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,
1,
1,
8
] |
[
"(1+1+1)×8"
] | true
| 4.46
| 0.988
| 4.66
| 1.25
|
[
1,
1,
1,
11
] |
[
"(11+1)×(1+1)"
] | true
| 5.28
| 0.974
| 5.6
| 1.67
|
[
1,
1,
1,
12
] |
[
"(1+1)×12×1"
] | true
| 4.82
| 0.993
| 5.15
| 1.6
|
[
1,
1,
1,
13
] |
[
"(13-1)×(1+1)"
] | true
| 5.55
| 0.974
| 5.88
| 1.78
|
[
1,
1,
2,
6
] |
[
"(1+1)×6×2",
"(2+1+1)×6"
] | true
| 5.07
| 0.986
| 5.4
| 1.61
|
[
1,
1,
2,
7
] |
[
"(7+1)×(2+1)"
] | true
| 6.73
| 0.955
| 6.95
| 2.06
|
[
1,
1,
2,
8
] |
[
"(2+1)×8×1"
] | true
| 4.97
| 0.978
| 5.33
| 1.74
|
[
1,
1,
2,
9
] |
[
"(9-1)×(2+1)"
] | true
| 6.8
| 0.95
| 7.11
| 2.31
|
[
1,
1,
2,
10
] |
[
"(10+2)×(1+1)",
"(10+1+1)×2"
] | true
| 5.7
| 0.957
| 6.01
| 1.84
|
[
1,
1,
2,
11
] |
[
"11×2+1+1",
"(1+1)×11+2",
"(11+1)×2×1"
] | true
| 5.08
| 0.99
| 5.42
| 1.7
|
[
1,
1,
2,
12
] |
[
"12×2+1-1",
"12/(1-1/2)"
] | true
| 4.61
| 0.992
| 4.93
| 1.53
|
[
1,
1,
2,
13
] |
[
"13×2-1-1",
"(1+1)×13-2",
"(13-1)×2×1"
] | true
| 5.19
| 0.988
| 5.51
| 1.79
|
[
1,
1,
3,
4
] |
[
"(1+1)×4×3"
] | true
| 6.15
| 0.981
| 6.48
| 2.05
|
[
1,
1,
3,
5
] |
[
"(5+1)×(3+1)"
] | true
| 6.92
| 0.954
| 7.24
| 2.32
|
[
1,
1,
3,
6
] |
[
"(6+1+1)×3",
"(3+1)×6×1"
] | true
| 5.2
| 0.979
| 5.56
| 1.79
|
[
1,
1,
3,
7
] |
[
"(7-1)×(3+1)",
"(7+1)×3×1"
] | true
| 5.5
| 0.971
| 5.83
| 1.94
|
[
1,
1,
3,
8
] |
[
"8×3+1-1"
] | true
| 4.4
| 0.992
| 4.68
| 1.47
|
[
1,
1,
3,
9
] |
[
"(9+3)×(1+1)",
"(9-1)×3×1"
] | true
| 5.19
| 0.97
| 5.53
| 1.84
|
[
1,
1,
3,
10
] |
[
"(10-1-1)×3"
] | true
| 9.04
| 0.884
| 9.05
| 3.91
|
[
1,
1,
3,
11
] |
[
"(11+1)×(3-1)"
] | true
| 6.47
| 0.946
| 6.73
| 2.01
|
[
1,
1,
3,
12
] |
[
"(3-1)×12×1"
] | true
| 5.02
| 0.975
| 5.37
| 1.83
|
[
1,
1,
3,
13
] |
[
"(13-1)×(3-1)"
] | true
| 6.02
| 0.953
| 6.37
| 2.13
|
[
1,
1,
4,
4
] |
[
"(4+1+1)×4"
] | true
| 6.11
| 0.946
| 6.4
| 2.45
|
[
1,
1,
4,
5
] |
[
"(4+1)×5-1",
"(5+1)×4×1"
] | true
| 5.4
| 0.979
| 5.79
| 2
|
[
1,
1,
4,
6
] |
[
"6×4+1-1"
] | true
| 4.36
| 0.992
| 4.63
| 1.45
|
[
1,
1,
4,
7
] |
[
"(7-1)×4×1",
"(7+1)×(4-1)"
] | true
| 5.59
| 0.972
| 5.94
| 2.07
|
[
1,
1,
4,
8
] |
