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
|
|---|---|---|---|---|---|---|
[
1,
7,
9,
10
] |
[
"(9-1)×(10-7)"
] | true
| 10.1
| 0.869
| 9.98
| 3.97
|
[
1,
7,
9,
11
] |
[
"(11+1)×(9-7)"
] | true
| 10.68
| 0.856
| 10.5
| 4.31
|
[
1,
7,
9,
12
] |
[
"(7+1)×(12-9)",
"(9-7)×12×1"
] | true
| 5.71
| 0.962
| 6.11
| 2.22
|
[
1,
7,
9,
13
] |
[
"(7-1)×(13-9)",
"(13-1)×(9-7)"
] | true
| 7.35
| 0.939
| 7.63
| 2.61
|
[
1,
7,
10,
12
] |
[
"(10-7-1)×12",
"10/(1-7/12)"
] | true
| 7.28
| 0.928
| 7.71
| 3.12
|
[
1,
7,
10,
13
] |
[
"(7+1)×(13-10)"
] | true
| 10.91
| 0.835
| 10.49
| 4.66
|
[
1,
7,
12,
12
] |
[
"12×12/(7-1)"
] | true
| 9.85
| 0.805
| 9.12
| 4.5
|
[
1,
7,
12,
13
] |
[
"(13+1)×12/7"
] | true
| 29.06
| 0.558
| 15.69
| 9.56
|
[
1,
7,
13,
13
] |
[
"(13×13-1)/7"
] | true
| 48.91
| 0.412
| 14.87
| 9.19
|
[
1,
8,
8,
8
] |
[
"(8+8+8)×1"
] | true
| 5.29
| 0.979
| 5.62
| 1.91
|
[
1,
8,
8,
9
] |
[
"9+8+8-1"
] | true
| 6.44
| 0.965
| 6.96
| 2.68
|
[
1,
8,
8,
10
] |
[
"(10+1-8)×8"
] | true
| 7.11
| 0.923
| 7.5
| 3.03
|
[
1,
8,
8,
11
] |
[
"(11-8)×8×1"
] | true
| 7.14
| 0.935
| 7.64
| 3.52
|
[
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
|
[
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
|
[
1,
8,
9,
12
] |
[
"(12-9)×8×1",
"(9+1-8)×12",
"8/(12/9-1)"
] | true
| 5.54
| 0.964
| 5.88
| 1.97
|
[
1,
8,
9,
13
] |
[
"(13-9-1)×8"
] | true
| 7.67
| 0.915
| 8.14
| 3.68
|
[
1,
8,
10,
11
] |
[
"(11+1)×(10-8)"
] | true
| 10.18
| 0.873
| 10.17
| 3.5
|
[
1,
8,
10,
12
] |
[
"(12+1-10)×8",
"(10-8)×12×1"
] | true
| 5.92
| 0.958
| 6.23
| 2.19
|
[
1,
8,
10,
13
] |
[
"(13-10)×8×1",
"(13-1)×(10-8)"
] | true
| 6.27
| 0.948
| 6.61
| 2.4
|
[
1,
8,
11,
12
] |
[
"(11-8-1)×12"
] | true
| 7.44
| 0.916
| 7.97
| 3.47
|
[
1,
8,
11,
13
] |
[
"(13+1-11)×8"
] | true
| 8.23
| 0.883
| 8.41
| 3.59
|
[
1,
8,
12,
12
] |
[
"12/(12/8-1)"
] | true
| 104.58
| 0.293
| 21.9
| 13.81
|
[
1,
9,
9,
12
] |
[
"(9-1)×(12-9)",
"(9/9+1)×12"
] | true
| 5.48
| 0.958
| 5.78
| 1.81
|
[
1,
9,
10,
12
] |
[
"(10+1-9)×12"
] | true
| 6.97
| 0.939
| 7.35
| 2.83
|
[
1,
9,
10,
13
] |
[
"(9-1)×(13-10)"
] | true
| 10.99
| 0.836
| 10.53
| 4.58
|
[
1,
9,
11,
11
] |
[
"(11+1)×(11-9)"
] | true
