numbers
listlengths 4
4
| solutions
listlengths 1
11
| solvable
bool 1
class | amt
float64 4.36
212
| solved_rate
float64 0.2
1
| mean_time
float64 4.63
41.1
| std_time
float64 1.25
23
| __index_level_0__
int64 0
1.36k
|
|---|---|---|---|---|---|---|---|
[
2,
6,
10,
12
] |
[
"(10-6-2)×12",
"(12-10)×6×2",
"(6×2-10)×12",
"(10+2)×12/6",
"(12+2-10)×6",
"(10-6)×12/2",
"(10-12/2)×6",
"(10×6-12)/2",
"(12/6+10)×2"
] | true
| 7.01
| 0.954
| 7.47
| 2.78
| 587
|
[
4,
7,
12,
12
] |
[
"(7-4)×12-12",
"(12×7+12)/4",
"(7-12/12)×4"
] | true
| 6.36
| 0.885
| 6.73
| 3
| 1,032
|
[
2,
12,
12,
13
] |
[
"(13-12)×12×2",
"(13-12/12)×2"
] | true
| 6.43
| 0.956
| 6.84
| 2.43
| 657
|
[
1,
5,
6,
9
] |
[
"(9-5)×6×1"
] | true
| 7.22
| 0.922
| 7.71
| 3.55
| 234
|
[
3,
4,
5,
12
] |
[
"12+5+4+3",
"(4+3-5)×12",
"(5+3)×12/4",
"12×4/(5-3)",
"12×5/3+4",
"5×4+12/3",
"(5×4-12)×3",
"(12/4+5)×3"
] | true
| 7.33
| 0.971
| 7.72
| 2.7
| 732
|
[
1,
4,
8,
12
] |
[
"12×8×1/4",
"(8+1)×4-12",
"(12+8+4)×1",
"12/(1-4/8)"
] | true
| 5.92
| 0.976
| 6.31
| 2.2
| 214
|
[
1,
3,
8,
10
] |
[
"(10-1)×8/3"
] | true
| 16.72
| 0.709
| 12.77
| 6.81
| 162
|
[
1,
3,
4,
8
] |
[
"(3+1)×4+8",
"(8+1-3)×4",
"(8+4)×(3-1)",
"8/(4/3-1)"
] | true
| 11.73
| 0.896
| 11.94
| 4.83
| 132
|
[
4,
6,
7,
12
] |
[
"12×6/(7-4)",
"(7-12/4)×6"
] | true
| 12
| 0.813
| 11.54
| 5.69
| 994
|
[
4,
4,
10,
13
] |
[
"(4+4)×(13-10)",
"4/4+13+10"
] | true
| 6.37
| 0.936
| 6.83
| 2.83
| 938
|
[
5,
6,
9,
12
] |
[
"(6+5-9)×12",
"(12-6)×(9-5)"
] | true
| 9.98
| 0.873
| 10.09
| 4.43
| 1,120
|
[
1,
4,
4,
10
] |
[
"(10-4)×4×1"
] | true
| 7.92
| 0.923
| 8.15
| 3.46
| 185
|
[
1,
1,
10,
12
] |
[
"12+10+1+1"
] | true
| 4.8
| 0.99
| 5.04
| 1.53
| 41
|
[
3,
3,
6,
12
] |
[
"12+6+3+3",
"(3+3)×6-12"
] | true
| 11.42
| 0.873
| 11.66
| 6.05
| 692
|
[
1,
2,
9,
13
] |
[
"(13+9+2)×1"
] | true
| 8.86
| 0.932
| 9.42
| 4.19
| 108
|
[
1,
1,
7,
10
] |
[
"(1+1)×7+10"
] | true
| 8.37
| 0.85
| 8.4
| 4.33
| 38
|
[
2,
6,
6,
13
] |
[
"(13-6/6)×2"
] | true
| 7.72
| 0.85
| 7.68
| 3.22
| 568
|
[
3,
6,
10,
11
] |
[
"11+10+6-3",