[
"(8+4)×(1+1)",
"(8-1-1)×4",
"(4-1)×8×1"
] | true
| 5.03
| 0.982
| 5.4
| 1.83
|
[
1,
1,
4,
9
] |
[
"(9-1)×(4-1)"
] | true
| 6.9
| 0.935
| 7.12
| 2.35
|
[
1,
1,
4,
10
] |
[
"(1+1)×10+4"
] | true
| 9.67
| 0.847
| 9.43
| 5.1
|
[
1,
1,
4,
12
] |
[
"12×4/(1+1)",
"(4-1-1)×12"
] | true
| 5.06
| 0.974
| 5.47
| 1.83
|
[
1,
1,
5,
5
] |
[
"(5+1)×(5-1)",
"(5×5-1)×1"
] | true
| 5.36
| 0.991
| 5.74
| 1.83
|
[
1,
1,
5,
6
] |
[
"(5-1)×6×1",
"(6-1)×5-1"
] | true
| 5.17
| 0.97
| 5.64
| 2.04
|
[
1,
1,
5,
7
] |
[
"(7+5)×(1+1)",
"(7-1)×(5-1)"
] | true
| 6.27
| 0.966
| 6.61
| 2.11
|
[
1,
1,
5,
8
] |
[
"(5-1-1)×8"
] | true
| 5.02
| 0.965
| 5.39
| 1.83
|
[
1,
1,
6,
6
] |
[
"(6+6)×(1+1)",
"(6-1-1)×6"
] | true
| 6.11
| 0.974
| 6.54
| 2.21
|
[
1,
1,
6,
8
] |
[
"8×6/(1+1)"
] | true
| 7.33
| 0.95
| 7.69
| 2.54
|
[
1,
1,
6,
9
] |
[
"(1+1)×9+6"
] | true
| 13.99
| 0.806
| 12.01
| 6.75
|
[
1,
1,
6,
12
] |
[
"(1+1)×6+12"
] | true
| 6.95
| 0.909
| 7.51
| 3.43
|
[
1,
1,
7,
10
] |
[
"(1+1)×7+10"
] | true
| 8.37
| 0.85
| 8.4
| 4.33
|
[
1,
1,
8,
8
] |
[
"(1+1)×8+8"
] | true
| 7.23
| 0.897
| 7.72
| 3.87
|
[
1,
1,
9,
13
] |
[
"13+9+1+1"
] | true
| 6.18
| 0.973
| 6.64
| 2.53
|
[
1,
1,
10,
12
] |
[
"12+10+1+1"
] | true
| 4.8
| 0.99
| 5.04
| 1.53
|
[
1,
1,
10,
13
] |
[
"(13+10+1)×1"
] | true
| 5.72
| 0.98
| 6.15
| 2.19
|
[
1,
1,
11,
11
] |
[
"11+11+1+1"
] | true
| 4.42
| 0.995
| 4.68
| 1.43
|
[
1,
1,
11,
12
] |
[
"(12+11+1)×1"
] | true
| 5.26
| 0.994
| 5.66
| 1.76
|
[
1,
1,
11,
13
] |
[
"13+11+1-1"
] | true
| 5.23
| 0.991
| 5.64
| 1.81
|
[
1,
1,
12,
12
] |
[
"12+12+1-1"
] | true
| 5
| 0.993
| 5.38
| 1.64
|
[
1,
1,
12,
13
] |
[
"(13+12-1)×1"
] | true
| 5.45
| 0.988
| 5.84
| 1.85
|
[
1,
1,
13,
13
] |
[
"13+13-1-1"
] | true
| 5.14
| 0.994
| 5.46
| 1.64
|
[
1,
2,
2,
4
] |
[
"(2+1)×4×2"
] | true
| 7.6
| 0.958
| 7.94
| 2.47
|
[
1,
2,
2,
5
] |
[
"(5+1)×(2+2)",
"(5+1)×2×2"
] | true
| 7.78
| 0.947
| 8.07
| 2.85
|
[
1,
2,
2,
6
] |
[
"(6+2)×(2+1)",
"6×2×2×1",
"(2+2)×6×1"
] | true
| 4.78
| 0.993
| 5.13
| 1.58
|
[
1,
2,
2,
7
] |
[
"(7-1)×(2+2)",
"(7-1)×2×2"
] | true
| 8.47
| 0.918
| 8.8
| 3.37
|
[
1,
2,
2,
8
] |
