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,
5,
11,
12
] |
[
"12/(11/2-5)",
"(11-5)×2+12"
] | true
| 12.56
| 0.772
| 10.88
| 5.66
| 558
|
[
3,
6,
7,
8
] |
[
"8+7+6+3",
"(8+3-7)×6",
"(7-6)×8×3"
] | true
| 6.4
| 0.979
| 6.82
| 2.31
| 810
|
[
1,
1,
2,
12
] |
[
"12×2+1-1",
"12/(1-1/2)"
] | true
| 4.61
| 0.992
| 4.93
| 1.53
| 10
|
[
1,
3,
6,
7
] |
[
"(7-3)×6×1",
"(7+1)×(6-3)",
"6×3+7-1",
"(7-1)×3+6"
] | true
| 6.98
| 0.963
| 7.38
| 2.79
| 147
|
[
2,
7,
8,
13
] |
[
"(13-7)×8/2",
"8/2+13+7",
"(13+7-8)×2"
] | true
| 7.48
| 0.942
| 8
| 3.17
| 602
|
[
1,
6,
9,
12
] |
[
"(9-6-1)×12",
"(12+1-9)×6",
"12/(9/6-1)",
"6/(1-9/12)"
] | true
| 5.71
| 0.957
| 6.08
| 2.11
| 282
|
[
1,
7,
8,
12
] |
[
"(8+1-7)×12",
"(7-1)×(12-8)"
] | true
| 6.58
| 0.956
| 7.03
| 2.67
| 298
|
[
3,
4,
7,
10
] |
[
"10+7+4+3",
"(10+3-7)×4",
"(10-4)×(7-3)"
] | true
| 8.45
| 0.933
| 8.73
| 3.49
| 744
|
[
1,
7,
7,
10
] |
[
"(7+1)×(10-7)",
"(10+7+7)×1"
] | true
| 5.76
| 0.98
| 6.19
| 2.13
| 291
|
[
3,
4,
9,
9
] |
[
"(9+9)×4/3",
"9×4-9-3",
"(9-9/3)×4",
"(9-4)×3+9"
] | true
| 12.83
| 0.845
| 12.48
| 5.23
| 752
|
[
3,
9,
11,
11
] |
[
"(3-9/11)×11",
"(9-11/11)×3"
] | true
| 7.55
| 0.855
| 7.71
| 3.43
| 885
|
[
4,
5,
10,
13
] |
[
"13+10+5-4"
] | true
| 9.3
| 0.914
| 9.81
| 4.45
| 977
|
[
2,
3,
3,
7
] |
[
"(7-3)×3×2",
"(7+3-2)×3",
"(7+2)×3-3"
] | true
| 8.63
| 0.919
| 8.99
| 3.71
| 413
|
[
2,
7,
7,
12
] |
[
"12+7+7-2",
"12×2+7-7"
] | true
| 5.3
| 0.988
| 5.69
| 1.9
| 596
|
[
2,
4,
6,
7
] |
[
"(6+2)×(7-4)",
"7×4+2-6",
"(6-2)×7-4",
"7×2+6+4",
"6/(2-7/4)"
] | true
| 10.58
| 0.899
| 10.66
| 4.37
| 493
|
[
2,
3,
3,
3
] |
[
"(3+3+2)×3",
"(3×3+3)×2"
] | true
| 13.24
| 0.822
| 12.17
| 6.04
| 410
|
[
2,
3,
4,
4
] |
[
"(3+2)×4+4",
"4×4×3/2",
"(4-2)×4×3"
] | true
| 9.43
| 0.942
| 9.83
| 3.62
| 420
|
[
1,
3,
4,
11
] |
[
"(11+1-4)×3",
"(11-3)×(4-1)",
"4×3+11+1"
] | true
| 7.24
| 0.96
| 7.77
| 2.95
| 135
|
[
5,
6,
10,
13
] |
[
"13+10+6-5"
] | true
| 8.63
| 0.912
