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
|
|---|---|---|---|---|---|---|---|
[
3,
5,
9,
12
] |
[
"(5+3)×(12-9)",
"(5-9/3)×12",
"(12+5-9)×3",
"(9-5)×3+12"
] | true
| 9.09
| 0.9
| 9.37
| 4.08
| 790
|
[
3,
6,
11,
12
] |
[
"(11-6-3)×12",
"(12+3-11)×6"
] | true
| 7.4
| 0.933
| 7.82
| 3.18
| 829
|
[
1,
2,
12,
13
] |
[
"13+12+1-2",
"2/(13/12-1)"
] | true
| 7.76
| 0.963
| 8.5
| 3.45
| 116
|
[
2,
4,
4,
4
] |
[
"4×4+4×2",
"(4+4-2)×4",
"(4/2+4)×4",
"(4+4+4)×2",
"(4×4-4)×2"
] | true
| 8.5
| 0.947
| 8.96
| 3.27
| 473
|
[
3,
4,
6,
13
] |
[
"(13+3)×6/4",
"6/(13/4-3)"
] | true
| 63.59
| 0.402
| 21.05
| 12.26
| 740
|
[
5,
8,
8,
9
] |
[
"9×8/(8-5)",
"(9-5)×8-8"
] | true
| 7.87
| 0.872
| 8.18
| 3.96
| 1,151
|
[
4,
5,
6,
7
] |
[
"(7+5)×(6-4)",
"(7+5-6)×4"
] | true
| 8.81
| 0.897
| 9.2
| 3.97
| 950
|
[
1,
2,
2,
12
] |
[
"(2-1)×12×2",
"(12+1)×2-2",
"(12-1)×2+2",
"(2/2+1)×12"
] | true
| 5.74
| 0.978
| 6.12
| 2
| 57
|
[
2,
7,
9,
10
] |
[
"10+9+7-2",
"(10+2)×(9-7)",
"(10+9-7)×2"
] | true
| 8.25
| 0.94
| 8.66
| 3.26
| 603
|
[
3,
5,
8,
12
] |
[
"(5×3-12)×8",
"(12+3)×8/5"
] | true
| 63.09
| 0.387
| 28.51
| 13.81
| 786
|
[
3,
6,
11,
13
] |
[
"(13+6-11)×3"
] | true
| 15.61
| 0.727
| 11.85
| 7.01
| 830
|
[
1,
3,
3,
4
] |
[
"(4+3+1)×3",
"(3-1)×4×3",
"(3+3)×4×1"
] | true
| 5.62
| 0.976
| 5.87
| 1.77
| 119
|
[
2,
12,
12,
12
] |
[
"12×2+12-12",
"(12+12)/2+12"
] | true
| 6.39
| 0.984
| 6.77
| 2.44
| 656
|
[
5,
5,
11,
12
] |
[
"5×5+11-12",
"5/5+12+11",
"(12-5)×5-11"
] | true
| 5.53
| 0.964
| 5.89
| 1.9
| 1,096
|
[
3,
3,
3,
12
] |
[
"(3+3)×12/3",
"3×3+12+3",
"(3-3/3)×12",
"(12-3)×3-3"
] | true
| 6.17
| 0.97
| 6.66
| 2.46
| 669
|
[
1,
2,
8,
13
] |
[
"13+8+2+1"
] | true
| 10.44
| 0.916
| 10.66
| 4.77
| 105
|
[
2,
9,
10,
10
] |
[
"10/2+10+9"
] | true
| 22.99
| 0.62
| 17.29
| 7.78
| 635
|
[
2,
2,
4,
10
] |
[
"(10-4)×(2+2)",
"(10-2-2)×4",
"(10-4)×2×2",
"(10-2×2)×4",
"(10+4-2)×2",
"(10+2)×(4-2)",
"(10+2)×4/2",
"(4/2+10)×2"
] | true
| 7.74
| 0.944
| 8.11
| 2.94
| 369
|
[
1,
6,
6,
12
] |
[