"(11+3-10)×6"
] | true
| 6.46
| 0.96
| 7.13
| 2.9
| 826
|
[
9,
9,
9,
12
] |
[
"(9+9)×12/9"
] | true
| 19.42
| 0.631
| 10.38
| 7.1
| 1,320
|
[
8,
9,
10,
13
] |
[
"9×8/(13-10)",
"13+10+9-8"
] | true
| 6.96
| 0.96
| 7.48
| 2.71
| 1,308
|
[
2,
4,
5,
5
] |
[
"(5+5)×2+4"
] | true
| 25.84
| 0.598
| 15.79
| 8.59
| 483
|
[
2,
3,
11,
12
] |
[
"12+11+3-2"
] | true
| 6.28
| 0.95
| 6.85
| 2.83
| 468
|
[
1,
1,
4,
6
] |
[
"6×4+1-1"
] | true
| 4.36
| 0.992
| 4.63
| 1.45
| 24
|
[
3,
7,
7,
13
] |
[
"13+7+7-3",
"(13-7)×(7-3)"
] | true
| 8.74
| 0.936
| 9.06
| 3.18
| 839
|
[
3,
8,
9,
10
] |
[
"(10-9)×8×3",
"10+9+8-3",
"(9+3)×(10-8)"
] | true
| 6.71
| 0.963
| 7.06
| 2.54
| 864
|
[
4,
5,
8,
8
] |
[
"(5-8/4)×8",
"(8/8+5)×4"
] | true
| 8.85
| 0.868
| 8.91
| 4.11
| 964
|
[
7,
8,
8,
12
] |
[
"(8+7-12)×8"
] | true
| 11.16
| 0.831
| 10.67
| 4.69
| 1,268
|
[
2,
2,
4,
7
] |
[
"7×4-2-2",
"(2+2)×7-4",
"7×4-2×2",
"7×2×2-4",
"(7-2/2)×4",
"(7+4)×2+2"
] | true
| 7.47
| 0.952
| 8.13
| 3.16
| 366
|
[
2,
4,
7,
12
] |
[
"(7+2)×4-12",
"12/(4-7/2)"
] | true
| 116.99
| 0.275
| 31.26
| 18.75
| 505
|
[
6,
6,
10,
13
] |
[
"6/6+13+10",
"(13-10)×6+6"
] | true
| 5.97
| 0.938
| 6.5
| 2.71
| 1,198
|
[
2,
2,
6,
8
] |
[
"(8-2-2)×6",
"(8-2×2)×6",
"8×2+6+2",
"(6+2)×2+8",
"(8+6-2)×2",
"(8-2)×(6-2)"
] | true
| 9.41
| 0.955
| 9.83
| 3.55
| 383
|
[
3,
4,
6,
6
] |
[
"4×3+6+6",
"6×6-4×3",
"(6+4)×3-6",
"(6+6-4)×3"
] | true
| 11.42
| 0.906
| 11.6
| 4.73
| 734
|
[
3,
4,
4,
6
] |
[
"(6-4)×4×3",
"(4×3-6)×4",
"(4-3)×6×4",
"(4+4)×(6-3)",
"(6/3+4)×4",
"(4/4+3)×6"
] | true
| 5.81
| 0.974
| 6.15
| 1.95
| 717
|
[
6,
7,
10,
10
] |
[
"(10-7)×10-6"
] | true
| 14.86
| 0.703
| 11.18
| 6.19
| 1,211
|
[
2,
3,
8,
8
] |
[
"(8-3-2)×8",
"(8+8)×3/2",
"(8×2-8)×3"
] | true
| 13.49
| 0.799
| 12.26
| 6.01
| 454
|
[
1,
6,
6,
8
] |
[
"6/(1-6/8)"
] | true
| 121.88
| 0.283
| 23.61
| 15.03
| 264
|
[
6,
7,
8,
10
] |
[
"(7+6-10)×8",
"7×6-10-8",
"(8-6)×7+10"
] | true
| 8.11
| 0.914
| 8.61
| 3.65
| 1,206
|
[
1,
5,
6,
7
] |
[
"6×5+1-7",
"(7-1)×5-6"
] | true
| 11.45
| 0.892
| 11.71