| 9.35
| 4.41
| 1,125
|
[
2,
2,
2,
3
] |
[
"(2+2)×3×2",
"3×2×2×2"
] | true
| 5.71
| 0.99
| 5.97
| 1.71
| 342
|
[
4,
6,
11,
12
] |
[
"(12-11)×6×4"
] | true
| 6.6
| 0.929
| 7.03
| 2.97
| 1,008
|
[
7,
8,
8,
9
] |
[
"(9-7)×8+8"
] | true
| 7.39
| 0.864
| 7.82
| 3.96
| 1,265
|
[
4,
6,
12,
12
] |
[
"(12-6-4)×12",
"6×4+12-12",
"12×6-12×4",
"(4-12/6)×12"
] | true
| 6.64
| 0.97
| 7.12
| 2.47
| 1,009
|
[
2,
5,
9,
12
] |
[
"(9-5-2)×12",
"12+9+5-2",
"12/(5-9/2)",
"(9-5)×12/2"
] | true
| 7.22
| 0.957
| 7.67
| 2.92
| 553
|
[
1,
3,
7,
12
] |
[
"(7-1)×12/3"
] | true
| 11.8
| 0.856
| 11.25
| 5.09
| 158
|
[
6,
6,
6,
8
] |
[
"(6+6)×(8-6)",
"(6+6-8)×6"
] | true
| 9.58
| 0.914
| 9.91
| 4.25
| 1,178
|
[
3,
5,
5,
11
] |
[
"11+5+5+3"
] | true
| 14.51
| 0.798
| 13.41
| 5.63
| 767
|
[
6,
6,
6,
11
] |
[
"(11-6)×6-6"
] | true
| 7.35
| 0.888
| 7.65
| 3.55
| 1,181
|
[
3,
6,
9,
12
] |
[
"12×6×3/9",
"12+9+6-3",
"(9+3)×12/6",
"(9-3)×6-12"
] | true
| 10.53
| 0.929
| 10.96
| 4.24
| 823
|
[
2,
8,
9,
11
] |
[
"8/2+11+9",
"(11+9-8)×2"
] | true
| 8.93
| 0.908
| 9.35
| 3.94
| 620
|
[
2,
3,
11,
11
] |
[
"11×3+2-11"
] | true
| 20.49
| 0.679
| 15.48
| 7.87
| 467
|
[
2,
5,
5,
12
] |
[
"12+5+5+2",
"12×2+5-5"
] | true
| 5.47
| 0.988
| 5.88
| 1.96
| 529
|
[
8,
8,
9,
13
] |
[
"(13-9)×8-8"
] | true
| 9.36
| 0.811
| 8.94
| 4.86
| 1,299
|
[
4,
5,
6,
6
] |
[
"(6-5)×6×4",
"(6/6+5)×4"
] | true
| 6.5
| 0.954
| 6.85
| 2.37
| 949
|
[
1,
12,
12,
12
] |
[
"(12/12+1)×12"
] | true
| 6.74
| 0.938
| 6.95
| 2.57
| 339
|
[
1,
2,
7,
7
] |
[
"(7×7-1)/2"
] | true
| 34.41
| 0.548
| 18.13
| 10.73
| 96
|
[
4,
4,
5,
5
] |
[
"5×5-4/4",
"(5+5-4)×4",
"(4/5+4)×5"
] | true
| 6.75
| 0.933
| 7.25
| 2.65
| 908
|
[
4,
5,
6,
10
] |
[
"5×4+10-6",
"6×5+4-10",
"(10-4)×5-6",
"(10-6)×5+4"
] | true
| 10.21
| 0.904
| 10.67
| 4.44
| 953
|
[
3,
4,
12,
13
] |
[
"13+12+3-4"
] | true
| 7.95
| 0.933
| 8.59
| 3.78
| 762
|
[
2,
4,
6,
8
] |
[
"8×6/(4-2)",
"8×6×2/4",
"8×4-6-2",
"(6+2)×4-8",
"6×2+8+4",
