 6, 3] Operation: 95-92=3 Moving to Node #0,1 Current State: 81:[83, 6, 3], Operations: ['95-92=3'] Exploring Operation: 6/3=2, Resulting Numbers: [83, 2] Generated Node #0,1,4: 81:[83, 2] Operation: 6/3=2 Moving to Node #0,1,4 Current State: 81:[83, 2], Operations: ['95-92=3', '6/3=2'] Exploring Operation: 83-2=81, Resulting Numbers: [81] 81,81 equal: Goal Reached Exit Sub Search at level 1
0.980035
hs_5
mult_heuristic
[ 5, 2, 47, 12 ]
34
[ "5*12=60", "2*47=94", "94-60=34" ]
Current State: 34:[5, 2, 47, 12], Operations: [] Exploring Operation: 5*12=60, Resulting Numbers: [2, 47, 60] Generated Node #2: [2, 47, 60] from Operation: 5*12=60 Current State: 34:[2, 47, 60], Operations: ['5*12=60'] Exploring Operation: 2*47=94, Resulting Numbers: [60, 94] Generated Node #3: [60, 94] from Operation: 2*47=94 Current State: 34:[60, 94], Operations: ['5*12=60', '2*47=94'] Exploring Operation: 94-60=34, Resulting Numbers: [34] 34,34 equal: Goal Reached
4
Current State: 34:[5, 2, 47, 12], Operations: [] Exploring Operation: 47-12=35, Resulting Numbers: [5, 2, 35] Generated Node #0,0: 34:[5, 2, 35] Operation: 47-12=35 Start Sub Search at level 1: Moving to Node #0,0 Current State: 34:[5, 2, 35], Operations: ['47-12=35'] Exploring Operation: 5-2=3, Resulting Numbers: [35, 3] Generated Node #0,0,0: 34:[35, 3] Operation: 5-2=3 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 34:[35, 3], Operations: ['47-12=35', '5-2=3'] Exploring Operation: 35-3=32, Resulting Numbers: [32] 32,34 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
[ 49, 83, 37, 72 ]
23
[ "49+83=132", "37+72=109", "132-109=23" ]
Current State: 23:[49, 83, 37, 72], Operations: [] Exploring Operation: 49+83=132, Resulting Numbers: [37, 72, 132] Generated Node #2: [37, 72, 132] from Operation: 49+83=132 Current State: 23:[37, 72, 132], Operations: ['49+83=132'] Exploring Operation: 37+72=109, Resulting Numbers: [132, 109] Generated Node #3: [132, 109] from Operation: 37+72=109 Current State: 23:[132, 109], Operations: ['49+83=132', '37+72=109'] Exploring Operation: 132-109=23, Resulting Numbers: [23] 23,23 equal: Goal Reached
4
Current State: 23:[49, 83, 37, 72], Operations: [] Exploring Operation: 83-49=34, Resulting Numbers: [37, 72, 34] Generated Node #0,0: 23:[37, 72, 34] Operation: 83-49=34 Exploring Operation: 83-72=11, Resulting Numbers: [49, 37, 11] Generated Node #0,1: 23:[49, 37, 11] Operation: 83-72=11 Exploring Operation: 83-37=46, Resulting Numbers: [49, 72, 46] Generated Node #0,2: 23:[49, 72, 46] Operation: 83-37=46 Exploring Operation: 72-49=23, Resulting Numbers: [83, 37, 23] Generated Node #0,3: 23:[83, 37, 23] Operation: 72-49=23 Moving to Node #0,1 Current State: 23:[49, 37, 11], Operations: ['83-72=11'] Exploring Operation: 49+11=60, Resulting Numbers: [37, 60] Generated Node #0,1,0: 23:[37, 60] Operation: 49+11=60 Exploring Operation: 49-11=38, Resulting Numbers: [37, 38] Generated Node #0,1,1: 23:[37, 38] Operation: 49-11=38 Exploring Operation: 49-37=12, Resulting Numbers: [11, 12] Generated Node #0,1,2: 23:[11, 12] Operation: 49-37=12 Exploring Operation: 37-11=26, Resulting Numbers: [49, 26] Generated Node #0,1,3: 23:[49, 26] Operation: 37-11=26 Moving to Node #0,3 Current State: 23:[83, 37, 23], Operations: ['72-49=23'] Exploring Operation: 83+37=120, Resulting Numbers: [23, 120] Generated Node #0,3,0: 23:[23, 120] Operation: 83+37=120 Exploring Operation: 37-23=14, Resulting Numbers: [83, 14] Generated Node #0,3,1: 23:[83, 14] Operation: 37-23=14 Exploring Operation: 83-23=60, Resulting Numbers: [37, 60] Generated Node #0,3,2: 23:[37, 60] Operation: 83-23=60 Exploring Operation: 83-37=46, Resulting Numbers: [23, 46] Generated Node #0,3,3: 23:[23, 46] Operation: 83-37=46 Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 23:[23, 46], Operations: ['72-49=23', '83-37=46'] Exploring Operation: 23*46=1058, Resulting Numbers: [1058] 1058,23 unequal: No Solution Exploring Operation: 46-23=23, Resulting Numbers: [23] 23,23 equal: Goal Reached Moving to Node #0 Current State: 23:[49, 83, 37, 72], Operations: [] Exploring Operation: 72-49=23, Resulting Numbers: [83, 37, 23] Generated Node #0,3: 23:[83, 37, 23] Operation: 72-49=23 Moving to Node #0,3 Current State: 23:[83, 37, 23], Operations: ['72-49=23'] Exploring Operation: 83-37=46, Resulting Numbers: [23, 46] Generated Node #0,3,3: 23:[23, 46] Operation: 83-37=46 Moving to Node #0,3,3 Current State: 23:[23, 46], Operations: ['72-49=23', '83-37=46'] Exploring Operation: 46-23=23, Resulting Numbers: [23] 23,23 equal: Goal Reached Exit Sub Search at level 1
0.984375
hs_4
mult_heuristic
[ 25, 77, 46, 68 ]
80
[ "25+77=102", "68-46=22", "102-22=80" ]
Current State: 80:[25, 77, 46, 68], Operations: [] Exploring Operation: 25+77=102, Resulting Numbers: [46, 68, 102] Generated Node #2: [46, 68, 102] from Operation: 25+77=102 Current State: 80:[46, 68, 102], Operations: ['25+77=102'] Exploring Operation: 68-46=22, Resulting Numbers: [102, 22] Generated Node #3: [102, 22] from Operation: 68-46=22 Current State: 80:[102, 22], Operations: ['25+77=102', '68-46=22'] Exploring Operation: 102-22=80, Resulting Numbers: [80] 80,80 equal: Goal Reached
4
Current State: 80:[25, 77, 46, 68], Operations: [] Exploring Operation: 68-46=22, Resulting Numbers: [25, 77, 22] Generated Node #0,0: 80:[25, 77, 22] Operation: 68-46=22 Exploring Operation: 68-25=43, Resulting Numbers: [77, 46, 43] Generated Node #0,1: 80:[77, 46, 43] Operation: 68-25=43 Start Sub Search at level 1: Moving to Node #0,0 Current State: 80:[25, 77, 22], Operations: ['68-46=22'] Exploring Operation: 25+22=47, Resulting Numbers: [77, 47] Generated Node #0,0,0: 80:[77, 47] Operation: 25+22=47 Exploring Operation: 25-22=3, Resulting Numbers: [77, 3] Generated Node #0,0,1: 80:[77, 3] Operation: 25-22=3 Moving to Node #0,0,1 Current State: 80:[77, 3], Operations: ['68-46=22', '25-22=3'] Exploring Operation: 77-3=74, Resulting Numbers: [74] 74,80 unequal: No Solution Exploring Operation: 77+3=80, Resulting Numbers: [80] 80,80 equal: Goal Reached Moving to Node #0 Current State: 80:[25, 77, 46, 68], Operations: [] Exploring Operation: 68-46=22, Resulting Numbers: [25, 77, 22] Generated Node #0,0: 80:[25, 77, 22] Operation: 68-46=22 Moving to Node #0,0 Current State: 80:[25, 77, 22], Operations: ['68-46=22'] Exploring Operation: 25-22=3, Resulting Numbers: [77, 3] Generated Node #0,0,1: 80:[77, 3] Operation: 25-22=3 Moving to Node #0,0,1 Current State: 80:[77, 3], Operations: ['68-46=22', '25-22=3'] Exploring Operation: 77+3=80, Resulting Numbers: [80] 80,80 equal: Goal Reached Exit Sub Search at level 1
0.991319
hs_2
mult_heuristic
[ 54, 36, 75, 87 ]
17
[ "36*87=3132", "3132/54=58", "75-58=17" ]
Current State: 17:[54, 36, 75, 87], Operations: [] Exploring Operation: 36*87=3132, Resulting Numbers: [54, 75, 3132] Generated Node #2: [54, 75, 3132] from Operation: 36*87=3132 Current State: 17:[54, 75, 3132], Operations: ['36*87=3132'] Exploring Operation: 3132/54=58, Resulting Numbers: [75, 58] Generated Node #3: [75, 58] from Operation: 3132/54=58 Current State: 17:[75, 58], Operations: ['36*87=3132', '3132/54=58'] Exploring Operation: 75-58=17, Resulting Numbers: [17] 17,17 equal: Goal Reached
4
Current State: 17:[54, 36, 75, 87], Operations: [] Exploring Operation: 87-75=12, Resulting Numbers: [54, 36, 12] Generated Node #0,0: 17:[54, 36, 12] Operation: 87-75=12 Moving to Node #0,0 Current State: 17:[54, 36, 12], Operations: ['87-75=12'] Exploring Operation: 54-36=18, Resulting Numbers: [12, 18] Generated Node #0,0,0: 17:[12, 18] Operation: 54-36=18 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 17:[12, 18], Operations: ['87-75=12', '54-36=18'] Exploring Operation: 18-12=6, Resulting Numbers: [6] 6,17 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
[ 88, 70, 61, 90 ]
78
[ "70-61=9", "90/9=10", "88-10=78" ]
Current State: 78:[88, 70, 61, 90], Operations: [] Exploring Operation: 70-61=9, Resulting Numbers: [88, 90, 9] Generated Node #2: [88, 90, 9] from Operation: 70-61=9 Current State: 78:[88, 90, 9], Operations: ['70-61=9'] Exploring Operation: 90/9=10, Resulting Numbers: [88, 10] Generated Node #3: [88, 10] from Operation: 90/9=10 Current State: 78:[88, 10], Operations: ['70-61=9', '90/9=10'] Exploring Operation: 88-10=78, Resulting Numbers: [78] 78,78 equal: Goal Reached
4
Current State: 78:[88, 70, 61, 90], Operations: [] Exploring Operation: 88-61=27, Resulting Numbers: [70, 90, 27] Generated Node #0,0: 78:[70, 90, 27] Operation: 88-61=27 Moving to Node #0,0 Current State: 78:[70, 90, 27], Operations: ['88-61=27'] Exploring Operation: 90-70=20, Resulting Numbers: [27, 20] Generated Node #0,0,0: 78:[27, 20] Operation: 90-70=20 Moving to Node #0,0,0 Current State: 78:[27, 20], Operations: ['88-61=27', '90-70=20'] Exploring Operation: 27-20=7, Resulting Numbers: [7] 7,78 unequal: No Solution No solution found.