| 7.77
| 0.901
| 7.97
| 3.09
|
[
1,
9,
11,
12
] |
[
"(11-9)×12×1"
] | true
| 6.78
| 0.938
| 7.29
| 3.09
|
[
1,
9,
11,
13
] |
[
"(13-1)×(11-9)"
] | true
| 9.62
| 0.876
| 9.79
| 4.2
|
[
1,
9,
12,
12
] |
[
"(12-9-1)×12"
] | true
| 6.54
| 0.929
| 6.93
| 2.79
|
[
1,
10,
10,
12
] |
[
"(10/10+1)×12"
] | true
| 6.04
| 0.926
| 6.27
| 2.12
|
[
1,
10,
11,
12
] |
[
"(11+1-10)×12",
"(11+1)×(12-10)"
] | true
| 6.74
| 0.949
| 7.15
| 2.56
|
[
1,
10,
12,
12
] |
[
"(12-10)×12×1"
] | true
| 6.31
| 0.959
| 6.89
| 2.91
|
[
1,
10,
12,
13
] |
[
"(13-10-1)×12",
"(13-1)×(12-10)"
] | true
| 7.2
| 0.945
| 7.58
| 2.85
|
[
1,
11,
11,
12
] |
[
"(11/11+1)×12"
] | true
| 5.95
| 0.936
| 6.19
| 2.22
|
[
1,
11,
11,
13
] |
[
"(11+1)×(13-11)",
"(13/11+1)×11"
] | true
| 10.33
| 0.875
| 10.27
| 4.31
|
[
1,
11,
12,
12
] |
[
"(12+1-11)×12"
] | true
| 7.04
| 0.943
| 7.62
| 3.19
|
[
1,
11,
12,
13
] |
[
"(13-11)×12×1"
] | true
| 7.44
| 0.943
| 7.87
| 3.18
|
[
1,
11,
13,
13
] |
[
"(13-1)×(13-11)",
"(11/13+1)×13"
] | true
| 8.79
| 0.913
| 9.1
| 3.85
|
[
1,
12,
12,
12
] |
[
"(12/12+1)×12"
] | true
| 6.74
| 0.938
| 6.95
| 2.57
|
[
1,
12,
12,
13
] |
[
"(13+1-12)×12"
] | true
| 7.44
| 0.944
| 7.97
| 3.27
|
[
1,
12,
13,
13
] |
[
"(13/13+1)×12"
] | true
| 5.96
| 0.945
| 6.29
| 2.18
|
[
2,
2,
2,
3
] |
[
"(2+2)×3×2",
"3×2×2×2"
] | true
| 5.71
| 0.99
| 5.97
| 1.71
|
[
2,
2,
2,
4
] |
[
"(4+2)×(2+2)",
"(2+2+2)×4",
"(4+2)×2×2",
"(2×2+2)×4"
] | true
| 6.8
| 0.961
| 7.15
| 2.49
|
[
2,
2,
2,
5
] |
[
"(5×2+2)×2"
] | true
| 10.29
| 0.787
| 9.3
| 4.85
|
[
2,
2,
2,
7
] |
[
"(7×2-2)×2"
] | true
| 13.48
| 0.728
| 10.26
| 6.18
|
[
2,
2,
2,
8
] |
[
"(8-2)×(2+2)",
"(8+2+2)×2",
"(8-2)×2×2",
"(2×2+8)×2",
"(2/2+2)×8"
] | true
| 6.29
| 0.964
| 6.86
| 2.72
|
[
2,
2,
2,
9
] |
[
"(9+2)×2+2"
] | true
| 14.13
| 0.757
| 11.48
| 6.62
|
[
2,
2,
2,
10
] |
[
"10×2+2+2",
"10×2+2×2"
] | true
| 7.75
| 0.939
| 8.18
| 3.36
|
[
2,
2,
2,
11
] |
[
"(2/2+11)×2",
"(11+2)×2-2"
] | true
| 6.62
| 0.923
| 6.97
| 2.8
|
[
2,
2,
2,
12
] |
[
"(2+2)×12/2",
"(2×2-2)×12",
"12×2+2-2"
] | true
| 5
| 0.992
| 5.36
| 1.71
|
[
2,
2,
2,
13
] |
[
"(13-2/2)×2",
"(13-2)×2+2"
] | true
| 6.84
| 0.935
| 7.23
| 2.8
|
[
