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,
7,
8,
9
] |
[
"(9+7)×2-8"
] | true
| 76.32
| 0.387
| 19.6
| 12.12
| 599
|
[
7,
9,
11,
11
] |
[
"11+11+9-7"
] | true
| 6.38
| 0.958
| 6.86
| 2.66
| 1,283
|
[
2,
4,
4,
12
] |
[
"(12-4-2)×4",
"4×2+12+4",
"12×4/(4-2)",
"(4-4/2)×12",
"12×2+4-4"
] | true
| 5.93
| 0.985
| 6.31
| 2.16
| 481
|
[
5,
6,
8,
10
] |
[
"8×6×5/10",
"8×5-10-6",
"(8-5)×10-6"
] | true
| 10.52
| 0.871
| 10.63
| 4.62
| 1,114
|
[
5,
6,
8,
9
] |
[
"(8+5-9)×6",
"(9+6)×8/5"
] | true
| 9.73
| 0.899
| 10.01
| 4.44
| 1,113
|
[
2,
2,
9,
10
] |
[
"(9-2)×2+10"
] | true
| 19.64
| 0.655
| 14.61
| 7.52
| 398
|
[
6,
7,
12,
13
] |
[
"13+12+6-7",
"(13-7)×6-12"
] | true
| 6.8
| 0.955
| 7.31
| 2.78
| 1,218
|
[
3,
4,
4,
13
] |
[
"13+4+4+3",
"(13-4-3)×4"
] | true
| 10.3
| 0.888
| 10.38
| 4.33
| 724
|
[
1,
9,
11,
13
] |
[
"(13-1)×(11-9)"
] | true
| 9.62
| 0.876
| 9.79
| 4.2
| 328
|
[
6,
6,
8,
10
] |
[
"(6+6)×(10-8)",
"(8+6-10)×6"
] | true
| 9.1
| 0.905
| 9.37
| 4.22
| 1,189
|
[
1,
8,
10,
12
] |
[
"(12+1-10)×8",
"(10-8)×12×1"
] | true
| 5.92
| 0.958
| 6.23
| 2.19
| 318
|
[
4,
8,
12,
12
] |
[
"(12+4)×12/8",
"(4-12/12)×8"
] | true
| 12.93
| 0.857
| 12.33
| 5.97
| 1,052
|
[
1,
2,
5,
8
] |
[
"(5+1)×8/2",
"(8+5-1)×2",
"(8-2)×(5-1)",
"(5-2)×8×1"
] | true
| 5.55
| 0.958
| 5.97
| 2.24
| 83
|
[
1,
3,
4,
5
] |
[
"5×4+3+1",
"(3+1)×5+4",
"(5+4-1)×3",
"(5+3)×(4-1)"
] | true
| 7.26
| 0.975
| 7.75
| 2.49
| 129
|
[
5,
8,
11,
13
] |
[
"(11+5-13)×8",
"(13-5)×(11-8)"
] | true
| 8.45
| 0.886
| 8.57
| 3.52
| 1,160
|
[
1,
1,
3,
4
] |
[
"(1+1)×4×3"
] | true
| 6.15
| 0.981
| 6.48
| 2.05
| 12
|
[
5,
6,
8,
12
] |
[
"(12+8)×6/5",
"12×6/(8-5)",
"(5-12/6)×8"
] | true
| 10.47
| 0.877
| 10.44
| 4.12
| 1,115
|
[
1,
3,
10,
10
] |
[
"10+10+3+1"
] | true
| 5.59
| 0.975
| 5.92
| 2.01
| 171
|
[
3,
9,
12,
12
] |
[
"12×12/(9-3)",
"12×9/3-12",
"(9-12/12)×3"
] | true
| 7.85
| 0.909
| 8.4
| 3.61
| 888
|
[
6,
10,
11,
12
] |
[