0
hs_1
mult_heuristic
[ 45, 42, 72, 64 ]
96
[ "45*64=2880", "72-42=30", "2880/30=96" ]
Current State: 96:[45, 42, 72, 64], Operations: [] Exploring Operation: 45*64=2880, Resulting Numbers: [42, 72, 2880] Generated Node #2: [42, 72, 2880] from Operation: 45*64=2880 Current State: 96:[42, 72, 2880], Operations: ['45*64=2880'] Exploring Operation: 72-42=30, Resulting Numbers: [2880, 30] Generated Node #3: [2880, 30] from Operation: 72-42=30 Current State: 96:[2880, 30], Operations: ['45*64=2880', '72-42=30'] Exploring Operation: 2880/30=96, Resulting Numbers: [96] 96,96 equal: Goal Reached
4
Current State: 96:[45, 42, 72, 64], Operations: [] Exploring Operation: 72-64=8, Resulting Numbers: [45, 42, 8] Generated Node #0,0: 96:[45, 42, 8] Operation: 72-64=8 Moving to Node #0,0 Current State: 96:[45, 42, 8], Operations: ['72-64=8'] Exploring Operation: 45-42=3, Resulting Numbers: [8, 3] Generated Node #0,0,0: 96:[8, 3] Operation: 45-42=3 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 96:[8, 3], Operations: ['72-64=8', '45-42=3'] Exploring Operation: 8*3=24, Resulting Numbers: [24] 24,96 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
sum_heuristic
[ 27, 42, 92, 13 ]
64
[ "42-27=15", "92-13=79", "79-15=64" ]
Current State: 64:[27, 42, 92, 13], Operations: [] Exploring Operation: 42-27=15, Resulting Numbers: [92, 13, 15] Generated Node #2: [92, 13, 15] from Operation: 42-27=15 Current State: 64:[92, 13, 15], Operations: ['42-27=15'] Exploring Operation: 92-13=79, Resulting Numbers: [15, 79] Generated Node #3: [15, 79] from Operation: 92-13=79 Current State: 64:[15, 79], Operations: ['42-27=15', '92-13=79'] Exploring Operation: 79-15=64, Resulting Numbers: [64] 64,64 equal: Goal Reached
4
Current State: 64:[27, 42, 92, 13], Operations: [] Exploring Operation: 92-27=65, Resulting Numbers: [42, 13, 65] Generated Node #0,0: 64:[42, 13, 65] Operation: 92-27=65 Moving to Node #0,0 Current State: 64:[42, 13, 65], Operations: ['92-27=65'] Exploring Operation: 42-13=29, Resulting Numbers: [65, 29] Generated Node #0,0,0: 64:[65, 29] Operation: 42-13=29 Moving to Node #0,0,0 Current State: 64:[65, 29], Operations: ['92-27=65', '42-13=29'] Exploring Operation: 65-29=36, Resulting Numbers: [36] 36,64 unequal: No Solution No solution found.
0
hs_1
sum_heuristic
[ 20, 72, 19, 3 ]
75
[ "20-19=1", "72+3=75", "1*75=75" ]
Current State: 75:[20, 72, 19, 3], Operations: [] Exploring Operation: 20-19=1, Resulting Numbers: [72, 3, 1] Generated Node #2: [72, 3, 1] from Operation: 20-19=1 Current State: 75:[72, 3, 1], Operations: ['20-19=1'] Exploring Operation: 72+3=75, Resulting Numbers: [1, 75] Generated Node #3: [1, 75] from Operation: 72+3=75 Current State: 75:[1, 75], Operations: ['20-19=1', '72+3=75'] Exploring Operation: 1*75=75, Resulting Numbers: [75] 75,75 equal: Goal Reached
4
Current State: 75:[20, 72, 19, 3], Operations: [] Exploring Operation: 20-19=1, Resulting Numbers: [72, 3, 1] Generated Node #0,0: 75:[72, 3, 1] Operation: 20-19=1 Exploring Operation: 20+3=23, Resulting Numbers: [72, 19, 23] Generated Node #0,1: 75:[72, 19, 23] Operation: 20+3=23 Exploring Operation: 20-3=17, Resulting Numbers: [72, 19, 17] Generated Node #0,2: 75:[72, 19, 17] Operation: 20-3=17 Moving to Node #0,0 Current State: 75:[72, 3, 1], Operations: ['20-19=1'] Exploring Operation: 72+3=75, Resulting Numbers: [1, 75] Generated Node #0,0,0: 75:[1, 75] Operation: 72+3=75 Exploring Operation: 72+1=73, Resulting Numbers: [3, 73] Generated Node #0,0,1: 75:[3, 73] Operation: 72+1=73 Exploring Operation: 72/3=24, Resulting Numbers: [1, 24] Generated Node #0,0,2: 75:[1, 24] Operation: 72/3=24 Moving to Node #0,1 Current State: 75:[72, 19, 23], Operations: ['20+3=23'] Exploring Operation: 19+23=42, Resulting Numbers: [72, 42] Generated Node #0,1,0: 75:[72, 42] Operation: 19+23=42 Exploring Operation: 23-19=4, Resulting Numbers: [72, 4] Generated Node #0,1,1: 75:[72, 4] Operation: 23-19=4 Exploring Operation: 72+19=91, Resulting Numbers: [23, 91] Generated Node #0,1,2: 75:[23, 91] Operation: 72+19=91 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 75:[72, 4], Operations: ['20+3=23', '23-19=4'] Exploring Operation: 72-4=68, Resulting Numbers: [68] 68,75 unequal: No Solution Exploring Operation: 72/4=18, Resulting Numbers: [18] 18,75 unequal: No Solution Exploring Operation: 72+4=76, Resulting Numbers: [76] 76,75 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: 75:[23, 91], Operations: ['20+3=23', '72+19=91'] Exploring Operation: 91-23=68, Resulting Numbers: [68] 68,75 unequal: No Solution Exploring Operation: 23*91=2093, Resulting Numbers: [2093] 2093,75 unequal: No Solution Exploring Operation: 23+91=114, Resulting Numbers: [114] 114,75 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: 75:[72, 42], Operations: ['20+3=23', '19+23=42'] Exploring Operation: 72+42=114, Resulting Numbers: [114] 114,75 unequal: No Solution Exploring Operation: 72-42=30, Resulting Numbers: [30] 30,75 unequal: No Solution Exploring Operation: 72*42=3024, Resulting Numbers: [3024] 3024,75 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: 75:[72, 19, 17], Operations: ['20-3=17'] Exploring Operation: 19+17=36, Resulting Numbers: [72, 36] Generated Node #0,2,0: 75:[72, 36] Operation: 19+17=36 Exploring Operation: 72+19=91, Resulting Numbers: [17, 91] Generated Node #0,2,1: 75:[17, 91] Operation: 72+19=91 Exploring Operation: 19-17=2, Resulting Numbers: [72, 2] Generated Node #0,2,2: 75:[72, 2] Operation: 19-17=2 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 75:[72, 2], Operations: ['20-3=17', '19-17=2'] Exploring Operation: 72+2=74, Resulting Numbers: [74] 74,75 unequal: No Solution Exploring Operation: 72-2=70, Resulting Numbers: [70] 70,75 unequal: No Solution Exploring Operation: 72/2=36, Resulting Numbers: [36] 36,75 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: 75:[72, 36], Operations: ['20-3=17', '19+17=36'] Exploring Operation: 72-36=36, Resulting Numbers: [36] 36,75 unequal: No Solution Exploring Operation: 72/36=2, Resulting Numbers: [2] 2,75 unequal: No Solution Exploring Operation: 72+36=108, Resulting Numbers: [108] 108,75 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: 75:[17, 91], Operations: ['20-3=17', '72+19=91'] Exploring Operation: 17*91=1547, Resulting Numbers: [1547] 1547,75 unequal: No Solution Exploring Operation: 17+91=108, Resulting Numbers: [108] 108,75 unequal: No Solution Exploring Operation: 91-17=74, Resulting Numbers: [74] 74,75 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: 75:[1, 75], Operations: ['20-19=1', '72+3=75'] Exploring Operation: 1+75=76, Resulting Numbers: [76] 76,75 unequal: No Solution Exploring Operation: 75/1=75, Resulting Numbers: [75] 75,75 equal: Goal Reached Moving to Node #0 Current State: 75:[20, 72, 19, 3], Operations: [] Exploring Operation: 20-19=1, Resulting Numbers: [72, 3, 1] Generated Node #0,0: 75:[72, 3, 1] Operation: 20-19=1 Moving to Node #0,0 Current State: 75:[72, 3, 1], Operations: ['20-19=1'] Exploring Operation: 72+3=75, Resulting Numbers: [1, 75] Generated Node #0,0,0: 75:[1, 75] Operation: 72+3=75 Moving to Node #0,0,0 Current State: 75:[1, 75], Operations: ['20-19=1', '72+3=75'] Exploring Operation: 75/1=75, Resulting Numbers: [75] 75,75 equal: Goal Reached
0.96875
hs_3
mult_heuristic
[ 40, 3, 77, 59 ]
94
[ "77-59=18", "3*18=54", "40+54=94" ]
Current State: 94:[40, 3, 77, 59], Operations: [] Exploring Operation: 77-59=18, Resulting Numbers: [40, 3, 18] Generated Node #2: [40, 3, 18] from Operation: 77-59=18 Current State: 94:[40, 3, 18], Operations: ['77-59=18'] Exploring Operation: 3*18=54, Resulting Numbers: [40, 54] Generated Node #3: [40, 54] from Operation: 3*18=54 Current State: 94:[40, 54], Operations: ['77-59=18', '3*18=54'] Exploring Operation: 40+54=94, Resulting Numbers: [94] 94,94 equal: Goal Reached
4
Current State: 94:[40, 3, 77, 59], Operations: [] Exploring Operation: 77-40=37, Resulting Numbers: [3, 59, 37] Generated Node #0,0: 94:[3, 59, 37] Operation: 77-40=37 Moving to Node #0,0 Current State: 94:[3, 59, 37], Operations: ['77-40=37'] Exploring Operation: 59+37=96, Resulting Numbers: [3, 96] Generated Node #0,0,0: 94:[3, 96] Operation: 59+37=96 Moving to Node #0,0,0 Current State: 94:[3, 96], Operations: ['77-40=37', '59+37=96'] Exploring Operation: 96-3=93, Resulting Numbers: [93] 93,94 unequal: No Solution No solution found.