"(12+6+6)×1",
"(6×6-12)×1",
"(6/6+1)×12"
] | true
| 5.27
| 0.988
| 5.59
| 1.7
| 268
|
[
2,
11,
13,
13
] |
[
"13×2+11-13",
"(13-11)×13-2",
"(13+13)/2+11",
"(13/13+11)×2"
] | true
| 6.56
| 0.942
| 6.99
| 2.58
| 655
|
[
3,
6,
8,
13
] |
[
"13+8+6-3"
] | true
| 15.3
| 0.817
| 14.74
| 6.46
| 819
|
[
4,
4,
9,
12
] |
[
"(4+4)×(12-9)",
"(9-12/4)×4"
] | true
| 11.53
| 0.782
| 10.45
| 4.91
| 935
|
[
3,
6,
9,
11
] |
[
"(6-3)×11-9",
"(11-3)×(9-6)",
"(11+6-9)×3",
"(11-6)×3+9"
] | true
| 10.36
| 0.868
| 10.18
| 4.84
| 822
|
[
3,
8,
9,
12
] |
[
"(8+3-9)×12",
"(9-3)×(12-8)"
] | true
| 9.71
| 0.902
| 10.13
| 4.56
| 866
|
[
1,
1,
12,
12
] |
[
"12+12+1-1"
] | true
| 5
| 0.993
| 5.38
| 1.64
| 46
|
[
5,
11,
12,
12
] |
[
"12×12/(11-5)",
"(12×11-12)/5"
] | true
| 9.69
| 0.827
| 9.23
| 4.34
| 1,176
|
[
4,
6,
7,
8
] |
[
"(6+4-7)×8",
"(8-7)×6×4"
] | true
| 6.57
| 0.957
| 7.02
| 2.51
| 991
|
[
3,
9,
9,
9
] |
[
"9+9+9-3",
"(9×9-9)/3",
"(9-9/9)×3"
] | true
| 6.12
| 0.976
| 6.56
| 2.19
| 876
|
[
3,
5,
6,
10
] |
[
"10+6+5+3",
"(10/5+6)×3"
] | true
| 12.15
| 0.858
| 11.87
| 5.63
| 773
|
[
1,
1,
2,
6
] |
[
"(1+1)×6×2",
"(2+1+1)×6"
] | true
| 5.07
| 0.986
| 5.4
| 1.61
| 4
|
[
4,
6,
9,
13
] |
[
"13+9+6-4"
] | true
| 12.94
| 0.856
| 12.87
| 5.31
| 1,003
|
[
1,
6,
6,
6
] |
[
"(6-1)×6-6"
] | true
| 11.03
| 0.858
| 10.51
| 5.12
| 263
|
[
5,
5,
7,
8
] |
[
"(5+5-7)×8",
"5×5+7-8"
] | true
| 7.32
| 0.927
| 7.81
| 3.01
| 1,080
|
[
6,
9,
11,
12
] |
[
"(11-9)×6+12"
] | true
| 13.81
| 0.75
| 11.45
| 6.17
| 1,242
|
[
2,
3,
6,
10
] |
[
"(10-6)×3×2",
"(10-3×2)×6",
"(10+6)×3/2",
"(10+2)×6/3",
"(10-2)×(6-3)",
"(6/3+10)×2"
] | true
| 9.25
| 0.924
| 9.51
| 3.82
| 443
|
[
4,
6,
9,
12
] |
[
"(12+4)×9/6",
"(12-4)×(9-6)",
"(9-6)×4+12"
] | true
| 14.9
| 0.772
| 12.82
| 6.98
| 1,002
|
[
3,
7,
7,
10
] |
[
"7×3+10-7",
"(10-7)×7+3"
] | true
| 9.43
| 0.894
| 9.74
| 4.31
| 837
|
[
10,
11,
11,
12
] |
[
"12+11+11-10"
] | true
| 7.45
| 0.968
| 7.93
| 2.82
| 1,342
|
[
1,
7,
10,
12
] |
[
"(10-7-1)×12",
"10/(1-7/12)"
] | true
| 7.28
| 0.928