"12×10/(11-6)"
] | true
| 17.58
| 0.692
| 13.65
| 6.66
| 1,248
|
[
1,
5,
11,
11
] |
[
"(11×11-1)/5"
] | true
| 42.99
| 0.436
| 17.17
| 10.45
| 260
|
[
4,
8,
8,
10
] |
[
"(8+4)×(10-8)",
"10×4-8-8",
"8×8-10×4",
"(8+8-10)×4"
] | true
| 12.11
| 0.858
| 11.92
| 5.58
| 1,037
|
[
3,
3,
7,
8
] |
[
"3×3+8+7"
] | true
| 21.74
| 0.691
| 17.49
| 8.32
| 695
|
[
6,
10,
12,
13
] |
[
"12×6/(13-10)"
] | true
| 11
| 0.824
| 10.46
| 4.9
| 1,250
|
[
5,
7,
9,
12
] |
[
"(9+5)×12/7"
] | true
| 59.78
| 0.396
| 18.45
| 11.83
| 1,140
|
[
3,
3,
11,
13
] |
[
"13+11+3-3"
] | true
| 6.2
| 0.971
| 6.74
| 2.56
| 712
|
[
1,
10,
12,
12
] |
[
"(12-10)×12×1"
] | true
| 6.31
| 0.959
| 6.89
| 2.91
| 332
|
[
2,
2,
3,
6
] |
[
"(2/2+3)×6",
"(6-2)×3×2",
"(3×2-2)×6",
"(3×2+6)×2"
] | true
| 9.14
| 0.917
| 9.46
| 4.14
| 355
|
[
1,
3,
5,
6
] |
[
"6×3+5+1",
"(5+1)×3+6"
] | true
| 14.96
| 0.866
| 14.63
| 6.03
| 138
|
[
2,
2,
6,
6
] |
[
"(6+2)×6/2",
"6×2+6×2"
] | true
| 7.57
| 0.96
| 8.1
| 3.08
| 381
|
[
1,
7,
7,
11
] |
[
"11+7+7-1",
"(7-1)×(11-7)"
] | true
| 6.7
| 0.97
| 7.28
| 2.64
| 292
|
[
6,
7,
12,
12
] |
[
"(12+12)×(7-6)"
] | true
| 5.58
| 0.958
| 5.95
| 2.03
| 1,217
|
[
2,
4,
7,
10
] |
[
"(10-7)×4×2",
"(4-2)×7+10",
"7×4/2+10",
"(10-2)×(7-4)"
] | true
| 8.56
| 0.912
| 8.82
| 3.86
| 503
|
[
1,
3,
5,
9
] |
[
"(9-3)×(5-1)",
"(5×3+9)×1",
"(5/3+1)×9"
] | true
| 10.47
| 0.907
| 10.72
| 4.59
| 141
|
[
5,
5,
7,
10
] |
[
"(7+5)×10/5"
] | true
| 13.71
| 0.742
| 11.78
| 5.2
| 1,081
|
[
6,
7,
7,
11
] |
[
"7×6-11-7"
] | true
| 50.13
| 0.43
| 28.85
| 15.28
| 1,204
|
[
2,
6,
6,
11
] |
[
"(6/6+11)×2"
] | true
| 7.74
| 0.831
| 7.51
| 3.24
| 566
|
[
1,
3,
5,
7
] |
[
"(7+5)×(3-1)",
"(5+1)×(7-3)"
] | true
| 9.32
| 0.895
| 9.53
| 4.12
| 139
|
[
6,
6,
9,
10
] |
[
"(9-6)×10-6",
"(10+6)×9/6"
] | true
| 17.62
| 0.702
| 13.9
| 7.22
| 1,193
|
[
4,
8,
12,
13
] |
[
"(12+4-13)×8",
"12/4+13+8"
] | true
| 7.67
| 0.919
| 8.32
| 3.73
| 1,053
|
[
1,
5,
5,
5
