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
|
|---|---|---|---|---|---|---|---|
[
5,
6,
6,
9
] |
[
"9×6-6×5"
] | true
| 26.19
| 0.595
| 14.88
| 9.1
| 1,104
|
[
1,
4,
7,
7
] |
[
"(7+1)×(7-4)"
] | true
| 11.67
| 0.853
| 11.52
| 4.79
| 205
|
[
1,
1,
6,
6
] |
[
"(6+6)×(1+1)",
"(6-1-1)×6"
] | true
| 6.11
| 0.974
| 6.54
| 2.21
| 34
|
[
3,
5,
6,
12
] |
[
"(5+3-6)×12",
"(12-5-3)×6",
"(5-3)×6+12"
] | true
| 7.67
| 0.934
| 8.19
| 3.29
| 775
|
[
2,
4,
8,
10
] |
[
"10+8+4+2",
"10×4-8×2",
"(8×2-10)×4",
"(10-4)×8/2",
"(10-8/2)×4",
"(10+2)×8/4",
"10×2+8-4",
"8×4+2-10",
"(10-2)×4-8",
"(8/4+10)×2",
"(10×4+8)/2"
] | true
| 7.58
| 0.978
| 8.07
| 2.66
| 508
|
[
10,
10,
12,
13
] |
[
"13+12-10/10"
] | true
| 7.21
| 0.923
| 7.49
| 2.61
| 1,341
|
[
1,
2,
6,
9
] |
[
"(9-1)×6/2",
"(9×2+6)×1"
] | true
| 7.96
| 0.945
| 8.55
| 3.6
| 91
|
[
3,
12,
12,
13
] |
[
"(12+3-13)×12"
] | true
| 8.07
| 0.925
| 8.47
| 3.32
| 897
|
[
2,
6,
6,
9
] |
[
"(6+2)×(9-6)",
"(9+6)×2-6",
"(9×6-6)/2"
] | true
| 17.45
| 0.725
| 13.7
| 6.89
| 564
|
[
3,
5,
6,
13
] |
[
"(13-5)×(6-3)"
] | true
| 13.62
| 0.76
| 11.75
| 5.82
| 776
|
[
1,
5,
7,
10
] |
[
"7×5-10-1",
"(7/5+1)×10"
] | true
| 20.8
| 0.697
| 16.68
| 7.9
| 241
|
[
1,
1,
3,
5
] |
[
"(5+1)×(3+1)"
] | true
| 6.92
| 0.954
| 7.24
| 2.32
| 13
|
[
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
| 315
|
[
2,
7,
8,
11
] |
[
"(7×2-11)×8",
"11+8+7-2",
"(8-2)×(11-7)",
"(11+8-7)×2"
] | true
| 8.23
| 0.949
| 8.76
| 3.58
| 600
|
[
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
| 387
|
[
8,
8,
9,
11
] |
[
"9×8/(11-8)",
"(11-9)×8+8"
] | true
| 7.27
| 0.894
| 7.82
| 3.81
| 1,297
|
[
1,
3,
9,
9
] |
[
"(9-1)×9/3"
] | true
| 10.78
| 0.848
| 10.33
| 4.14
| 166
|
[
3,
7,
8,
8
] |
[
"(7-3)×8-8",
"(8-7)×8×3",
"(8/8+7)×3"
] | true
| 5.64
| 0.963
| 6.03
| 2.05
| 840
|
[
1,
1,
3,
12
] |
[
"(3-1)×12×1"
] | true
| 5.02
| 0.975
| 5.37
| 1.83
| 20
|
[
2,
10,
11,
11
] |
[
"(11+11-10)×2"
] | true
| 9.39
| 0.862
| 9.37
| 4.07
| 646
|
[
5,
8,
9,
11
] |
[
"(8-5)×11-9",
"(9+5-11)×8",
"(11-8)×5+9"
] | true
| 8.44
| 0.897
| 8.73
| 3.84
| 1,154
|
[
3,
6,
12,
12
] |
[
"(6-3)×12-12",
"(12-6)×12/3",
"(6-12/3)×12",
"(12/12+3)×6"
] | true
| 7.8
| 0.931
| 8.36
| 3.55
| 831
|
[
7,
8,
8,
11
] |
[
"(11-7)×8-8"
] | true
| 8.89
| 0.809
| 8.38
| 4.53
| 1,267
|
[
2,
6,
6,
7
] |
[
"(7-6/2)×6",
"(7-2)×6-6",
"(7×6+6)/2"
] | true
| 12.85
| 0.784
| 11.18
| 5.89
| 562
|
[
9,
10,
10,
13
] |
[
"13+10+10-9"
] | true
| 7.61
| 0.953
| 8.04
| 3.09
| 1,326
|
[
3,
3,
6,
6
] |
[
"(6/3+6)×3"
] | true
| 30.23
| 0.575
| 14.99
| 9.07
| 686
|
[
4,
5,
7,
7