0
hs_1
sum_heuristic
[ 99, 15, 16, 12 ]
51
[ "15-12=3", "16*3=48", "99-48=51" ]
Current State: 51:[99, 15, 16, 12], Operations: [] Exploring Operation: 15-12=3, Resulting Numbers: [99, 16, 3] Generated Node #2: [99, 16, 3] from Operation: 15-12=3 Current State: 51:[99, 16, 3], Operations: ['15-12=3'] Exploring Operation: 16*3=48, Resulting Numbers: [99, 48] Generated Node #3: [99, 48] from Operation: 16*3=48 Current State: 51:[99, 48], Operations: ['15-12=3', '16*3=48'] Exploring Operation: 99-48=51, Resulting Numbers: [51] 51,51 equal: Goal Reached
4
Current State: 51:[99, 15, 16, 12], Operations: [] Exploring Operation: 99-15=84, Resulting Numbers: [16, 12, 84] Generated Node #0,0: 51:[16, 12, 84] Operation: 99-15=84 Moving to Node #0,0 Current State: 51:[16, 12, 84], Operations: ['99-15=84'] Exploring Operation: 84/12=7, Resulting Numbers: [16, 7] Generated Node #0,0,0: 51:[16, 7] Operation: 84/12=7 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 51:[16, 7], Operations: ['99-15=84', '84/12=7'] Exploring Operation: 16+7=23, Resulting Numbers: [23] 23,51 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
[ 26, 47, 10, 14 ]
51
[ "26+14=40", "40/10=4", "47+4=51" ]
Current State: 51:[26, 47, 10, 14], Operations: [] Exploring Operation: 26+14=40, Resulting Numbers: [47, 10, 40] Generated Node #2: [47, 10, 40] from Operation: 26+14=40 Current State: 51:[47, 10, 40], Operations: ['26+14=40'] Exploring Operation: 40/10=4, Resulting Numbers: [47, 4] Generated Node #3: [47, 4] from Operation: 40/10=4 Current State: 51:[47, 4], Operations: ['26+14=40', '40/10=4'] Exploring Operation: 47+4=51, Resulting Numbers: [51] 51,51 equal: Goal Reached
4
Current State: 51:[26, 47, 10, 14], Operations: [] Exploring Operation: 26-10=16, Resulting Numbers: [47, 14, 16] Generated Node #0,0: 51:[47, 14, 16] Operation: 26-10=16 Start Sub Search at level 1: Moving to Node #0,0 Current State: 51:[47, 14, 16], Operations: ['26-10=16'] Exploring Operation: 16-14=2, Resulting Numbers: [47, 2] Generated Node #0,0,0: 51:[47, 2] Operation: 16-14=2 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 51:[47, 2], Operations: ['26-10=16', '16-14=2'] Exploring Operation: 47+2=49, Resulting Numbers: [49] 49,51 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
[ 93, 71, 99, 12 ]
54
[ "93-71=22", "99*12=1188", "1188/22=54" ]
Current State: 54:[93, 71, 99, 12], Operations: [] Exploring Operation: 93-71=22, Resulting Numbers: [99, 12, 22] Generated Node #2: [99, 12, 22] from Operation: 93-71=22 Current State: 54:[99, 12, 22], Operations: ['93-71=22'] Exploring Operation: 99*12=1188, Resulting Numbers: [22, 1188] Generated Node #3: [22, 1188] from Operation: 99*12=1188 Current State: 54:[22, 1188], Operations: ['93-71=22', '99*12=1188'] Exploring Operation: 1188/22=54, Resulting Numbers: [54] 54,54 equal: Goal Reached
4
Current State: 54:[93, 71, 99, 12], Operations: [] Exploring Operation: 93-71=22, Resulting Numbers: [99, 12, 22] Generated Node #0,0: 54:[99, 12, 22] Operation: 93-71=22 Exploring Operation: 99-93=6, Resulting Numbers: [71, 12, 6] Generated Node #0,1: 54:[71, 12, 6] Operation: 99-93=6 Exploring Operation: 99-71=28, Resulting Numbers: [93, 12, 28] Generated Node #0,2: 54:[93, 12, 28] Operation: 99-71=28 Exploring Operation: 93-12=81, Resulting Numbers: [71, 99, 81] Generated Node #0,3: 54:[71, 99, 81] Operation: 93-12=81 Exploring Operation: 71-12=59, Resulting Numbers: [93, 99, 59] Generated Node #0,4: 54:[93, 99, 59] Operation: 71-12=59 Start Sub Search at level 1: Moving to Node #0,1 Current State: 54:[71, 12, 6], Operations: ['99-93=6'] Exploring Operation: 71-12=59, Resulting Numbers: [6, 59] Generated Node #0,1,0: 54:[6, 59] Operation: 71-12=59 Exploring Operation: 12/6=2, Resulting Numbers: [71, 2] Generated Node #0,1,1: 54:[71, 2] Operation: 12/6=2 Exploring Operation: 12-6=6, Resulting Numbers: [71, 6] Generated Node #0,1,2: 54:[71, 6] Operation: 12-6=6 Exploring Operation: 12+6=18, Resulting Numbers: [71, 18] Generated Node #0,1,3: 54:[71, 18] Operation: 12+6=18 Exploring Operation: 71-6=65, Resulting Numbers: [12, 65] Generated Node #0,1,4: 54:[12, 65] Operation: 71-6=65 Moving to Node #0,1,0 Current State: 54:[6, 59], Operations: ['99-93=6', '71-12=59'] Exploring Operation: 6*59=354, Resulting Numbers: [354] 354,54 unequal: No Solution Exploring Operation: 59-6=53, Resulting Numbers: [53] 53,54 unequal: No Solution Exploring Operation: 6+59=65, Resulting Numbers: [65] 65,54 unequal: No Solution Moving to Node #0,1,4 Current State: 54:[12, 65], Operations: ['99-93=6', '71-6=65'] Exploring Operation: 12+65=77, Resulting Numbers: [77] 77,54 unequal: No Solution Exploring Operation: 65-12=53, Resulting Numbers: [53] 53,54 unequal: No Solution Exploring Operation: 12*65=780, Resulting Numbers: [780] 780,54 unequal: No Solution Moving to Node #0,1,1 Current State: 54:[71, 2], Operations: ['99-93=6', '12/6=2'] Exploring Operation: 71+2=73, Resulting Numbers: [73] 73,54 unequal: No Solution Exploring Operation: 71*2=142, Resulting Numbers: [142] 142,54 unequal: No Solution Exploring Operation: 71-2=69, Resulting Numbers: [69] 69,54 unequal: No Solution Moving to Node #0,1,2 Current State: 54:[71, 6], Operations: ['99-93=6', '12-6=6'] Exploring Operation: 71+6=77, Resulting Numbers: [77] 77,54 unequal: No Solution Exploring Operation: 71*6=426, Resulting Numbers: [426] 426,54 unequal: No Solution Exploring Operation: 71-6=65, Resulting Numbers: [65] 65,54 unequal: No Solution Moving to Node #0,1,3 Current State: 54:[71, 18], Operations: ['99-93=6', '12+6=18'] Exploring Operation: 71*18=1278, Resulting Numbers: [1278] 1278,54 unequal: No Solution Exploring Operation: 71-18=53, Resulting Numbers: [53] 53,54 unequal: No Solution Exploring Operation: 71+18=89, Resulting Numbers: [89] 89,54 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:[93, 12, 28], Operations: ['99-71=28'] Exploring Operation: 93-12=81, Resulting Numbers: [28, 81] Generated Node #0,2,0: 54:[28, 81] Operation: 93-12=81 Exploring Operation: 12+28=40, Resulting Numbers: [93, 40] Generated Node #0,2,1: 54:[93, 40] Operation: 12+28=40 Exploring Operation: 93+12=105, Resulting Numbers: [28, 105] Generated Node #0,2,2: 54:[28, 105] Operation: 93+12=105 Exploring Operation: 93-28=65, Resulting Numbers: [12, 65] Generated Node #0,2,3: 54:[12, 65] Operation: 93-28=65 Exploring Operation: 28-12=16, Resulting Numbers: [93, 16] Generated Node #0,2,4: 54:[93, 16] Operation: 28-12=16 Moving to Node #0,2,3 Current State: 54:[12, 65], Operations: ['99-71=28', '93-28=65'] Exploring Operation: 12+65=77, Resulting Numbers: [77] 77,54 unequal: No Solution Exploring Operation: 12*65=780, Resulting Numbers: [780] 780,54 unequal: No Solution Exploring Operation: 65-12=53, Resulting Numbers: [53] 53,54 unequal: No Solution Moving to Node #0,2,0 Current State: 54:[28, 81], Operations: ['99-71=28', '93-12=81'] Exploring Operation: 81-28=53, Resulting Numbers: [53] 53,54 unequal: No Solution Exploring Operation: 28*81=2268, Resulting Numbers: [2268] 2268,54 unequal: No Solution Exploring Operation: 28+81=109, Resulting Numbers: [109] 109,54 unequal: No Solution Moving to Node #0,2,4 Current State: 54:[93, 16], Operations: ['99-71=28', '28-12=16'] Exploring Operation: 93*16=1488, Resulting Numbers: [1488] 1488,54 unequal: No Solution Exploring Operation: 93-16=77, Resulting Numbers: [77] 77,54 unequal: No Solution Exploring Operation: 93+16=109, Resulting Numbers: [109] 