| 4.74
| 232
|
[
2,
3,
6,
11
] |
[
"(11-3)×6/2",
"(11-6/2)×3",
"11×2+6/3",
"11×6/3+2"
] | true
| 9.84
| 0.901
| 10.09
| 4.48
| 444
|
[
2,
2,
8,
9
] |
[
"9×2+8-2"
] | true
| 11.62
| 0.868
| 11.84
| 5.24
| 395
|
[
6,
6,
9,
13
] |
[
"13×6-9×6"
] | true
| 31.03
| 0.538
| 14.15
| 9.07
| 1,196
|
[
1,
3,
12,
12
] |
[
"(12×3-12)×1"
] | true
| 8.47
| 0.855
| 8.74
| 4.78
| 176
|
[
1,
1,
3,
10
] |
[
"(10-1-1)×3"
] | true
| 9.04
| 0.884
| 9.05
| 3.91
| 18
|
[
6,
8,
8,
11
] |
[
"(8+6-11)×8"
] | true
| 8.75
| 0.871
| 8.86
| 3.95
| 1,222
|
[
4,
4,
4,
6
] |
[
"6×4+4-4"
] | true
| 5.27
| 0.982
| 5.66
| 1.95
| 901
|
[
1,
12,
13,
13
] |
[
"(13/13+1)×12"
] | true
| 5.96
| 0.945
| 6.29
| 2.18
| 341
|
[
3,
8,
12,
13
] |
[
"(13-8-3)×12",
"(13-12)×8×3",
"(13+3)×12/8"
] | true
| 5.85
| 0.961
| 6.22
| 2.19
| 874
|
[
2,
7,
7,
11
] |
[
"(7-2)×7-11",
"(7/7+11)×2"
] | true
| 7.95
| 0.863
| 7.99
| 3.74
| 595
|
[
1,
2,
3,
5
] |
[
"(5+3)×(2+1)",
"(5+2+1)×3",
"(5-1)×3×2",
"(3+2)×5-1"
] | true
| 7.12
| 0.955
| 7.45
| 2.41
| 61
|
[
1,
6,
7,
11
] |
[
"(11-7)×6×1",
"(6-1)×7-11",
"(11+7+6)×1"
] | true
| 6.56
| 0.973
| 7.16
| 2.88
| 272
|
[
5,
6,
6,
8
] |
[
"(8-5)×6+6"
] | true
| 11.39
| 0.812
| 10.82
| 6.07
| 1,103
|
[
7,
8,
12,
12
] |
[
"(12+12)×(8-7)"
] | true
| 5.72
| 0.96
| 6.15
| 2.16
| 1,278
|
[
1,
6,
8,
12
] |
[
"(12-8)×6×1",
"(8-6)×12×1",
"(12/6+1)×8"
] | true
| 5.4
| 0.971
| 5.79
| 2
| 278
|
[
4,
9,
10,
12
] |
[
"12×10/(9-4)"
] | true
| 26.14
| 0.622
| 17.69
| 9.53
| 1,058
|
[
3,
3,
7,
7
] |
[
"(3/7+3)×7"
] | true
| 51.64
| 0.407
| 13.53
| 8.22
| 694
|
[
2,
2,
4,
9
] |
[
"9×2+4+2",
"(9+4)×2-2"
] | true
| 9.94
| 0.904
| 10.16
| 4.44
| 368
|
[
6,
11,
12,
13
] |
[
"(13-11)×6+12"
] | true
| 10.69
| 0.802
| 9.84
| 5.1
| 1,253
|
[
1,
1,
6,
9
] |
[
"(1+1)×9+6"
] | true
| 13.99
| 0.806
| 12.01
| 6.75
| 36
|
[
3,
4,
6,
8
] |
[
"(8-6)×4×3",
"(4×3-8)×6",
"(8+4)×6/3",
"(8-6/3)×4",
"(8/4+6)×3"
] | true
| 10.95
| 0.907
| 11.41
| 5.07
| 735
|
[
6,
7,
9,
9
] |
[
"7×6-9-9",
"(9+7)×9/6",
"(9-7)×9+6"
] | true
| 12.04
| 0.806
| 11.2
| 6.1
| 1,209