"(6-2)×4+8",
"(8/4+2)×6",
"(8+6)×2-4"
] | true
| 11.45
| 0.935
| 11.83
| 4.36
| 494
|
[
1,
3,
7,
9
] |
[
"(7+1)×9/3"
] | true
| 14.55
| 0.802
| 13.05
| 5.69
| 156
|
[
4,
4,
8,
10
] |
[
"(10+4-8)×4",
"(10-4)×(8-4)",
"10×8/4+4"
] | true
| 9.03
| 0.912
| 9.38
| 4.47
| 930
|
[
2,
5,
6,
11
] |
[
"11+6+5+2",
"(11-5-2)×6",
"(11-5)×(6-2)",
"(11+6-5)×2"
] | true
| 6.76
| 0.963
| 7.25
| 2.64
| 536
|
[
3,
3,
9,
9
] |
[
"9+9+3+3",
"9×3-9/3",
"(3-3/9)×9",
"9×9/3-3"
] | true
| 7.43
| 0.959
| 7.78
| 2.79
| 705
|
[
4,
6,
12,
13
] |
[
"(13-12)×6×4"
] | true
| 6.4
| 0.938
| 6.88
| 2.91
| 1,010
|
[
4,
5,
5,
6
] |
[
"6×4+5-5"
] | true
| 5.65
| 0.975
| 6.08
| 2.12
| 944
|
[
2,
3,
9,
12
] |
[
"(9-3)×2+12"
] | true
| 21.55
| 0.664
| 13.76
| 8.07
| 462
|
[
2,
4,
5,
12
] |
[
"(12-4)×(5-2)",
"(5-2)×4+12",
"(5-4)×12×2"
] | true
| 6.58
| 0.947
| 7.02
| 2.86
| 490
|
[
2,
5,
6,
7
] |
[
"(7+2-5)×6",
"6×2+7+5",
"(7-5)×6×2"
] | true
| 8.24
| 0.924
| 8.68
| 3.67
| 532
|
[
2,
2,
2,
12
] |
[
"(2+2)×12/2",
"(2×2-2)×12",
"12×2+2-2"
] | true
| 5
| 0.992
| 5.36
| 1.71
| 350
|
[
2,
2,
4,
4
] |
[
"(4×2-2)×4",
"(4×2+4)×2"
] | true
| 20.23
| 0.716
| 15.55
| 8.4
| 363
|
[
1,
7,
13,
13
] |
[
"(13×13-1)/7"
] | true
| 48.91
| 0.412
| 14.87
| 9.19
| 308
|
[
2,
10,
12,
13
] |
[
"13×2+10-12",
"(12+10)/2+13",
"(12-10)×13-2"
] | true
| 14.51
| 0.813
| 13.58
| 6.28
| 649
|
[
2,
5,
5,
9
] |
[
"5×2+9+5",
"(5-2)×5+9"
] | true
| 16.2
| 0.785
| 14.74
| 6.1
| 526
|
[
5,
6,
11,
13
] |
[
"(13+11)×(6-5)",
"(13-6)×5-11"
] | true
| 7.42
| 0.914
| 7.91
| 3.42
| 1,128
|
[
3,
6,
12,
13
] |
[
"(13+3-12)×6"
] | true
| 9.27
| 0.865
| 9.18
| 4.46
| 832
|
[
5,
7,
10,
10
] |
[
"10×7/5+10"
] | true
| 13.65
| 0.772
| 12.45
| 5.53
| 1,142
|
[
8,
9,
11,
11
] |
[
"(11-8)×11-9"
] | true
| 26.08
| 0.584
| 16.62
| 8.85
| 1,309
|
[
2,
2,
3,
3
] |
[
"(3+3)×(2+2)",
"(3+3)×2×2",
"(3×2+2)×3"
] | true
| 8.01
| 0.934
| 8.35
| 3.24
| 352
|
[
1,
3,
3,
9
] |
[
"(9-3)×(3+1)",
"(9+3)×(3-1)",