] |
[
"(5-1/5)×5"
] | true
| 47.66
| 0.434
| 12.55
| 7.76
| 224
|
[
4,
4,
5,
12
] |
[
"(5+4)×4-12",
"(12-5)×4-4"
] | true
| 13.64
| 0.791
| 12.1
| 6.42
| 914
|
[
1,
6,
8,
8
] |
[
"(8+1-6)×8",
"8/(8/6-1)"
] | true
| 7.08
| 0.932
| 7.41
| 2.98
| 274
|
[
1,
9,
9,
12
] |
[
"(9-1)×(12-9)",
"(9/9+1)×12"
] | true
| 5.48
| 0.958
| 5.78
| 1.81
| 323
|
[
2,
3,
9,
10
] |
[
"10+9+3+2",
"10×3/2+9",
"(9×2-10)×3",
"(10-2)×9/3"
] | true
| 10.79
| 0.899
| 11.02
| 4.36
| 461
|
[
2,
2,
13,
13
] |
[
"(2-2/13)×13"
] | true
| 68.63
| 0.368
| 15.35
| 9.38
| 409
|
[
1,
9,
10,
13
] |
[
"(9-1)×(13-10)"
] | true
| 10.99
| 0.836
| 10.53
| 4.58
| 325
|
[
2,
7,
9,
13
] |
[
"9×2+13-7",
"13×2+7-9",
"(9-7)×13-2"
] | true
| 9.86
| 0.874
| 10.04
| 4.92
| 605
|
[
1,
7,
9,
9
] |
[
"9+9+7-1"
] | true
| 7.56
| 0.948
| 8.02
| 3.16
| 299
|
[
4,
5,
5,
10
] |
[
"10+5+5+4"
] | true
| 12.02
| 0.812
| 11.13
| 4.48
| 948
|
[
2,
3,
8,
12
] |
[
"(12-8)×3×2",
"(8-3×2)×12",
"8×3/2+12",
"(8-2)×12/3",
"(12-8/2)×3",
"(12/2-3)×8",
"(8×3-12)×2",
"(12/3+8)×2"
] | true
| 9.41
| 0.932
| 9.93
| 3.89
| 458
|
[
3,
8,
9,
11
] |
[
"9×3+8-11",
"(11-8)×9-3"
] | true
| 14.32
| 0.797
| 13.13
| 7.09
| 865
|
[
7,
7,
12,
12
] |
[
"(7+7-12)×12",
"12+12+7-7"
] | true
| 5.22
| 0.986
| 5.59
| 1.84
| 1,263
|
[
6,
6,
7,
11
] |
[
"11×6-7×6"
] | true
| 25.91
| 0.581
| 13.95
| 8.68
| 1,185
|
[
5,
9,
12,
12
] |
[
"(9+5-12)×12",
"(12×9+12)/5"
] | true
| 11.15
| 0.832
| 10.93
| 4.85
| 1,168
|
[
3,
5,
8,
13
] |
[
"8×5-13-3"
] | true
| 52.88
| 0.426
| 31.55
| 14.74
| 787
|
[
3,
4,
4,
12
] |
[
"(3-4/4)×12",
"(12/4+3)×4"
] | true
| 7.77
| 0.906
| 8.05
| 3.35
| 723
|
[
6,
8,
10,
13
] |
[
"(10+6-13)×8"
] | true
| 8.65
| 0.865
| 8.73
| 3.87
| 1,231
|
[
4,
5,
13,
13
] |
[
"(13/13+5)×4"
] | true
| 6.58
| 0.876
| 6.78
| 2.89
| 983
|
[
4,
5,
9,
13
] |
[
"5×4+13-9",
"(13-9)×5+4"
] | true
| 9.01
| 0.893
| 9.68
| 4.99
| 973
|
[
2,
6,
8,
8
] |
[
"8+8+6+2",
"(6-2)×8-8",
"(8-8/2)×6"