| 7.71
| 3.12
| 304
|
[
5,
5,
10,
13
] |
[
"5/5+13+10",
"(5-13/5)×10"
] | true
| 7.19
| 0.9
| 7.6
| 3.43
| 1,094
|
[
1,
8,
8,
12
] |
[
"(12-8-1)×8",
"(8/8+1)×12",
"8/(1-8/12)"
] | true
| 5.64
| 0.963
| 5.95
| 1.91
| 313
|
[
1,
3,
6,
9
] |
[
"(3-1)×9+6",
"(6-1)×3+9",
"(9+1)×3-6",
"(9-1)×(6-3)",
"(9/3+1)×6"
] | true
| 8.18
| 0.928
| 8.67
| 3.35
| 149
|
[
2,
6,
7,
13
] |
[
"13+7+6-2",
"(13-7)×(6-2)",
"(13-7-2)×6",
"(13+6-7)×2"
] | true
| 7.11
| 0.967
| 7.51
| 2.7
| 574
|
[
1,
2,
2,
5
] |
[
"(5+1)×(2+2)",
"(5+1)×2×2"
] | true
| 7.78
| 0.947
| 8.07
| 2.85
| 50
|
[
5,
5,
9,
10
] |
[
"5×5+9-10"
] | true
| 8.87
| 0.866
| 9.23
| 4.43
| 1,090
|
[
3,
4,
5,
6
] |
[
"(5+3-4)×6"
] | true
| 10.56
| 0.839
| 10.3
| 5.21
| 726
|
[
3,
6,
13,
13
] |
[
"13+13-6/3",
"(13/13+3)×6"
] | true
| 5.92
| 0.945
| 6.18
| 1.99
| 833
|
[
2,
3,
12,
12
] |
[
"12×12/3/2",
"(12+12)×(3-2)",
"(12×3+12)/2",
"(12/3-2)×12"
] | true
| 5.58
| 0.974
| 5.96
| 1.97
| 470
|
[
4,
5,
9,
10
] |
[
"(10-4)×(9-5)",
"(10+5-9)×4"
] | true
| 8.25
| 0.905
| 8.59
| 3.68
| 971
|
[
2,
11,
12,
12
] |
[
"(12-11)×12×2",
"(12/12+11)×2"
] | true
| 6.14
| 0.956
| 6.56
| 2.28
| 653
|
[
2,
2,
9,
11
] |
[
"11+9+2+2",
"2×2+11+9"
] | true
| 7.89
| 0.917
| 8.18
| 3.26
| 399
|
[
2,
4,
8,
13
] |
[
"13×2-8/4",
"13×8/4-2"
] | true
| 13.23
| 0.821
| 12.37
| 6
| 511
|
[
1,
8,
11,
12
] |
[
"(11-8-1)×12"
] | true
| 7.44
| 0.916
| 7.97
| 3.47
| 320
|
[
1,
1,
3,
11
] |
[
"(11+1)×(3-1)"
] | true
| 6.47
| 0.946
| 6.73
| 2.01
| 19
|
[
3,
3,
5,
12
] |
[
"5×3+12-3",
"(12-5)×3+3"
] | true
| 11.66
| 0.873
| 11.77
| 5.3
| 684
|
[
1,
1,
6,
8
] |
[
"8×6/(1+1)"
] | true
| 7.33
| 0.95
| 7.69
| 2.54
| 35
|
[
4,
4,
4,
7
] |
[
"(4+4)×(7-4)",
"(7-4/4)×4"
] | true
| 7.55
| 0.914
| 7.94
| 3.42
| 902
|
[
3,
6,
10,
12
] |
[
"6/3+12+10",
"10×3+6-12",
"10×6-12×3",
"(10×6+12)/3",
"(12+6-10)×3",
"(10-6)×3+12",
"(10-12/6)×3"
] | true
| 7.68
| 0.931
| 8.24
| 3.53
| 827
|
[
6,
8,
8,
8
] |
[
"(8-6)×8+8"
] | true
| 7.08
| 0.882
| 7.54
| 3.59
| 1,219
|
[
2,
2,
12,
12
] |
[