"(3-1/3)×9",
"(9×3-3)×1"
] | true
| 6.65
| 0.968
| 7.28
| 2.87
| 124
|
[
1,
3,
13,
13
] |
[
"13+13+1-3"
] | true
| 6.7
| 0.972
| 7.22
| 2.65
| 178
|
[
1,
6,
11,
13
] |
[
"(13×11+1)/6"
] | true
| 55.57
| 0.385
| 19.72
| 10.9
| 287
|
[
8,
9,
11,
13
] |
[
"(13+11)×(9-8)"
] | true
| 7.83
| 0.905
| 8.29
| 3.8
| 1,311
|
[
5,
7,
7,
9
] |
[
"(7+5)×(9-7)"
] | true
| 13.42
| 0.74
| 11.42
| 5.28
| 1,132
|
[
1,
7,
8,
8
] |
[
"8+8+7+1"
] | true
| 6.16
| 0.967
| 6.67
| 2.66
| 294
|
[
4,
4,
6,
10
] |
[
"10+6+4+4",
"(6-4)×10+4"
] | true
| 12.64
| 0.88
| 12.64
| 5.29
| 918
|
[
2,
2,
7,
8
] |
[
"(7-2-2)×8",
"(7-2×2)×8",
"7×2+8+2"
] | true
| 7.62
| 0.936
| 8
| 3.05
| 390
|
[
2,
2,
4,
11
] |
[
"11×2+4-2",
"(4-2)×11+2",
"11×4/2+2",
"11×2+4/2"
] | true
| 8.28
| 0.918
| 8.72
| 3.72
| 370
|
[
12,
12,
12,
12
] |
[
"12+12+12-12"
] | true
| 5.27
| 0.993
| 5.72
| 2.08
| 1,358
|
[
4,
6,
6,
6
] |
[
"6×4+6-6",
"(6+6)×(6-4)"
] | true
| 5.6
| 0.985
| 5.99
| 2.03
| 984
|
[
1,
2,
6,
6
] |
[
"(2+1)×6+6",
"(6+6)×2×1",
"(6-2)×6×1",
"(6/2+1)×6"
] | true
| 5.99
| 0.976
| 6.43
| 2.22
| 88
|
[
3,
5,
6,
8
] |
[
"8×6/(5-3)",
"(5-6/3)×8",
"(6-5)×8×3"
] | true
| 7.43
| 0.938
| 7.96
| 3.23
| 771
|
[
2,
11,
12,
13
] |
[
"(13+11-12)×2",
"(13+11)/2+12"
] | true
| 9.15
| 0.898
| 9.57
| 4.11
| 654
|
[
2,
5,
8,
11
] |
[
"(11-5)×8/2",
"(11+5)×2-8"
] | true
| 10.29
| 0.859
| 10.45
| 5.18
| 548
|
[
3,
5,
7,
13
] |
[
"(13×5+7)/3"
] | true
| 127.36
| 0.236
| 41.1
| 22.81
| 782
|
[
2,
6,
8,
12
] |
[
"12+8+6-2",
"12×8/(6-2)",
"(8×2-12)×6",
"(8-2)×6-12",
"(12-6)×8/2",
"(6-8/2)×12",
"8×6-12×2"
] | true
| 10.55
| 0.942
| 11.28
| 4.55
| 579
|
[
4,
10,
11,
12
] |
[
"12/4+11+10"
] | true
| 25.19
| 0.631
| 17.86
| 9.14
| 1,065
|
[
3,
4,
5,
10
] |
[
"10×4×3/5",
"(5-3)×10+4"
] | true
| 8.56
| 0.903
| 8.9
| 4.12
| 730
|
[
1,
7,
7,
9
] |
[
"9+7+7+1"
] | true
| 7.19
| 0.961
| 7.57
| 2.88
| 290
|
[
1,
6,
10,
13
] |
[
"(13+1-10)×6"
] | true
| 8.64
| 0.882
| 8.87
| 4.22