109,54 unequal: No Solution Moving to Node #0,2,1 Current State: 54:[93, 40], Operations: ['99-71=28', '12+28=40'] Exploring Operation: 93+40=133, Resulting Numbers: [133] 133,54 unequal: No Solution Exploring Operation: 93*40=3720, Resulting Numbers: [3720] 3720,54 unequal: No Solution Exploring Operation: 93-40=53, Resulting Numbers: [53] 53,54 unequal: No Solution Moving to Node #0,2,2 Current State: 54:[28, 105], Operations: ['99-71=28', '93+12=105'] Exploring Operation: 105-28=77, Resulting Numbers: [77] 77,54 unequal: No Solution Exploring Operation: 28*105=2940, Resulting Numbers: [2940] 2940,54 unequal: No Solution Exploring Operation: 28+105=133, Resulting Numbers: [133] 133,54 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 #0,0 Current State: 54:[99, 12, 22], Operations: ['93-71=22'] Exploring Operation: 12+22=34, Resulting Numbers: [99, 34] Generated Node #0,0,0: 54:[99, 34] Operation: 12+22=34 Exploring Operation: 22-12=10, Resulting Numbers: [99, 10] Generated Node #0,0,1: 54:[99, 10] Operation: 22-12=10 Exploring Operation: 99+12=111, Resulting Numbers: [22, 111] Generated Node #0,0,2: 54:[22, 111] Operation: 99+12=111 Exploring Operation: 99-12=87, Resulting Numbers: [22, 87] Generated Node #0,0,3: 54:[22, 87] Operation: 99-12=87 Exploring Operation: 99-22=77, Resulting Numbers: [12, 77] Generated Node #0,0,4: 54:[12, 77] Operation: 99-22=77 Start Sub Search at level 2: Moving to Node #0,0,4 Current State: 54:[12, 77], Operations: ['93-71=22', '99-22=77'] Exploring Operation: 12+77=89, Resulting Numbers: [89] 89,54 unequal: No Solution Exploring Operation: 12*77=924, Resulting Numbers: [924] 924,54 unequal: No Solution Exploring Operation: 77-12=65, Resulting Numbers: [65] 65,54 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: 54:[22, 87], Operations: ['93-71=22', '99-12=87'] Exploring Operation: 22+87=109, Resulting Numbers: [109] 109,54 unequal: No Solution Exploring Operation: 22*87=1914, Resulting Numbers: [1914] 1914,54 unequal: No Solution Exploring Operation: 87-22=65, Resulting Numbers: [65] 65,54 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: 54:[99, 10], Operations: ['93-71=22', '22-12=10'] Exploring Operation: 99+10=109, Resulting Numbers: [109] 109,54 unequal: No Solution Exploring Operation: 99*10=990, Resulting Numbers: [990] 990,54 unequal: No Solution Exploring Operation: 99-10=89, Resulting Numbers: [89] 89,54 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: 54:[99, 34], Operations: ['93-71=22', '12+22=34'] Exploring Operation: 99*34=3366, Resulting Numbers: [3366] 3366,54 unequal: No Solution Exploring Operation: 99+34=133, Resulting Numbers: [133] 133,54 unequal: No Solution Exploring Operation: 99-34=65, Resulting Numbers: [65] 65,54 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: 54:[22, 111], Operations: ['93-71=22', '99+12=111'] Exploring Operation: 22*111=2442, Resulting Numbers: [2442] 2442,54 unequal: No Solution Exploring Operation: 111-22=89, Resulting Numbers: [89] 89,54 unequal: No Solution Exploring Operation: 22+111=133, Resulting Numbers: [133] 133,54 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: 54:[71, 99, 81], Operations: ['93-12=81'] Exploring Operation: 71+81=152, Resulting Numbers: [99, 152] Generated Node #0,3,0: 54:[99, 152] Operation: 71+81=152 Exploring Operation: 81-71=10, Resulting Numbers: [99, 10] Generated Node #0,3,1: 54:[99, 10] Operation: 81-71=10 Exploring Operation: 99-71=28, Resulting Numbers: [81, 28] Generated Node #0,3,2: 54:[81, 28] Operation: 99-71=28 Exploring Operation: 99-81=18, Resulting Numbers: [71, 18] Generated Node #0,3,3: 54:[71, 18] Operation: 99-81=18 Exploring Operation: 71+99=170, Resulting Numbers: [81, 170] Generated Node #0,3,4: 54:[81, 170] Operation: 71+99=170 Moving to Node #0,3,3 Current State: 54:[71, 18], Operations: ['93-12=81', '99-81=18'] Exploring Operation: 71*18=1278, Resulting Numbers: [1278] 1278,54 unequal: No Solution Exploring Operation: 71-18=53, Resulting Numbers: [53] 53,54 unequal: No Solution Exploring Operation: 71+18=89, Resulting Numbers: [89] 89,54 unequal: No Solution Moving to Node #0,3,2 Current State: 54:[81, 28], Operations: ['93-12=81', '99-71=28'] Exploring Operation: 81+28=109, Resulting Numbers: [109] 109,54 unequal: No Solution Exploring Operation: 81-28=53, Resulting Numbers: [53] 53,54 unequal: No Solution Exploring Operation: 81*28=2268, Resulting Numbers: [2268] 2268,54 unequal: No Solution Moving to Node #0,3,1 Current State: 54:[99, 10], Operations: ['93-12=81', '81-71=10'] Exploring Operation: 99*10=990, Resulting Numbers: [990] 990,54 unequal: No Solution Exploring Operation: 99-10=89, Resulting Numbers: [89] 89,54 unequal: No Solution Exploring Operation: 99+10=109, Resulting Numbers: [109] 109,54 unequal: No Solution Moving to Node #0,3,0 Current State: 54:[99, 152], Operations: ['93-12=81', '71+81=152'] Exploring Operation: 99+152=251, Resulting Numbers: [251] 251,54 unequal: No Solution Exploring Operation: 152-99=53, Resulting Numbers: [53] 53,54 unequal: No Solution Exploring Operation: 99*152=15048, Resulting Numbers: [15048] 15048,54 unequal: No Solution Moving to Node #0,3,4 Current State: 54:[81, 170], Operations: ['93-12=81', '71+99=170'] Exploring Operation: 81*170=13770, Resulting Numbers: [13770] 13770,54 unequal: No Solution Exploring Operation: 170-81=89, Resulting Numbers: [89] 89,54 unequal: No Solution Exploring Operation: 81+170=251, Resulting Numbers: [251] 251,54 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 Current State: 54:[93, 99, 59], Operations: ['71-12=59'] Exploring Operation: 99-59=40, Resulting Numbers: [93, 40] Generated Node #0,4,0: 54:[93, 40] Operation: 99-59=40 Exploring Operation: 93+99=192, Resulting Numbers: [59, 192] Generated Node #0,4,1: 54:[59, 192] Operation: 93+99=192 Exploring Operation: 93+59=152, Resulting Numbers: [99, 152] Generated Node #0,4,2: 54:[99, 152] Operation: 93+59=152 Exploring Operation: 93-59=34, Resulting Numbers: [99, 34] Generated Node #0,4,3: 54:[99, 34] Operation: 93-59=34 Exploring Operation: 99-93=6, Resulting Numbers: [59, 6] Generated Node #0,4,4: 54:[59, 6] Operation: 99-93=6 Moving to Node #0,4,4 Current State: 54:[59, 6], Operations: ['71-12=59', '99-93=6'] Exploring Operation: 59+6=65, Resulting Numbers: [65] 65,54 unequal: No Solution Exploring Operation: 59-6=53, Resulting Numbers: [53] 53,54 unequal: No Solution Exploring Operation: 59*6=354, Resulting Numbers: [354] 354,54 unequal: No Solution Moving to Node #0,4,3 Current State: 54:[99, 34], Operations: ['71-12=59', '93-59=34'] Exploring Operation: 99+34=133, Resulting Numbers: [133] 133,54 unequal: No Solution Exploring Operation: 99*34=3366, Resulting Numbers: [3366] 3366,54 unequal: No Solution Exploring Operation: 99-34=65, Resulting Numbers: [65] 65,54 unequal: No Solution Moving to Node #0,4,0 Current State: 54:[93, 40], Operations: ['71-12=59', '99-59=40'] Exploring Operation: 93*40=3720, Resulting Numbers: [3720] 3720,54 unequal: No Solution Exploring Operation: 93+40=133, Resulting Numbers: [133] 133,54 unequal: No Solution Exploring Operation: 93-40=53, Resulting Numbers: [53] 53,54 unequal: No Solution Moving to Node #0,4,1 Current State: 54:[59, 192], Operations: ['71-12=59', '93+99=192'] Exploring Operation: 59+192=251, Resulting Numbers: [251] 251,54 unequal: No Solution Exploring Operation: 192-59=133, Resulting Numbers: [133] 133,54 unequal: No Solution Exploring Operation: 59*192=11328, Resulting Numbers: [11328] 11328,54 unequal: No Solution Moving to Node #0,4,2 Current State: 54:[99, 152], Operations: ['71-12=59', '93+59=152'] Exploring Operation: 99*152=15048, Resulting Numbers: [15048] 15048,54 unequal: No Solution Exploring Operation: 152-99=53, Resulting Numbers: [53] 53,54 unequal: No Solution Exploring Operation: 99+152=251, Resulting Numbers: [251] 251,54 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