] | true
| 9.63
| 0.928
| 10.04
| 4.14
| 575
|
[
5,
7,
13,
13
] |
[
"13+13+5-7"
] | true
| 7.6
| 0.941
| 8.01
| 3.25
| 1,149
|
[
4,
7,
9,
11
] |
[
"(7-4)×11-9",
"(9-4)×7-11"
] | true
| 37.33
| 0.523
| 23.35
| 11.52
| 1,023
|
[
2,
7,
12,
12
] |
[
"(7×2-12)×12",
"(12+2)×12/7"
] | true
| 22.11
| 0.621
| 12.95
| 7.89
| 610
|
[
6,
9,
12,
12
] |
[
"(9-6)×12-12",
"(12+6)×12/9",
"12×6/(12-9)"
] | true
| 6.97
| 0.893
| 7.53
| 3.73
| 1,244
|
[
2,
8,
11,
12
] |
[
"(12+2-11)×8"
] | true
| 8.68
| 0.884
| 8.9
| 4.23
| 628
|
[
3,
4,
9,
13
] |
[
"(13+4-9)×3"
] | true
| 10.96
| 0.792
| 9.82
| 5.58
| 755
|
[
1,
8,
11,
13
] |
[
"(13+1-11)×8"
] | true
| 8.23
| 0.883
| 8.41
| 3.59
| 321
|
[
2,
4,
8,
8
] |
[
"4×2+8+8",
"(4-2)×8+8",
"8×4/2+8",
"(8-2)×(8-4)",
"(8+8-4)×2"
] | true
| 8.25
| 0.937
| 8.89
| 4.13
| 506
|
[
3,
6,
7,
7
] |
[
"(7+7-6)×3",
"(7/7+3)×6"
] | true
| 5.96
| 0.935
| 6.35
| 2.43
| 809
|
[
3,
3,
9,
10
] |
[
"10×3+3-9"
] | true
| 15.55
| 0.777
| 13.99
| 6.4
| 706
|
[
4,
9,
9,
10
] |
[
"10+9+9-4"
] | true
| 10.03
| 0.899
| 10.28
| 4.17
| 1,055
|
[
4,
4,
7,
9
] |
[
"9+7+4+4",
"(9+4-7)×4"
] | true
| 7.71
| 0.935
| 8.13
| 3.48
| 924
|
[
1,
1,
8,
8
] |
[
"(1+1)×8+8"
] | true
| 7.23
| 0.897
| 7.72
| 3.87
| 39
|
[
1,
1,
5,
5
] |
[
"(5+1)×(5-1)",
"(5×5-1)×1"
] | true
| 5.36
| 0.991
| 5.74
| 1.83
| 30
|
[
1,
5,
7,
11
] |
[
"11+7+5+1",
"(5+1)×(11-7)",
"(11+1)×(7-5)",
"(7×5-11)×1"
] | true
| 6
| 0.986
| 6.49
| 2.17
| 242
|
[
9,
11,
13,
13
] |
[
"13+13+9-11"
] | true
| 7.72
| 0.922
| 8.27
| 3.29
| 1,334
|
[
4,
5,
10,
10
] |
[
"10×10/5+4",
"(10/10+5)×4"
] | true
| 7.1
| 0.913
| 7.49
| 3.25
| 974
|
[
1,
3,
4,
12
] |
[
"(12-4)×3×1",
"(4+1-3)×12",
"12×4/(3-1)",
"(4×3+12)×1"
] | true
| 5.57
| 0.986
| 5.99
| 1.95
| 136
|
[
1,
8,
8,
9
] |
[
"9+8+8-1"
] | true
| 6.44
| 0.965
| 6.96
| 2.68
| 310
|
[
6,
6,
10,
12
] |
[
"(6+6)×(12-10)",
"(6+6-10)×12",
"(10+6-12)×6",
"(12-6)×(10-6)"
] | true
| 7.95
| 0.939