|
[
3,
3,
3,
5
] |
[
"5×3+3×3"
] | true
| 10.14
| 0.856
| 9.81
| 4.22
| 662
|
[
4,
4,
6,
11
] |
[
"(11-6)×4+4"
] | true
| 8.94
| 0.864
| 8.91
| 4.57
| 919
|
[
4,
6,
7,
7
] |
[
"7+7+6+4",
"6×4+7-7"
] | true
| 5.21
| 0.987
| 5.55
| 1.84
| 990
|
[
2,
5,
8,
10
] |
[
"(10-5-2)×8",
"(10-2)×(8-5)"
] | true
| 11.99
| 0.828
| 11.16
| 4.89
| 547
|
[
5,
5,
8,
13
] |
[
"(13-5-5)×8",
"(13-5)×(8-5)"
] | true
| 11.44
| 0.808
| 10.88
| 4.63
| 1,088
|
[
3,
3,
6,
8
] |
[
"(3×3-6)×8",
"(6+3)×8/3"
] | true
| 12.97
| 0.744
| 10.8
| 5.9
| 688
|
[
3,
4,
6,
11
] |
[
"11+6+4+3",
"(11-4-3)×6",
"6/(3-11/4)"
] | true
| 10.49
| 0.89
| 10.69
| 4.72
| 738
|
[
1,
4,
5,
8
] |
[
"(5+1)×(8-4)",
"(5-1)×4+8"
] | true
| 13.77
| 0.823
| 12.93
| 5.94
| 191
|
[
2,
3,
8,
10
] |
[
"3×2+10+8",
"10×3+2-8"
] | true
| 16.25
| 0.819
| 15.39
| 6.72
| 456
|
[
3,
8,
10,
10
] |
[
"8×3+10-10"
] | true
| 5.42
| 0.956
| 5.86
| 2.22
| 868
|
[
2,
2,
7,
13
] |
[
"13+7+2+2",
"(13-7)×(2+2)",
"2×2+13+7",
"(13-7)×2×2"
] | true
| 7.27
| 0.963
| 7.68
| 2.9
| 393
|
[
3,
3,
4,
9
] |
[
"4×3+9+3",
"(9+3-4)×3",
"(9/3+3)×4"
] | true
| 9.6
| 0.922
| 9.9
| 3.86
| 675
|
[
3,
4,
11,
13
] |
[
"(13-11)×4×3",
"(13+11)×(4-3)",
"11×3+4-13",
"13×3-11-4"
] | true
| 5.93
| 0.966
| 6.42
| 2.38
| 760
|
[
10,
10,
12,
12
] |
[
"12+12+10-10"
] | true
| 5.34
| 0.987
| 5.8
| 1.93
| 1,340
|
[
3,
4,
5,
8
] |
[
"8×4-5-3",
"(5+3)×4-8",
"(8+3-5)×4",
"(8+4)×(5-3)",
"(5-4)×8×3",
"(5+4)×8/3"
] | true
| 6.6
| 0.963
| 7.09
| 2.7
| 728
|
[
2,
3,
3,
13
] |
[
"(13-3-2)×3",
"(13+3)×3/2",
"3×3+13+2",
"(13-3/3)×2"
] | true
| 7.17
| 0.94
| 7.73
| 3
| 419
|
[
2,
2,
5,
7
] |
[
"7×2+5×2"
] | true
| 9.19
| 0.892
| 9.23
| 3.72
| 375
|
[
2,
3,
3,
6
] |
[
"6×3+3×2",
"3×3×2+6",
"(3+3-2)×6",
"(3+3)×(6-2)",
"(6+3+3)×2"
] | true
| 8.07
| 0.963
| 8.53
| 2.96
| 412
|
[
1,
2,
4,
8
] |
[
"(8+4)×2×1",
"(4+1-2)×8",
"(8-2)×4×1",
"(4/2+1)×8"
] | true
| 6.18
| 0.966
| 6.6
| 2.38
| 74
|
[
7,
8,
10,
11
] |
[
"(11+10)×8/7"
] | true
| 104.51
| 0.299
| 26.05
| 15.84
| 1,274
|
[
4,
12,
12,
12
] |
[
"12×4-12-12",