[ 6, 5, 69, 26 ]
96
[ "6-5=1", "69+26=95", "1+95=96" ]
Current State: 96:[6, 5, 69, 26], Operations: [] Exploring Operation: 6-5=1, Resulting Numbers: [69, 26, 1] Generated Node #2: [69, 26, 1] from Operation: 6-5=1 Current State: 96:[69, 26, 1], Operations: ['6-5=1'] Exploring Operation: 69+26=95, Resulting Numbers: [1, 95] Generated Node #3: [1, 95] from Operation: 69+26=95 Current State: 96:[1, 95], Operations: ['6-5=1', '69+26=95'] Exploring Operation: 1+95=96, Resulting Numbers: [96] 96,96 equal: Goal Reached
4
Current State: 96:[6, 5, 69, 26], Operations: [] Exploring Operation: 69+26=95, Resulting Numbers: [6, 5, 95] Generated Node #0,0: 96:[6, 5, 95] Operation: 69+26=95 Exploring Operation: 69-26=43, Resulting Numbers: [6, 5, 43] Generated Node #0,1: 96:[6, 5, 43] Operation: 69-26=43 Moving to Node #0,0 Current State: 96:[6, 5, 95], Operations: ['69+26=95'] Exploring Operation: 6-5=1, Resulting Numbers: [95, 1] Generated Node #0,0,0: 96:[95, 1] Operation: 6-5=1 Exploring Operation: 6+5=11, Resulting Numbers: [95, 11] Generated Node #0,0,1: 96:[95, 11] Operation: 6+5=11 Moving to Node #0,1 Current State: 96:[6, 5, 43], Operations: ['69-26=43'] Exploring Operation: 5+43=48, Resulting Numbers: [6, 48] Generated Node #0,1,0: 96:[6, 48] Operation: 5+43=48 Exploring Operation: 6+43=49, Resulting Numbers: [5, 49] Generated Node #0,1,1: 96:[5, 49] Operation: 6+43=49 Moving to Node #0,1,0 Current State: 96:[6, 48], Operations: ['69-26=43', '5+43=48'] Exploring Operation: 48/6=8, Resulting Numbers: [8] 8,96 unequal: No Solution Exploring Operation: 6+48=54, Resulting Numbers: [54] 54,96 unequal: No Solution Moving to Node #0,0,0 Current State: 96:[95, 1], Operations: ['69+26=95', '6-5=1'] Exploring Operation: 95+1=96, Resulting Numbers: [96] 96,96 equal: Goal Reached Moving to Node #0 Current State: 96:[6, 5, 69, 26], Operations: [] Exploring Operation: 69+26=95, Resulting Numbers: [6, 5, 95] Generated Node #0,0: 96:[6, 5, 95] Operation: 69+26=95 Moving to Node #0,0 Current State: 96:[6, 5, 95], Operations: ['69+26=95'] Exploring Operation: 6-5=1, Resulting Numbers: [95, 1] Generated Node #0,0,0: 96:[95, 1] Operation: 6-5=1 Moving to Node #0,0,0 Current State: 96:[95, 1], Operations: ['69+26=95', '6-5=1'] Exploring Operation: 95+1=96, Resulting Numbers: [96] 96,96 equal: Goal Reached
0.988715
hs_2
sum_heuristic
[ 66, 26, 47, 99 ]
64
[ "99-47=52", "52/26=2", "66-2=64" ]
Current State: 64:[66, 26, 47, 99], Operations: [] Exploring Operation: 99-47=52, Resulting Numbers: [66, 26, 52] Generated Node #2: [66, 26, 52] from Operation: 99-47=52 Current State: 64:[66, 26, 52], Operations: ['99-47=52'] Exploring Operation: 52/26=2, Resulting Numbers: [66, 2] Generated Node #3: [66, 2] from Operation: 52/26=2 Current State: 64:[66, 2], Operations: ['99-47=52', '52/26=2'] Exploring Operation: 66-2=64, Resulting Numbers: [64] 64,64 equal: Goal Reached
4
Current State: 64:[66, 26, 47, 99], Operations: [] Exploring Operation: 99-26=73, Resulting Numbers: [66, 47, 73] Generated Node #0,0: 64:[66, 47, 73] Operation: 99-26=73 Exploring Operation: 47-26=21, Resulting Numbers: [66, 99, 21] Generated Node #0,1: 64:[66, 99, 21] Operation: 47-26=21 Exploring Operation: 99-47=52, Resulting Numbers: [66, 26, 52] Generated Node #0,2: 64:[66, 26, 52] Operation: 99-47=52 Exploring Operation: 99-66=33, Resulting Numbers: [26, 47, 33] Generated Node #0,3: 64:[26, 47, 33] Operation: 99-66=33 Moving to Node #0,2 Current State: 64:[66, 26, 52], Operations: ['99-47=52'] Exploring Operation: 66-52=14, Resulting Numbers: [26, 14] Generated Node #0,2,0: 64:[26, 14] Operation: 66-52=14 Exploring Operation: 52/26=2, Resulting Numbers: [66, 2] Generated Node #0,2,1: 64:[66, 2] Operation: 52/26=2 Exploring Operation: 26+52=78, Resulting Numbers: [66, 78] Generated Node #0,2,2: 64:[66, 78] Operation: 26+52=78 Exploring Operation: 52-26=26, Resulting Numbers: [66, 26] Generated Node #0,2,3: 64:[66, 26] Operation: 52-26=26 Moving to Node #0,3 Current State: 64:[26, 47, 33], Operations: ['99-66=33'] Exploring Operation: 47-26=21, Resulting Numbers: [33, 21] Generated Node #0,3,0: 64:[33, 21] Operation: 47-26=21 Exploring Operation: 47-33=14, Resulting Numbers: [26, 14] Generated Node #0,3,1: 64:[26, 14] Operation: 47-33=14 Exploring Operation: 33-26=7, Resulting Numbers: [47, 7] Generated Node #0,3,2: 64:[47, 7] Operation: 33-26=7 Exploring Operation: 26+47=73, Resulting Numbers: [33, 73] Generated Node #0,3,3: 64:[33, 73] Operation: 26+47=73 Moving to Node #0,0 Current State: 64:[66, 47, 73], Operations: ['99-26=73'] Exploring Operation: 73-47=26, Resulting Numbers: [66, 26] Generated Node #0,0,0: 64:[66, 26] Operation: 73-47=26 Exploring Operation: 66+47=113, Resulting Numbers: [73, 113] Generated Node #0,0,1: 64:[73, 113] Operation: 66+47=113 Exploring Operation: 73-66=7, Resulting Numbers: [47, 7] Generated Node #0,0,2: 64:[47, 7] Operation: 73-66=7 Exploring Operation: 66-47=19, Resulting Numbers: [73, 19] Generated Node #0,0,3: 64:[73, 19] Operation: 66-47=19 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 64:[66, 26], Operations: ['99-26=73', '73-47=26'] Exploring Operation: 66+26=92, Resulting Numbers: [92] 92,64 unequal: No Solution Exploring Operation: 66*26=1716, Resulting Numbers: [1716] 1716,64 unequal: No Solution Exploring Operation: 66-26=40, Resulting Numbers: [40] 40,64 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: 64:[73, 19], Operations: ['99-26=73', '66-47=19'] Exploring Operation: 73-19=54, Resulting Numbers: [54] 54,64 unequal: No Solution Exploring Operation: 73+19=92, Resulting Numbers: [92] 92,64 unequal: No Solution Exploring Operation: 73*19=1387, Resulting Numbers: [1387] 1387,64 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: 64:[47, 7], Operations: ['99-26=73', '73-66=7'] Exploring Operation: 47-7=40, Resulting Numbers: [40] 40,64 unequal: No Solution Exploring Operation: 47*7=329, Resulting Numbers: [329] 329,64 unequal: No Solution Exploring Operation: 47+7=54, Resulting Numbers: [54] 54,64 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: 64:[73, 113], Operations: ['99-26=73', '66+47=113'] Exploring Operation: 73*113=8249, Resulting Numbers: [8249] 8249,64 unequal: No Solution Exploring Operation: 113-73=40, Resulting Numbers: [40] 40,64 unequal: No Solution Exploring Operation: 73+113=186, Resulting Numbers: [186] 186,64 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: 64:[66, 99, 21], Operations: ['47-26=21'] Exploring Operation: 99-21=78, Resulting Numbers: [66, 78] Generated Node #0,1,0: 64:[66, 78] Operation: 99-21=78 Exploring Operation: 66-21=45, Resulting Numbers: [99, 45] Generated Node #0,1,1: 64:[99, 45] Operation: 66-21=45 Exploring Operation: 66+21=87, Resulting Numbers: [99, 87] Generated Node #0,1,2: 64:[99, 87] Operation: 66+21=87 Exploring Operation: 99-66=33, Resulting Numbers: [21, 33] Generated Node #0,1,3: 64:[21, 33] Operation: 99-66=33 Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 64:[21, 33], Operations: ['47-26=21', '99-66=33'] Exploring Operation: 21*33=693, Resulting Numbers: [693] 693,64 unequal: No Solution Exploring Operation: 21+33=54, Resulting Numbers: [54] 54,64 unequal: No Solution Exploring Operation: 33-21=12, Resulting Numbers: [12] 12,64 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: 64:[66, 78], Operations: ['47-26=21', '99-21=78'] Exploring Operation: 78-66=12, Resulting Numbers: [12] 12,64 unequal: No Solution Exploring Operation: 66+78=144, Resulting Numbers: [144] 144,64 unequal: No Solution Exploring Operation: 66*78=5148, Resulting Numbers: [5148] 5148,64 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: 64:[99, 45], Operations: ['47-26=21', '66-21=45'] Exploring Operation: 99+45=144, Resulting Numbers: [144] 144,64 unequal: No Solution Exploring Operation: 99-45=54, Resulting Numbers: [54] 54,64 unequal: No Solution Exploring Operation: 99*45=4455, Resulting Numbers: [4455] 4455,64 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: 64:[99, 87], Operations: ['47-26=21', '66+21=87'] Exploring Operation: 99*87=8613, Resulting Numbers: [8613] 8613,64 unequal: No Solution Exploring Operation: 99-87=12, Resulting Numbers: [12] 12,64 unequal: No Solution Exploring Operation: 99+87=186, Resulting Numbers: [186] 186,64 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: 64:[66, 2], Operations: ['99-47=52', '52/26=2'] Exploring Operation: 66-2=64, Resulting Numbers: [64] 64,64 equal: Goal Reached Moving to Node #0 Current State: 64:[66, 26, 47, 99], Operations: [] Exploring Operation: 99-47=52, Resulting Numbers: [66, 26, 52] Generated Node #0,2: 64:[66, 26, 52] Operation: 99-47=52 Moving to Node #0,2 Current State: 64:[66, 26, 52], Operations: ['99-47=52'] Exploring Operation: 52/26=2, Resulting Numbers: [66, 2] Generated Node #0,2,1: 64:[66, 2] Operation: 52/26=2 Moving to Node #0,2,1 Current State: 64:[66, 2], Operations: ['99-47=52', '52/26=2'] Exploring Operation: 66-2=64, Resulting Numbers: [64] 64,64 equal: Goal Reached
0.957465
hs_4
sum_heuristic
[ 10, 29, 70, 11 ]
11
[ "70/10=7", "29-11=18", "18-7=11" ]
Current State: 11:[10, 29, 70, 11], Operations: [] Exploring Operation: 70/10=7, Resulting Numbers: [29, 11, 7] Generated Node #2: [29, 11, 7] from Operation: 70/10=7 Current State: 11:[29, 11, 7], Operations: ['70/10=7'] Exploring Operation: 29-11=18, Resulting Numbers: [7, 18] Generated Node #3: [7, 18] from Operation: 29-11=18 Current State: 11:[7, 18], Operations: ['70/10=7', '29-11=18'] Exploring Operation: 18-7=11, Resulting Numbers: [11] 11,11 equal: Goal Reached
4
Current State: 11:[10, 29, 70, 11], Operations: [] Exploring Operation: 70/10=7, Resulting Numbers: [29, 11, 7] Generated Node #0,0: 11:[29, 11, 7] Operation: 70/10=7 Moving to Node #0,0 Current State: 11:[29, 11, 7], Operations: ['70/10=7'] Exploring Operation: 29-11=18, Resulting Numbers: [7, 18] Generated Node #0,0,0: 11:[7, 18] Operation: 29-11=18 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 11:[7, 18], Operations: ['70/10=7', '29-11=18'] Exploring Operation: 18-7=11, Resulting Numbers: [11] 11,11 equal: Goal Reached Moving to Node #0 Current State: 11:[10, 29, 70, 11], Operations: [] Exploring Operation: 70/10=7, Resulting Numbers: [29, 11, 7] Generated Node #0,0: 11:[29, 11, 7] Operation: 70/10=7 Moving to Node #0,0 Current State: 11:[29, 11, 7], Operations: ['70/10=7'] Exploring Operation: 29-11=18, Resulting Numbers: [7, 18] Generated Node #0,0,0: 11:[7, 18] Operation: 29-11=18 Moving to Node #0,0,0 Current State: 11:[7, 18], Operations: ['70/10=7', '29-11=18'] Exploring Operation: 18-7=11, Resulting Numbers: [11] 11,11 equal: Goal Reached Exit Sub Search at level 1
0.993924
hs_1
mult_heuristic
[ 2, 94, 9, 92 ]
99
[ "2*92=184", "94-9=85", "184-85=99" ]
Current State: 99:[2, 94, 9, 92], Operations: [] Exploring Operation: 2*92=184, Resulting Numbers: [94, 9, 184] Generated Node #2: [94, 9, 184] from Operation: 2*92=184 Current State: 99:[94, 9, 184], Operations: ['2*92=184'] Exploring Operation: 94-9=85, Resulting Numbers: [184, 85] Generated Node #3: [184, 85] from Operation: 94-9=85 Current State: 99:[184, 85], Operations: ['2*92=184', '94-9=85'] Exploring Operation: 184-85=99, Resulting Numbers: [99] 99,99 equal: Goal Reached
4
Current State: 99:[2, 94, 9, 92], Operations: [] Exploring Operation: 94-92=2, Resulting Numbers: [2, 9, 2] Generated Node #0,0: 99:[2, 9, 2] Operation: 94-92=2 Moving to Node #0,0 Current State: 99:[2, 9, 2], Operations: ['94-92=2'] Exploring Operation: 2+9=11, Resulting Numbers: [2, 11] Generated Node #0,0,0: 99:[2, 11] Operation: 2+9=11 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 99:[2, 11], Operations: ['94-92=2', '2+9=11'] Exploring Operation: 11-2=9, Resulting Numbers: [9] 9,99 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
[ 2, 21, 95, 88 ]
35
[ "2*21=42", "95-88=7", "42-7=35" ]
Current State: 35:[2, 21, 95, 88], Operations: [] Exploring Operation: 2*21=42, Resulting Numbers: [95, 88, 42] Generated Node #2: [95, 88, 42] from Operation: 2*21=42 Current State: 35:[95, 88, 42], Operations: ['2*21=42'] Exploring Operation: 95-88=7, Resulting Numbers: [42, 7] Generated Node #3: [42, 7] from Operation: 95-88=7 Current State: 35:[42, 7], Operations: ['2*21=42', '95-88=7'] Exploring Operation: 42-7=35, Resulting Numbers: [35] 35,35 equal: Goal Reached
4
Current State: 35:[2, 21, 95, 88], Operations: [] Exploring Operation: 88/2=44, Resulting Numbers: [21, 95, 44] Generated Node #0,0: 35:[21, 95, 44] Operation: 88/2=44 Exploring Operation: 95-88=7, Resulting Numbers: [2, 21, 7] Generated Node #0,1: 35:[2, 21, 7] Operation: 95-88=7 Moving to Node #0,1 Current State: 35:[2, 21, 7], Operations: ['95-88=7'] Exploring Operation: 2*21=42, Resulting Numbers: [7, 42] Generated Node #0,1,0: 35:[7, 42] Operation: 2*21=42 Exploring Operation: 21/7=3, Resulting Numbers: [2, 3] Generated Node #0,1,1: 35:[2, 3] Operation: 21/7=3 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 35:[2, 3], Operations: ['95-88=7', '21/7=3'] Exploring Operation: 2*3=6, Resulting Numbers: [6] 6,35 unequal: No Solution Exploring Operation: 2+3=5, Resulting Numbers: [5] 5,35 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:[7, 42], Operations: ['95-88=7', '2*21=42'] Exploring Operation: 42-7=35, Resulting Numbers: [35] 35,35 equal: Goal Reached Moving to Node #0 Current State: 35:[2, 21, 95, 88], Operations: [] Exploring Operation: 95-88=7, Resulting Numbers: [2, 21, 7] Generated Node #0,1: 35:[2, 21, 7] Operation: 95-88=7 Moving to Node #0,1 Current State: 35:[2, 21, 7], Operations: ['95-88=7'] Exploring Operation: 2*21=42, Resulting Numbers: [7, 42] Generated Node #0,1,0: 35:[7, 42] Operation: 2*21=42 Moving to Node #0,1,0 Current State: 35:[7, 42], Operations: ['95-88=7', '2*21=42'] Exploring Operation: 42-7=35, Resulting Numbers: [35] 35,35 equal: Goal Reached Exit Sub Search at level 1
0.990451
hs_2
sum_heuristic
[ 38, 4, 25, 23 ]
35
[ "38-23=15", "4*15=60", "60-25=35" ]
Current State: 35:[38, 4, 25, 23], Operations: [] Exploring Operation: 38-23=15, Resulting Numbers: [4, 25, 15] Generated Node #2: [4, 25, 15] from Operation: 38-23=15 Current State: 35:[4, 25, 15], Operations: ['38-23=15'] Exploring Operation: 4*15=60, Resulting Numbers: [25, 60] Generated Node #3: [25, 60] from Operation: 4*15=60 Current State: 35:[25, 60], Operations: ['38-23=15', '4*15=60'] Exploring Operation: 60-25=35, Resulting Numbers: [35] 35,35 equal: Goal Reached
4