[
"(2+2-1)×8",
"(2×2-1)×8"
] | true
| 6.36
| 0.935
| 6.8
| 2.7
|
[
1,
2,
2,
9
] |
[
"(9+2+1)×2"
] | true
| 10.95
| 0.824
| 10.15
| 4.57
|
[
1,
2,
2,
10
] |
[
"(10-2)×(2+1)",
"(10+2)×2×1",
"(10+1)×2+2"
] | true
| 5.73
| 0.965
| 6.11
| 2.16
|
[
1,
2,
2,
11
] |
[
"(11+2-1)×2",
"(11×2+2)×1"
] | true
| 7.03
| 0.972
| 7.57
| 2.96
|
[
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
|
[
1,
2,
2,
13
] |
[
"(13+1-2)×2",
"(13×2-2)×1"
] | true
| 7.2
| 0.967
| 7.73
| 3.12
|
[
1,
2,
3,
3
] |
[
"(3+1)×3×2"
] | true
| 8.59
| 0.956
| 8.97
| 2.99
|
[
1,
2,
3,
4
] |
[
"(3+2+1)×4",
"4×3×2×1",
"(4+2)×(3+1)"
] | true
| 5.16
| 0.992
| 5.51
| 1.83
|
[
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
|
[
1,
2,
3,
6
] |
[
"(3+2-1)×6",
"(6+2)×3×1",
"(3-1)×6×2"
] | true
| 6.68
| 0.971
| 7.13
| 2.42
|
[
1,
2,
3,
7
] |
[
"7×3+2+1",
"(2+1)×7+3",
"(7+2-1)×3"
] | true
| 7.52
| 0.962
| 8.23
| 3.24
|
[
1,
2,
3,
8
] |
[
"(2-1)×8×3",
"(8-2)×(3+1)",
"(8+3+1)×2",
"8/(1-2/3)"
] | true
| 6.23
| 0.971
| 6.68
| 2.42
|
[
1,
2,
3,
9
] |
[
"9×3-2-1",
"(2+1)×9-3",
"(9+3)×2×1",
"(9+1-2)×3"
] | true
| 7.56
| 0.965
| 8.14
| 3.18
|
[
1,
2,
3,
10
] |
[
"10×2+3+1",
"(10-2)×3×1",
"(10+3-1)×2",
"(10+2)×(3-1)"
] | true
| 6.17
| 0.983
| 6.49
| 1.99
|
[
1,
2,
3,
11
] |
[
"(11-3)×(2+1)",
"(11-2-1)×3",
"11×2+3-1",
"(3-1)×11+2"
] | true
| 8.77
| 0.957
| 9.13
| 3.4
|
[
1,
2,
3,
12
] |
[
"(3+1-2)×12",
"(3+1)×12/2",
"12/(3/2-1)"
] | true
| 6.35
| 0.962
| 6.88
| 2.56
|
[
1,
2,
3,
13
] |
[
"13×2+1-3",
"(3-1)×13-2"
] | true
| 10.8
| 0.915
| 11.16
| 4.86
|
[
1,
2,
4,
4
] |
[
"(4+4)×(2+1)",
"(4+2)×4×1",
"(4-1)×4×2"
] | true
| 6
| 0.971
| 6.36
| 2.12
|
[
1,
2,
4,
5
] |
[
"(5+2-1)×4",
"(4+2)×(5-1)"
] | true
| 9.09
| 0.905
| 9.44
| 4.21
|
[
1,
2,
4,
6
] |
[
"(2-1)×6×4",
"(6+2)×(4-1)"
] | true
| 6.5
| 0.96
| 6.92
| 2.54
|
[
1,
2,
4,
7
] |
[
"(7+1-2)×4",
"(7+4+1)×2"
] | true
| 10.41
| 0.891
| 10.73
| 5.06
|
[
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
|
[
1,
2,
4,
9
] |
[
"(9-2-1)×4",
"(9+4-1)×2",
"(9+1)×2+4"
] | true
| 9.12
| 0.91
| 9.56
| 4.03
|
[
1,
2,
4,
10
] |
[
"(10-2)×(4-1)",
"(10×2+4)×1",
"(10/2+1)×4"