| 285
|
[
4,
5,
8,
11
] |
[
"(11-5)×(8-4)",
"(11+4)×8/5"
] | true
| 15.8
| 0.729
| 12.56
| 7.24
| 967
|
[
7,
10,
11,
13
] |
[
"(13-11)×7+10"
] | true
| 13.72
| 0.74
| 11.37
| 5.96
| 1,289
|
[
5,
8,
9,
12
] |
[
"12+9+8-5",
"12×8/(9-5)"
] | true
| 9.59
| 0.922
| 10.02
| 4.04
| 1,155
|
[
4,
10,
12,
13
] |
[
"(12-4)×(13-10)",
"(13-10)×4+12"
] | true
| 11.42
| 0.815
| 10.62
| 5.63
| 1,068
|
[
1,
6,
6,
10
] |
[
"(10-6)×6×1"
] | true
| 6.94
| 0.936
| 7.29
| 3.12
| 266
|
[
1,
9,
11,
12
] |
[
"(11-9)×12×1"
] | true
| 6.78
| 0.938
| 7.29
| 3.09
| 327
|
[
2,
2,
2,
10
] |
[
"10×2+2+2",
"10×2+2×2"
] | true
| 7.75
| 0.939
| 8.18
| 3.36
| 348
|
[
2,
3,
4,
7
] |
[
"(7+2-3)×4",
"(4+2)×(7-3)",
"(7+3)×2+4"
] | true
| 11.16
| 0.867
| 11.04
| 4.95
| 423
|
[
1,
2,
3,
3
] |
[
"(3+1)×3×2"
] | true
| 8.59
| 0.956
| 8.97
| 2.99
| 59
|
[
2,
3,
5,
7
] |
[
"7×3+5-2",
"(5-2)×7+3",
"5×3+7+2"
] | true
| 11.68
| 0.892
| 11.78
| 4.92
| 432
|
[
7,
9,
11,
12
] |
[
"(11+7)×12/9",
"(11-7)×9-12"
] | true
| 37.51
| 0.503
| 18.63
| 10.96
| 1,284
|
[
2,
3,
5,
10
] |
[
"(10+2)×(5-3)",
"(10+5-3)×2"
] | true
| 13.48
| 0.802
| 12.18
| 5.42
| 435
|
[
3,
10,
11,
13
] |
[
"(11-3)×(13-10)",
"(11+10-13)×3"
] | true
| 17.14
| 0.71
| 13.86
| 6.6
| 893
|
[
4,
4,
12,
13
] |
[
"13+12-4/4",
"(13-4)×4-12"
] | true
| 6.75
| 0.922
| 7.13
| 2.64
| 942
|
[
2,
4,
4,
9
] |
[
"(9-2)×4-4"
] | true
| 17.19
| 0.732
| 13.77
| 7.61
| 478
|
[
4,
7,
10,
11
] |
[
"11+10+7-4",
"(10-4)×(11-7)",
"(10+7-11)×4"
] | true
| 6.96
| 0.971
| 7.55
| 2.81
| 1,027
|
[
3,
3,
8,
13
] |
[
"(13+3-8)×3"
] | true
| 16.59
| 0.692
| 11.86
| 6.48
| 704
|
[
1,
10,
12,
13
] |
[
"(13-10-1)×12",
"(13-1)×(12-10)"
] | true
| 7.2
| 0.945
| 7.58
| 2.85
| 333
|
[
6,
7,
9,
12
] |
[
"(9+7-12)×6",
"(9-7)×6+12"
] | true
| 10.11
| 0.864
| 10.04
| 4.91
| 1,210
|
[
3,
6,
9,
9
] |
[
"9×3+6-9",
"(9-6)×9-3",
"(9/9+3)×6"
] | true
| 7.08
| 0.94
| 7.65
| 3.29
| 820
|
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