Current State: 35:[38, 4, 25, 23], Operations: [] Exploring Operation: 25-23=2, Resulting Numbers: [38, 4, 2] Generated Node #0,0: 35:[38, 4, 2] Operation: 25-23=2 Start Sub Search at level 1: Moving to Node #0,0 Current State: 35:[38, 4, 2], Operations: ['25-23=2'] Exploring Operation: 38-2=36, Resulting Numbers: [4, 36] Generated Node #0,0,0: 35:[4, 36] Operation: 38-2=36 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 35:[4, 36], Operations: ['25-23=2', '38-2=36'] Exploring Operation: 36/4=9, Resulting Numbers: [9] 9,35 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
[ 42, 33, 94, 98 ]
71
[ "42+33=75", "98-94=4", "75-4=71" ]
Current State: 71:[42, 33, 94, 98], Operations: [] Exploring Operation: 42+33=75, Resulting Numbers: [94, 98, 75] Generated Node #2: [94, 98, 75] from Operation: 42+33=75 Current State: 71:[94, 98, 75], Operations: ['42+33=75'] Exploring Operation: 98-94=4, Resulting Numbers: [75, 4] Generated Node #3: [75, 4] from Operation: 98-94=4 Current State: 71:[75, 4], Operations: ['42+33=75', '98-94=4'] Exploring Operation: 75-4=71, Resulting Numbers: [71] 71,71 equal: Goal Reached
4
Current State: 71:[42, 33, 94, 98], Operations: [] Exploring Operation: 98-33=65, Resulting Numbers: [42, 94, 65] Generated Node #0,0: 71:[42, 94, 65] Operation: 98-33=65 Exploring Operation: 42+33=75, Resulting Numbers: [94, 98, 75] Generated Node #0,1: 71:[94, 98, 75] Operation: 42+33=75 Start Sub Search at level 1: Moving to Node #0,1 Current State: 71:[94, 98, 75], Operations: ['42+33=75'] Exploring Operation: 98-75=23, Resulting Numbers: [94, 23] Generated Node #0,1,0: 71:[94, 23] Operation: 98-75=23 Exploring Operation: 98-94=4, Resulting Numbers: [75, 4] Generated Node #0,1,1: 71:[75, 4] Operation: 98-94=4 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 71:[94, 23], Operations: ['42+33=75', '98-75=23'] Exploring Operation: 94+23=117, Resulting Numbers: [117] 117,71 unequal: No Solution Exploring Operation: 94-23=71, Resulting Numbers: [71] 71,71 equal: Goal Reached Moving to Node #0 Current State: 71:[42, 33, 94, 98], Operations: [] Exploring Operation: 42+33=75, Resulting Numbers: [94, 98, 75] Generated Node #0,1: 71:[94, 98, 75] Operation: 42+33=75 Moving to Node #0,1 Current State: 71:[94, 98, 75], Operations: ['42+33=75'] Exploring Operation: 98-75=23, Resulting Numbers: [94, 23] Generated Node #0,1,0: 71:[94, 23] Operation: 98-75=23 Moving to Node #0,1,0 Current State: 71:[94, 23], Operations: ['42+33=75', '98-75=23'] Exploring Operation: 94-23=71, Resulting Numbers: [71] 71,71 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.991319
hs_2
sum_heuristic
[ 95, 53, 17, 51 ]
14
[ "95-53=42", "51/17=3", "42/3=14" ]
Current State: 14:[95, 53, 17, 51], Operations: [] Exploring Operation: 95-53=42, Resulting Numbers: [17, 51, 42] Generated Node #2: [17, 51, 42] from Operation: 95-53=42 Current State: 14:[17, 51, 42], Operations: ['95-53=42'] Exploring Operation: 51/17=3, Resulting Numbers: [42, 3] Generated Node #3: [42, 3] from Operation: 51/17=3 Current State: 14:[42, 3], Operations: ['95-53=42', '51/17=3'] Exploring Operation: 42/3=14, Resulting Numbers: [14] 14,14 equal: Goal Reached
4
Current State: 14:[95, 53, 17, 51], Operations: [] Exploring Operation: 95-53=42, Resulting Numbers: [17, 51, 42] Generated Node #0,0: 14:[17, 51, 42] Operation: 95-53=42 Exploring Operation: 51/17=3, Resulting Numbers: [95, 53, 3] Generated Node #0,1: 14:[95, 53, 3] Operation: 51/17=3 Exploring Operation: 95-17=78, Resulting Numbers: [53, 51, 78] Generated Node #0,2: 14:[53, 51, 78] Operation: 95-17=78 Exploring Operation: 95-51=44, Resulting Numbers: [53, 17, 44] Generated Node #0,3: 14:[53, 17, 44] Operation: 95-51=44 Exploring Operation: 53-51=2, Resulting Numbers: [95, 17, 2] Generated Node #0,4: 14:[95, 17, 2] Operation: 53-51=2 Moving to Node #0,0 Current State: 14:[17, 51, 42], Operations: ['95-53=42'] Exploring Operation: 51-17=34, Resulting Numbers: [42, 34] Generated Node #0,0,0: 14:[42, 34] Operation: 51-17=34 Exploring Operation: 51-42=9, Resulting Numbers: [17, 9] Generated Node #0,0,1: 14:[17, 9] Operation: 51-42=9 Exploring Operation: 42-17=25, Resulting Numbers: [51, 25] Generated Node #0,0,2: 14:[51, 25] Operation: 42-17=25 Exploring Operation: 17+51=68, Resulting Numbers: [42, 68] Generated Node #0,0,3: 14:[42, 68] Operation: 17+51=68 Exploring Operation: 51/17=3, Resulting Numbers: [42, 3] Generated Node #0,0,4: 14:[42, 3] Operation: 51/17=3 Moving to Node #0,3 Current State: 14:[53, 17, 44], Operations: ['95-51=44'] Exploring Operation: 44-17=27, Resulting Numbers: [53, 27] Generated Node #0,3,0: 14:[53, 27] Operation: 44-17=27 Exploring Operation: 53+17=70, Resulting Numbers: [44, 70] Generated Node #0,3,1: 14:[44, 70] Operation: 53+17=70 Exploring Operation: 53-44=9, Resulting Numbers: [17, 9] Generated Node #0,3,2: 14:[17, 9] Operation: 53-44=9 Exploring Operation: 53-17=36, Resulting Numbers: [44, 36] Generated Node #0,3,3: 14:[44, 36] Operation: 53-17=36 Exploring Operation: 53+44=97, Resulting Numbers: [17, 97] Generated Node #0,3,4: 14:[17, 97] Operation: 53+44=97 Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 14:[17, 9], Operations: ['95-51=44', '53-44=9'] Exploring Operation: 17+9=26, Resulting Numbers: [26] 26,14 unequal: No Solution Exploring Operation: 17-9=8, Resulting Numbers: [8] 8,14 unequal: No Solution Exploring Operation: 17*9=153, Resulting Numbers: [153] 153,14 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 #0,3,0 Current State: 14:[53, 27], Operations: ['95-51=44', '44-17=27'] Exploring Operation: 53-27=26, Resulting Numbers: [26] 26,14 unequal: No Solution Exploring Operation: 53*27=1431, Resulting Numbers: [1431] 1431,14 unequal: No Solution Exploring Operation: 53+27=80, Resulting Numbers: [80] 80,14 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 #0,3,3 Current State: 14:[44, 36], Operations: ['95-51=44', '53-17=36'] Exploring Operation: 44+36=80, Resulting Numbers: [80] 80,14 unequal: No Solution Exploring Operation: 44*36=1584, Resulting Numbers: [1584] 1584,14 unequal: No Solution Exploring Operation: 44-36=8, Resulting Numbers: [8] 8,14 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 #0,3,1 Current State: 14:[44, 70], Operations: ['95-51=44', '53+17=70'] Exploring Operation: 70-44=26, Resulting Numbers: [26] 26,14 unequal: No Solution Exploring Operation: 44+70=114, Resulting Numbers: [114] 114,14 unequal: No Solution Exploring Operation: 44*70=3080, Resulting Numbers: [3080] 3080,14 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 #0,3,4 Current State: 14:[17, 97], Operations: ['95-51=44', '53+44=97'] Exploring Operation: 17+97=114, Resulting Numbers: [114] 114,14 unequal: No Solution Exploring Operation: 17*97=1649, Resulting Numbers: [1649] 1649,14 unequal: No Solution Exploring Operation: 97-17=80, Resulting Numbers: [80] 80,14 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: 14:[95, 17, 2], Operations: ['53-51=2'] Exploring Operation: 95-17=78, Resulting Numbers: [2, 78] Generated Node #0,4,0: 14:[2, 78] Operation: 95-17=78 Exploring Operation: 95+2=97, Resulting Numbers: [17, 97] Generated Node #0,4,1: 14:[17, 97] Operation: 95+2=97 Exploring Operation: 17-2=15, Resulting Numbers: [95, 15] Generated Node #0,4,2: 14:[95, 15] Operation: 17-2=15 Exploring Operation: 95-2=93, Resulting Numbers: [17, 93] Generated Node #0,4,3: 14:[17, 93] Operation: 95-2=93 Exploring Operation: 17+2=19, Resulting Numbers: [95, 