] | true
| 7.34
| 0.963
| 7.79
| 3.18
|
[
1,
2,
4,
11
] |
[
"(11+1)×(4-2)",
"(11+1)×4/2",
"(11-1)×2+4"
] | true
| 7.77
| 0.92
| 8.01
| 2.8
|
[
1,
2,
4,
12
] |
[
"(12-4)×(2+1)",
"(2+1)×4+12",
"12×4×1/2",
"(4-2)×12×1",
"12/(1-2/4)"
] | true
| 5.18
| 0.976
| 5.61
| 2
|
[
1,
2,
4,
13
] |
[
"(13+1)×2-4",
"(13-1)×(4-2)",
"(13-1)×4/2"
] | true
| 7.59
| 0.939
| 7.94
| 2.98
|
[
1,
2,
5,
5
] |
[
"5×5+1-2"
] | true
| 6.72
| 0.951
| 7.25
| 2.96
|
[
1,
2,
5,
6
] |
[
"(5+1-2)×6",
"(5+1)×(6-2)",
"(6+5+1)×2"
] | true
| 6.74
| 0.944
| 7.24
| 2.8
|
[
1,
2,
5,
7
] |
[
"(7+5)×2×1",
"(7+1)×(5-2)",
"(7-2)×5-1"
] | true
| 6.84
| 0.952
| 7.17
| 2.64
|
[
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
|
[
1,
2,
5,
9
] |
[
"(2+1)×5+9",
"9×2+5+1",
"(9-1)×(5-2)"
] | true
| 8.07
| 0.952
| 8.5
| 3.07
|
[
1,
2,
5,
10
] |
[
"10×2+5-1",
"10×5/2-1"
] | true
| 10.06
| 0.918
| 10.31
| 4.12
|
[
1,
2,
5,
12
] |
[
"(5-2-1)×12",
"(5+1)×2+12",
"(5-1)×12/2"
] | true
| 5.72
| 0.955
| 6.15
| 2.2
|
[
1,
2,
5,
13
] |
[
"(13-5)×(2+1)",
"5×2+13+1"
] | true
| 8.7
| 0.944
| 9.2
| 3.61
|
[
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
|
[
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
|
[
1,
2,
6,
8
] |
[
"(6-2-1)×8",
"8×6×1/2",
"(8+1)×2+6"
] | true
| 6.15
| 0.961
| 6.49
| 2.36
|
[
1,
2,
6,
9
] |
[
"(9-1)×6/2",
"(9×2+6)×1"
] | true
| 7.96
| 0.945
| 8.55
| 3.6
|
[
1,
2,
6,
10
] |
[
"(2+1)×10-6",
"(6+1)×2+10",
"(10-1)×2+6",
"(10/2-1)×6"
] | true
| 11.01
| 0.867
| 10.99
| 4.99
|
[
1,
2,
6,
11
] |
[
"6×2+11+1"
] | true
| 8.96
| 0.898
| 9.36
| 4.29
|
[
1,
2,
6,
12
] |
[
"12×6/(2+1)",
"(6×2+12)×1",
"(6/2-1)×12"
] | true
| 6.06
| 0.969
| 6.44
| 2.26
|
[
1,
2,
6,
13
] |
[
"6×2+13-1"
] | true
| 8.53
| 0.912
| 9.06
| 3.98
|
[
1,
2,
7,
7
] |
[
"(7×7-1)/2"
] | true
| 34.41
| 0.548
| 18.13
| 10.73
|
[
1,
2,
7,
8
] |
[
"8×2+7+1",
"(7+1)×2+8",
"(7-1)×8/2"
] | true
| 8.73
| 0.946
| 9.22
| 3.59
|
[
1,
2,
7,
9
] |
[
"9×2+7-1",
"7×2+9+1"
] | true
| 9.52
| 0.934
| 10.01
| 3.92
|
[
1,
2,
7,
10
] |
[
"(7×2+10)×1"
] | true
| 7.44
| 0.907
| 8.05
| 4.11
|
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