"12+12+2-2",
"(12×2-12)×2"
] | true
| 5.77
| 0.986
| 6.27
| 2.24
| 407
|
[
4,
4,
6,
12
] |
[
"(4+4-6)×12",
"(12-4-4)×6",
"(4×4-12)×6",
"12×4-6×4",
"12×4/(6-4)",
"(12+4)×6/4",
"(12/6+4)×4"
] | true
| 8.22
| 0.942
| 8.94
| 3.9
| 920
|
[
2,
5,
6,
12
] |
[
"12×6/(5-2)",
"12×5/2-6",
"(5-6/2)×12",
"(6-5)×12×2",
"6×5-12/2"
] | true
| 6.45
| 0.954
| 6.86
| 2.56
| 537
|
[
3,
4,
10,
13
] |
[
"13+10+4-3",
"(13+3-10)×4",
"10×4-13-3"
] | true
| 6.82
| 0.966
| 7.28
| 2.83
| 758
|
[
4,
9,
12,
12
] |
[
"(12-4)×(12-9)",
"12/4+12+9",
"(12×9-12)/4",
"(12-9)×4+12"
] | true
| 10.05
| 0.896
| 10.47
| 4.48
| 1,062
|
[
1,
5,
8,
8
] |
[
"(5-1)×8-8",
"(8-5)×8×1"
] | true
| 5.87
| 0.95
| 6.43
| 2.66
| 245
|
[
3,
5,
8,
9
] |
[
"9×3+5-8",
"(8-5)×9-3"
] | true
| 18.21
| 0.757
| 16.23
| 7.71
| 784
|
[
2,
4,
5,
11
] |
[
"4×2+11+5",
"(11+5-4)×2"
] | true
| 10.13
| 0.873
| 10.25
| 4.77
| 489
|
[
1,
3,
7,
7
] |
[
"(7-1)×(7-3)"
] | true
| 12.01
| 0.853
| 11.74
| 4.81
| 154
|
[
4,
5,
7,
11
] |
[
"5×4+11-7",
"(11-7)×5+4"
] | true
| 9.8
| 0.871
| 9.97
| 5.04
| 961
|
[
3,
7,
11,
11
] |
[
"(11/11+7)×3"
] | true
| 6.71
| 0.878
| 6.94
| 3.15
| 853
|
[
2,
8,
10,
12
] |
[
"10×2+12-8",
"12/2+10+8",
"(10+8)×2-12"
] | true
| 18.48
| 0.803
| 17.06
| 7.86
| 625
|
[
3,
3,
5,
13
] |
[
"13+5+3+3",
"13×3-5×3"
] | true
| 11.86
| 0.852
| 11.62
| 4.87
| 685
|
[
2,
6,
7,
8
] |
[
"(7+2-6)×8",
"(8+7)×2-6"
] | true
| 8.94
| 0.896
| 9.24
| 4.04
| 569
|
[
8,
10,
11,
11
] |
[
"11+11+10-8"
] | true
| 7.13
| 0.95
| 7.55
| 2.78
| 1,315
|
[
1,
1,
3,
9
] |
[
"(9+3)×(1+1)",
"(9-1)×3×1"
] | true
| 5.19
| 0.97
| 5.53
| 1.84
| 17
|
[
1,
3,
3,
12
] |
[
"(3+1)×3+12",
"(12-3-1)×3",
"(3/3+1)×12"
] | true
| 5.99
| 0.954
| 6.39
| 2.35
| 127
|
[
4,
4,
7,
13
] |
[
"13×4-7×4"
] | true
| 31.7
| 0.536
| 15.61
| 9.66
| 927
|
[
4,
5,
11,
13
] |
[
"(13+11)×(5-4)"
] | true
| 7.28
| 0.906
| 7.76
| 3.39
| 980
|
[
9,
12,
12,
12
] |
[
"(12-9)×12-12"
] | true
| 7.35
| 0.816
| 7.21
| 3.72
| 1,335
|
[
1,
4,
5,
7
] |
[
"7×4+1-5",
"(5-1)×7-4"
] | true
| 12.8