19] Generated Node #0,4,4: 14:[95, 19] Operation: 17+2=19 Moving to Node #0,1 Current State: 14:[95, 53, 3], Operations: ['51/17=3'] Exploring Operation: 53-3=50, Resulting Numbers: [95, 50] Generated Node #0,1,0: 14:[95, 50] Operation: 53-3=50 Exploring Operation: 95-53=42, Resulting Numbers: [3, 42] Generated Node #0,1,1: 14:[3, 42] Operation: 95-53=42 Exploring Operation: 53+3=56, Resulting Numbers: [95, 56] Generated Node #0,1,2: 14:[95, 56] Operation: 53+3=56 Exploring Operation: 95-3=92, Resulting Numbers: [53, 92] Generated Node #0,1,3: 14:[53, 92] Operation: 95-3=92 Exploring Operation: 95+3=98, Resulting Numbers: [53, 98] Generated Node #0,1,4: 14:[53, 98] Operation: 95+3=98 Moving to Node #0,2 Current State: 14:[53, 51, 78], Operations: ['95-17=78'] Exploring Operation: 78-53=25, Resulting Numbers: [51, 25] Generated Node #0,2,0: 14:[51, 25] Operation: 78-53=25 Exploring Operation: 53+78=131, Resulting Numbers: [51, 131] Generated Node #0,2,1: 14:[51, 131] Operation: 53+78=131 Exploring Operation: 53+51=104, Resulting Numbers: [78, 104] Generated Node #0,2,2: 14:[78, 104] Operation: 53+51=104 Exploring Operation: 78-51=27, Resulting Numbers: [53, 27] Generated Node #0,2,3: 14:[53, 27] Operation: 78-51=27 Exploring Operation: 53-51=2, Resulting Numbers: [78, 2] Generated Node #0,2,4: 14:[78, 2] Operation: 53-51=2 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 14:[51, 25], Operations: ['95-17=78', '78-53=25'] Exploring Operation: 51+25=76, Resulting Numbers: [76] 76,14 unequal: No Solution Exploring Operation: 51-25=26, Resulting Numbers: [26] 26,14 unequal: No Solution Exploring Operation: 51*25=1275, Resulting Numbers: [1275] 1275,14 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 #0,2,3 Current State: 14:[53, 27], Operations: ['95-17=78', '78-51=27'] Exploring Operation: 53*27=1431, Resulting Numbers: [1431] 1431,14 unequal: No Solution Exploring Operation: 53-27=26, Resulting Numbers: [26] 26,14 unequal: No Solution Exploring Operation: 53+27=80, Resulting Numbers: [80] 80,14 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 #0,2,4 Current State: 14:[78, 2], Operations: ['95-17=78', '53-51=2'] Exploring Operation: 78/2=39, Resulting Numbers: [39] 39,14 unequal: No Solution Exploring Operation: 78+2=80, Resulting Numbers: [80] 80,14 unequal: No Solution Exploring Operation: 78*2=156, Resulting Numbers: [156] 156,14 unequal: No Solution Exploring Operation: 78-2=76, Resulting Numbers: [76] 76,14 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 #0,2,1 Current State: 14:[51, 131], Operations: ['95-17=78', '53+78=131'] Exploring Operation: 51+131=182, Resulting Numbers: [182] 182,14 unequal: No Solution Exploring Operation: 51*131=6681, Resulting Numbers: [6681] 6681,14 unequal: No Solution Exploring Operation: 131-51=80, Resulting Numbers: [80] 80,14 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 #0,2,2 Current State: 14:[78, 104], Operations: ['95-17=78', '53+51=104'] Exploring Operation: 78+104=182, Resulting Numbers: [182] 182,14 unequal: No Solution Exploring Operation: 104-78=26, Resulting Numbers: [26] 26,14 unequal: No Solution Exploring Operation: 78*104=8112, Resulting Numbers: [8112] 8112,14 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: 14:[17, 9], Operations: ['95-53=42', '51-42=9'] Exploring Operation: 17+9=26, Resulting Numbers: [26] 26,14 unequal: No Solution Exploring Operation: 17-9=8, Resulting Numbers: [8] 8,14 unequal: No Solution Exploring Operation: 17*9=153, Resulting Numbers: [153] 153,14 unequal: No Solution Moving to Node #0,0,4 Current State: 14:[42, 3], Operations: ['95-53=42', '51/17=3'] Exploring Operation: 42*3=126, Resulting Numbers: [126] 126,14 unequal: No Solution Exploring Operation: 42+3=45, Resulting Numbers: [45] 45,14 unequal: No Solution Exploring Operation: 42/3=14, Resulting Numbers: [14] 14,14 equal: Goal Reached Moving to Node #0 Current State: 14:[95, 53, 17, 51], Operations: [] Exploring Operation: 95-53=42, Resulting Numbers: [17, 51, 42] Generated Node #0,0: 14:[17, 51, 42] Operation: 95-53=42 Moving to Node #0,0 Current State: 14:[17, 51, 42], Operations: ['95-53=42'] Exploring Operation: 51/17=3, Resulting Numbers: [42, 3] Generated Node #0,0,4: 14:[42, 3] Operation: 51/17=3 Moving to Node #0,0,4 Current State: 14:[42, 3], Operations: ['95-53=42', '51/17=3'] Exploring Operation: 42/3=14, Resulting Numbers: [14] 14,14 equal: Goal Reached
0.938368
hs_5
mult_heuristic
[ 37, 37, 47, 99 ]
22
[ "37+37=74", "99-47=52", "74-52=22" ]
Current State: 22:[37, 37, 47, 99], Operations: [] Exploring Operation: 37+37=74, Resulting Numbers: [47, 99, 74] Generated Node #2: [47, 99, 74] from Operation: 37+37=74 Current State: 22:[47, 99, 74], Operations: ['37+37=74'] Exploring Operation: 99-47=52, Resulting Numbers: [74, 52] Generated Node #3: [74, 52] from Operation: 99-47=52 Current State: 22:[74, 52], Operations: ['37+37=74', '99-47=52'] Exploring Operation: 74-52=22, Resulting Numbers: [22] 22,22 equal: Goal Reached
4
Current State: 22:[37, 37, 47, 99], Operations: [] Exploring Operation: 99-37=62, Resulting Numbers: [37, 47, 62] Generated Node #0,0: 22:[37, 47, 62] Operation: 99-37=62 Exploring Operation: 99-47=52, Resulting Numbers: [37, 37, 52] Generated Node #0,1: 22:[37, 37, 52] Operation: 99-47=52 Exploring Operation: 99-37=62, Resulting Numbers: [37, 47, 62] Generated Node #0,2: 22:[37, 47, 62] Operation: 99-37=62 Moving to Node #0,1 Current State: 22:[37, 37, 52], Operations: ['99-47=52'] Exploring Operation: 52-37=15, Resulting Numbers: [37, 15] Generated Node #0,1,0: 22:[37, 15] Operation: 52-37=15 Exploring Operation: 37/37=1, Resulting Numbers: [52, 1] Generated Node #0,1,1: 22:[52, 1] Operation: 37/37=1 Exploring Operation: 52-37=15, Resulting Numbers: [37, 15] Generated Node #0,1,2: 22:[37, 15] Operation: 52-37=15 Moving to Node #0,0 Current State: 22:[37, 47, 62], Operations: ['99-37=62'] Exploring Operation: 62-47=15, Resulting Numbers: [37, 15] Generated Node #0,0,0: 22:[37, 15] Operation: 62-47=15 Exploring Operation: 62-37=25, Resulting Numbers: [47, 25] Generated Node #0,0,1: 22:[47, 25] Operation: 62-37=25 Exploring Operation: 47-37=10, Resulting Numbers: [62, 10] Generated Node #0,0,2: 22:[62, 10] Operation: 47-37=10 Moving to Node #0,2 Current State: 22:[37, 47, 62], Operations: ['99-37=62'] Exploring Operation: 47-37=10, Resulting Numbers: [62, 10] Generated Node #0,2,0: 22:[62, 10] Operation: 47-37=10 Exploring Operation: 62-47=15, Resulting Numbers: [37, 15] Generated Node #0,2,1: 22:[37, 15] Operation: 62-47=15 Exploring Operation: 62-37=25, Resulting Numbers: [47, 25] Generated Node #0,2,2: 22:[47, 25] Operation: 62-37=25 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 22:[37, 15], Operations: ['99-37=62', '62-47=15'] Exploring Operation: 37-15=22, Resulting Numbers: [22] 22,22 equal: Goal Reached Moving to Node #0 Current State: 22:[37, 37, 47, 99], Operations: [] Exploring Operation: 99-37=62, Resulting Numbers: [37, 47, 62] Generated Node #0,2: 22:[37, 47, 62] Operation: 99-37=62 Moving to Node #0,2 Current State: 22:[37, 47, 62], Operations: ['99-37=62'] Exploring Operation: 62-47=15, Resulting Numbers: [37, 15] Generated Node #0,2,1: 22:[37, 15] Operation: 62-47=15 Moving to Node #0,2,1 Current State: 22:[37, 15], Operations: ['99-37=62', '62-47=15'] Exploring Operation: 37-15=22, Resulting Numbers: [22] 22,22 equal: Goal Reached Exit Sub Search at level 1
0.985243
hs_3
sum_heuristic