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
|
[
2,
2,
3,
4
] |
[
"(4+2+2)×3",
"(2×2+4)×3"
] | true
| 15.01
| 0.772
| 13.14
| 6.06
|
[
2,
2,
3,
5
] |
[
"(5×2-2)×3"
] | true
| 40.25
| 0.511
| 16.11
| 9.45
|
[
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
|
[
2,
2,
3,
7
] |
[
"(2/2+7)×3",
"(7+3+2)×2"
] | true
| 8.26
| 0.884
| 8.57
| 3.86
|
[
2,
2,
3,
8
] |
[
"8×3+2-2",
"(8+3)×2+2"
] | true
| 5.3
| 0.982
| 5.68
| 1.89
|
[
2,
2,
3,
9
] |
[
"(9-3)×(2+2)",
"(9-3)×2×2",
"(9-2/2)×3",
"9×2+3×2",
"(2/3+2)×9"
] | true
| 7.34
| 0.948
| 7.83
| 2.9
|
[
2,
2,
3,
10
] |
[
"(10+3)×2-2"
] | true
| 36.04
| 0.547
| 18.71
| 10.73
|
[
2,
2,
3,
11
] |
[
"(11+3-2)×2"
] | true
| 9.31
| 0.861
| 9.3
| 4.21
|
[
2,
2,
3,
12
] |
[
"(2+2)×3+12",
"(12-2-2)×3",
"3×2×2+12",
"(12-2×2)×3",
"(3-2/2)×12",
"(3-2)×12×2",
"12/(2-3/2)",
"(12/2+2)×3"
] | true
| 5.78
| 0.982
| 6.21
| 2.05
|
[
2,
2,
3,
13
] |
[
"(13+2-3)×2"
] | true
| 8.69
| 0.875
| 8.75
| 3.74
|
[
2,
2,
4,
4
] |
[
"(4×2-2)×4",
"(4×2+4)×2"
] | true
| 20.23
| 0.716
| 15.55
| 8.4
|
[
2,
2,
4,
5
] |
[
"5×4+2+2",
"(2+2)×5+4",
"5×4+2×2",
"5×2×2+4",
"(2/2+5)×4",
"(5-2)×4×2"
] | true
| 6.25
| 0.983
| 6.61
| 2.08
|
[
2,
2,
4,
6
] |
[
"6×4+2-2",
"(4+2)×(6-2)",
"(6+4+2)×2",
"(4-2)×6×2",
"(4/2+2)×6"
] | true
| 5.58
| 0.99
| 5.93
| 1.88
|
[
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
|
[
2,
2,
4,
8
] |
[
"(2+2)×4+8",
"4×2×2+8",
"(4-2/2)×8",
"(4+2)×8/2",
"8×2+4×2",
"(8+2)×2+4",
"(8×2-4)×2",
"(8/2+2)×4"
] | true
| 7.96
| 0.959
| 8.49
| 3.1
|
[
2,
2,
4,
9
] |
[
"9×2+4+2",
"(9+4)×2-2"
] | true
| 9.94
| 0.904
| 10.16
| 4.44
|
[
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
|
[
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
|
[
2,
2,
4,
12
] |
[
"(4+2)×2+12",
"(12+2)×2-4",
"(12-2)×2+4"
] | true
| 20.54
| 0.757
| 16.22
| 9.62
|
[
2,
2,
4,
13
] |
[
"13×2+2-4",
"(4-2)×13-2",
"13×4/2-2",
"13×2-4/2"
] | true
| 8.74
| 0.911
| 9.24
| 4.19
|
[
2,
2,
5,
5
] |
[
"5×5-2/2",
"(5+5+2)×2"
] | true
| 6.73
| 0.934
| 7.1
| 2.49
|
[
2,
2,
5,
6
] |
[
"(5-2/2)×6",
"(6+2)×(5-2)",
"(6+5)×2+2"
] | true
| 9.16
| 0.885
| 9.47
| 4.58
|
[
2,
2,
5,
7
] |
[
"7×2+5×2"
] | true
| 9.19
| 0.892
| 9.23
| 3.72
|
[
2,
2,
5,
8
] |