| 0.879
| 12.72
| 5.32
| 190
|
[
4,
6,
7,
9
] |
[
"(9+7)×6/4"
] | true
| 59.92
| 0.421
| 20.42
| 12.69
| 992
|
[
9,
10,
12,
12
] |
[
"(12+12)×(10-9)"
] | true
| 5.96
| 0.959
| 6.29
| 2.05
| 1,329
|
[
2,
7,
10,
10
] |
[
"(10-2)×(10-7)",
"(10+7)×2-10"
] | true
| 17.77
| 0.678
| 13.95
| 6.11
| 606
|
[
1,
4,
4,
5
] |
[
"(5×4+4)×1"
] | true
| 6.41
| 0.967
| 6.97
| 2.74
| 180
|
[
1,
7,
9,
11
] |
[
"(11+1)×(9-7)"
] | true
| 10.68
| 0.856
| 10.5
| 4.31
| 301
|
[
2,
4,
6,
10
] |
[
"(4+2)×(10-6)",
"(10-4-2)×6",
"4×2+10+6",
"(10+2-6)×4",
"(10-4)×(6-2)",
"(10+2)×(6-4)",
"(10+6-4)×2"
] | true
| 7.95
| 0.94
| 8.41
| 3.4
| 496
|
[
6,
6,
6,
6
] |
[
"6+6+6+6",
"6×6-6-6"
] | true
| 4.57
| 0.995
| 4.81
| 1.47
| 1,177
|
[
5,
7,
10,
11
] |
[
"(10-5)×7-11"
] | true
| 64.03
| 0.362
| 25.09
| 14.01
| 1,143
|
[
8,
8,
8,
13
] |
[
"(8+8-13)×8"
] | true
| 9.44
| 0.843
| 9.4
| 4.42
| 1,296
|
[
2,
4,
10,
11
] |
[
"11×4-10×2",
"(11-10/2)×4",
"(11-4)×2+10"
] | true
| 15.73
| 0.796
| 14.41
| 6.58
| 517
|
[
4,
11,
12,
13
] |
[
"(11+4-13)×12",
"12×4-13-11",
"12×4/(13-11)"
] | true
| 9.01
| 0.913
| 9.39
| 3.91
| 1,069
|
[
2,
4,
4,
7
] |
[
"(7-4)×4×2",
"(7-2)×4+4"
] | true
| 9.56
| 0.894
| 9.7
| 4.33
| 476
|
[
1,
3,
7,
10
] |
[
"(3-1)×7+10",
"10×3+1-7"
] | true
| 11.36
| 0.863
| 11.38
| 5.4
| 157
|
[
1,
1,
3,
8
] |
[
"8×3+1-1"
] | true
| 4.4
| 0.992
| 4.68
| 1.47
| 16
|
[
5,
5,
5,
6
] |
[
"5×5+5-6",
"(5-5/5)×6"
] | true
| 6.23
| 0.964
| 6.68
| 2.33
| 1,072
|
[
2,
5,
8,
9
] |
[
"9+8+5+2",
"9×8/(5-2)",
"(8-2)×(9-5)",
"(9+8-5)×2"
] | true
| 9.26
| 0.928
| 9.61
| 3.82
| 546
|
[
2,
12,
13,
13
] |
[
"12×2+13-13"
] | true
| 5.5
| 0.972
| 5.86
| 2.03
| 658
|
[
5,
6,
9,
11
] |
[
"(11+9)×6/5",
"(11+5)×9/6"
] | true
| 75.91
| 0.334
| 27.08
| 15.22
| 1,119
|
[
4,
7,
8,
12
] |
[
"7×4+8-12",
"(12-8)×7-4"
] | true
| 15.82
| 0.792
| 14.42
| 6.97
| 1,019
|
[
5,
7,
10,
12
] |
[
"(7+5)×(12-10)",
"(7+5-10)×12",
"12+10+7-5"
] | true
| 6.76
| 0.968
| 7.25
| 2.52
| 1,144
|
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