"12×12/4-12"
] | true
| 9.13
| 0.865
| 9.45
| 4.85
| 1,070
|
[
2,
4,
7,
7
] |
[
"(7+7)×2-4"
] | true
| 35.74
| 0.512
| 17.72
| 9.75
| 500
|
[
3,
6,
10,
10
] |
[
"(3-6/10)×10",
"(10/10+3)×6"
] | true
| 8.01
| 0.855
| 8
| 3.76
| 825
|
[
1,
4,
5,
12
] |
[
"(5+1-4)×12",
"(12-5-1)×4"
] | true
| 5.96
| 0.957
| 6.4
| 2.36
| 195
|
[
2,
8,
8,
12
] |
[
"(8-2)×(12-8)",
"8/2+12+8",
"12×2+8-8"
] | true
| 6.01
| 0.975
| 6.54
| 2.48
| 616
|
[
1,
2,
11,
13
] |
[
"(13+11)×(2-1)"
] | true
| 6.92
| 0.935
| 7.54
| 3.16
| 114
|
[
2,
3,
3,
11
] |
[
"(11-2)×3-3",
"(3/3+11)×2"
] | true
| 7.37
| 0.897
| 7.69
| 3.36
| 417
|
[
2,
7,
8,
12
] |
[
"(12-7-2)×8",
"(8-7)×12×2"
] | true
| 6.37
| 0.952
| 6.83
| 2.6
| 601
|
[
2,
7,
9,
11
] |
[
"11×2+9-7",
"(9-7)×11+2"
] | true
| 12.03
| 0.837
| 11.6
| 5.5
| 604
|
[
8,
8,
11,
13
] |
[
"13+11+8-8",
"(13-11)×8+8"
] | true
| 5.64
| 0.971
| 6.16
| 2.3
| 1,303
|
[
1,
2,
6,
7
] |
[
"(7-2-1)×6",
"(7+6-1)×2",
"(7+1)×6/2",
"(7-1)×(6-2)"
] | true
| 7.09
| 0.955
| 7.48
| 2.61
| 89
|
[
3,
7,
9,
12
] |
[
"7×3+12-9",
"(7-3)×9-12",
"(12-7)×3+9",
"(12-9)×7+3"
] | true
| 12.14
| 0.857
| 11.99
| 5.73
| 848
|
[
5,
6,
7,
13
] |
[
"6×5+7-13",
"(13+7)×6/5",
"7×6-13-5",
"(13-7)×5-6"
] | true
| 10.72
| 0.862
| 10.82
| 5.55
| 1,111
|
[
8,
8,
11,
12
] |
[
"8/8+12+11"
] | true
| 6.19
| 0.91
| 6.59
| 2.71
| 1,302
|
[
3,
4,
9,
11
] |
[
"(11-9)×4×3",
"(11×9-3)/4"
] | true
| 8.3
| 0.897
| 8.55
| 4.06
| 753
|
[
2,
4,
6,
12
] |
[
"12+6+4+2",
"(4+2)×6-12",
"(4×2-6)×12",
"(12-4×2)×6",
"(4-2)×6+12",
"6×4/2+12",
"(6+2)×12/4",
"(12-4)×6/2",
"(6×4-12)×2",
"12/(2-6/4)"
] | true
| 10.44
| 0.944
| 11.21
| 4.84
| 498
|
[
5,
5,
6,
11
] |
[
"6×5+5-11",
"(11-5)×5-6"
] | true
| 10.3
| 0.872
| 10.3
| 4.72
| 1,078
|
[
8,
9,
10,
12
] |
[
"(10+8)×12/9",
"12×10/8+9"
] | true
| 51.92
| 0.431
| 23.06
| 14.34
| 1,307
|
[
5,
5,
8,
9
] |
[
"5×5+8-9",
"(8-5)×5+9"
] | true
| 8.37
| 0.899
| 8.84
| 4
| 1,084
|
[
9,
11,
11,
11
] |
[
"11+11+11-9"
] | true
| 6.95
| 0.955
| 7.3
| 2.75
| 1,331
|
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