[
"(8+5)×2-2"
] | true
| 26.55
| 0.632
| 17.21
| 9.35
|
[
2,
2,
5,
9
] |
[
"(9+5-2)×2"
] | true
| 14.53
| 0.739
| 12.14
| 6.46
|
[
2,
2,
5,
10
] |
[
"(5+2)×2+10",
"(10-2)×(5-2)",
"(2/5+2)×10",
"(10×5-2)/2"
] | true
| 15.47
| 0.783
| 13.87
| 6.02
|
[
2,
2,
5,
11
] |
[
"(11-5)×(2+2)",
"(11-5)×2×2"
] | true
| 9.36
| 0.877
| 9.67
| 4.57
|
[
2,
2,
5,
12
] |
[
"5×2+12+2",
"12/(5/2-2)"
] | true
| 11.08
| 0.844
| 10.84
| 5.23
|
[
2,
2,
6,
6
] |
[
"(6+2)×6/2",
"6×2+6×2"
] | true
| 7.57
| 0.96
| 8.1
| 3.08
|
[
2,
2,
6,
7
] |
[
"(7+2)×2+6",
"(7+6)×2-2"
] | true
| 17.37
| 0.724
| 13.71
| 7.25
|
[
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
|
[
2,
2,
6,
9
] |
[
"(6/2+9)×2",
"(9×2-6)×2"
] | true
| 38.12
| 0.516
| 19
| 10.81
|
[
2,
2,
6,
10
] |
[
"6×2+10+2",
"10×2+6-2",
"(10-2)×6/2"
] | true
| 8.38
| 0.954
| 8.81
| 3.08
|
[
2,
2,
6,
11
] |
[
"(11-2)×2+6"
] | true
| 26.25
| 0.622
| 19.02
| 8.98
|
[
2,
2,
6,
12
] |
[
"(12-6)×(2+2)",
"(6-2-2)×12",
"(12-6)×2×2",
"(6-2×2)×12",
"(6-2)×12/2",
"(12/2-2)×6",
"(12/2+6)×2"
] | true
| 8.01
| 0.941
| 8.59
| 3.57
|
[
2,
2,
6,
13
] |
[
"(13+2)×2-6"
] | true
| 74.75
| 0.334
| 31.47
| 17.1
|
[
2,
2,
7,
7
] |
[
"(7+7-2)×2"
] | true
| 15.7
| 0.697
| 11.73
| 6.19
|
[
2,
2,
7,
8
] |
[
"(7-2-2)×8",
"(7-2×2)×8",
"7×2+8+2"
] | true
| 7.62
| 0.936
| 8
| 3.05
|
[
2,
2,
7,
10
] |
[
"(10/2+7)×2"
] | true
| 32.81
| 0.532
| 17.19
| 9.45
|
[
2,
2,
7,
12
] |
[
"7×2+12-2"
] | true
| 10.6
| 0.836
| 10.24
| 4.65
|
[
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
|
[
2,
2,
8,
8
] |
[
"(2+2)×8-8",
"8×2×2-8",
"(8-2)×8/2",
"(8/2+8)×2"
] | true
| 10.62
| 0.913
| 10.93
| 4.78
|
[
2,
2,
8,
9
] |
[
"9×2+8-2"
] | true
| 11.62
| 0.868
| 11.84
| 5.24
|
[
2,
2,
8,
10
] |
[
"8×2+10-2",
"10×2+8/2",
"(10×2-8)×2",
"(10-2)×2+8",
"(10/2-2)×8"
] | true
| 8.74
| 0.944
| 9.31
| 3.29
|
[
2,
2,
8,
12
] |
[
"12+8+2+2",
"12×8/(2+2)",
"12×8/2/2",
"2×2+12+8",
"(8-2)×2+12",
"(8/2-2)×12"
] | true
| 6.71
| 0.981
| 7.14
| 2.32
|
[
2,
2,
9,
10
] |
[
"(9-2)×2+10"
] | true
| 19.64
| 0.655
| 14.61
| 7.52
|
[
2,
2,
9,
11
] |
[
"11+9+2+2",
"2×2+11+9"
] | true
| 7.89
| 0.917
| 8.18
| 3.26
|
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