| 8.36
| 3.19
| 1,197
|
[
2,
6,
11,
13
] |
[
"(13-11)×6×2",
"(13+2-11)×6"
] | true
| 7.82
| 0.901
| 8.01
| 3.44
| 590
|
[
2,
4,
5,
8
] |
[
"(8-5)×4×2",
"(4×2-5)×8",
"(5+2-4)×8",
"(5-4/2)×8",
"8×5/2+4",
"5×4+8/2",
"(5×4-8)×2"
] | true
| 7.04
| 0.952
| 7.44
| 2.81
| 486
|
[
6,
7,
7,
10
] |
[
"(7+7-10)×6"
] | true
| 14.08
| 0.722
| 11.24
| 5.54
| 1,203
|
[
8,
11,
12,
12
] |
[
"(11-8)×12-12"
] | true
| 8.24
| 0.772
| 7.55
| 3.8
| 1,319
|
[
11,
11,
12,
12
] |
[
"12+12+11-11"
] | true
| 5.15
| 0.988
| 5.54
| 1.87
| 1,352
|
[
2,
6,
6,
6
] |
[
"6×2+6+6",
"6×6-6×2",
"6×6/2+6"
] | true
| 7.61
| 0.961
| 8.13
| 3.05
| 561
|
[
1,
1,
1,
13
] |
[
"(13-1)×(1+1)"
] | true
| 5.55
| 0.974
| 5.88
| 1.78
| 3
|
[
1,
2,
10,
13
] |
[
"13+10+2-1"
] | true
| 6.69
| 0.971
| 7.2
| 2.74
| 111
|
[
3,
5,
6,
7
] |
[
"(7+5)×6/3",
"(7+6-5)×3"
] | true
| 9.17
| 0.896
| 9.23
| 3.89
| 770
|
[
5,
10,
13,
13
] |
[
"10×5-13-13",
"13+13-10/5",
"(13-5)×(13-10)"
] | true
| 7.58
| 0.927
| 8.01
| 2.78
| 1,175
|
[
3,
8,
12,
12
] |
[
"8×3+12-12",
"12/3+12+8",
"(12-8)×3+12"
] | true
| 6.09
| 0.967
| 6.54
| 2.47
| 873
|
[
4,
8,
9,
9
] |
[
"(4-9/9)×8"
] | true
| 6.38
| 0.907
| 6.59
| 2.38
| 1,041
|
[
3,
6,
6,
7
] |
[
"7×6-6×3",
"(7+3-6)×6",
"(6/6+7)×3"
] | true
| 6.71
| 0.937
| 7.18
| 2.71
| 802
|
[
4,
6,
10,
12
] |
[
"12+10+6-4",
"(10-4)×6-12",
"12×10/4-6",
"12×10/6+4"
] | true
| 8.85
| 0.939
| 9.4
| 4.05
| 1,006
|
[
2,
2,
5,
8
] |
[
"(8+5)×2-2"
] | true
| 26.55
| 0.632
| 17.21
| 9.35
| 376
|
[
5,
7,
12,
12
] |
[
"12×7-12×5"
] | true
| 16.1
| 0.66
| 10.65
| 6.25
| 1,148
|
[
2,
3,
7,
13
] |
[
"7×2+13-3",
"(13+2-7)×3"
] | true
| 12.18
| 0.863
| 11.97
| 5.41
| 453
|
[
2,
6,
7,
9
] |
[
"9+7+6+2",
"(9-7)×6×2",
"(9+2-7)×6",
"7×6-9×2"
] | true
| 7.34
| 0.961
| 7.85
| 3.01
| 570
|
[
1,
8,
9,
11
] |
[
"(11+1-9)×8",
"(9-1)×(11-8)",
"9/(11/8-1)"
] | true
| 7.42
| 0.928
| 7.71
| 3.07
| 314
|
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