] |
[
"7×5-7-4",
"(7/7+5)×4"
] | true
| 6.93
| 0.911
| 7.53
| 3.6
| 957
|
[
1,
4,
5,
6
] |
[
"6/(5/4-1)",
"4/(1-5/6)"
] | true
| 193.11
| 0.287
| 19.49
| 12.95
| 189
|
[
4,
5,
10,
11
] |
[
"10×4-11-5",
"(11+5-10)×4"
] | true
| 8.06
| 0.881
| 8.5
| 4.35
| 975
|
[
3,
3,
7,
13
] |
[
"(7×3-13)×3"
] | true
| 94.36
| 0.273
| 33.82
| 19.64
| 699
|
[
2,
4,
8,
12
] |
[
"(4+2)×(12-8)",
"(8-4-2)×12",
"8×2+12-4",
"(12+2-8)×4",
"(8-4)×12/2",
"(12+4)×2-8",
"(12-4)×2+8"
] | true
| 8.38
| 0.94
| 9.08
| 4.28
| 510
|
[
5,
5,
7,
11
] |
[
"(7-11/5)×5"
] | true
| 93.75
| 0.266
| 27.68
| 14.77
| 1,082
|
[
2,
4,
4,
5
] |
[
"(5+2)×4-4",
"(5×2-4)×4",
"(4+4)×(5-2)"
] | true
| 12.55
| 0.818
| 11.63
| 5.34
| 474
|
[
3,
7,
12,
13
] |
[
"(13-7)×12/3",
"12/3+13+7",
"(13+7-12)×3"
] | true
| 7.19
| 0.939
| 7.68
| 3.11
| 856
|
[
3,
4,
8,
9
] |
[
"9+8+4+3",
"(4×3-9)×8",
"(9+3)×8/4",
"(9-3)×(8-4)"
] | true
| 12.51
| 0.881
| 12.57
| 5.16
| 747
|
[
1,
5,
9,
10
] |
[
"(10+9+5)×1"
] | true
| 8.35
| 0.931
| 8.83
| 3.87
| 252
|
[
1,
1,
3,
13
] |
[
"(13-1)×(3-1)"
] | true
| 6.02
| 0.953
| 6.37
| 2.13
| 21
|
[
10,
10,
10,
13
] |
[
"10/10+13+10"
] | true
| 6.46
| 0.93
| 6.9
| 3.01
| 1,337
|
[
2,
3,
8,
13
] |
[
"(13+3)×2-8"
] | true
| 100.37
| 0.316
| 24.58
| 13.57
| 459
|
[
6,
6,
7,
10
] |
[
"(10-7)×6+6"
] | true
| 8.05
| 0.841
| 8.08
| 4.22
| 1,184
|
[
1,
6,
8,
10
] |
[
"(10-6-1)×8",
"(10+8+6)×1",
"6/(10/8-1)"
] | true
| 6.65
| 0.973
| 7.09
| 2.43
| 276
|
[
4,
5,
6,
12
] |
[
"(6+4)×12/5"
] | true
| 59.96
| 0.439
| 22.08
| 16.11
| 955
|
[
6,
7,
11,
12
] |
[
"(7+6-11)×12",
"12+11+7-6",
"(12-6)×(11-7)"
] | true
| 6.36
| 0.97
| 6.9
| 2.62
| 1,215
|
[
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
| 385
|
[
3,
6,
6,
10
] |
[
"(6-3)×10-6"
] | true
| 40.65
| 0.501
| 19.28
| 11.18
| 805
|
[
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
| 343
|
[
3,
5,
6,
6
] |
[
"(6+3-5)×6",
"(6+6)×(5-3)"
] | true
| 8.25
| 0.921
| 8.79
| 3.63
| 769
|
[
9,
11,
12,
12
] |
[
"12×11-12×9"
] | true
| 21.38
| 0.593
| 11.02
| 6.56
| 1,332
|
[
1,
3,
4,
6
] |
[
"6/(1-3/4)"
] | true
| 209.67
| 0.268
| 20.65
| 13.17
| 130
|
[
3,
8,
11,
11
] |
[
"8×3+11-11",
"(11-3)×(11-8)"
] | true
| 5.38
| 0.963
| 5.74
| 2.05
| 871
|
[
5,
6,
10,
11
] |
[
"(10+5-11)×6",
"(11-5)×(10-6)"
] | true
| 7.91
| 0.905
| 8.27
| 3.58
| 1,123
|
[
1,
2,
5,
13
] |
[
"(13-5)×(2+1)",
"5×2+13+1"
] | true
| 8.7
| 0.944
| 9.2
| 3.61
| 87
|
[
1,
10,
10,
12
] |
[
"(10/10+1)×12"
] | true
| 6.04
| 0.926
| 6.27
| 2.12
| 330
|
[
6,
9,
9,
11
] |
[
"(9-6)×11-9",
"(11-9)×9+6"
] | true
| 10.63
| 0.825
| 9.98
| 5.16
| 1,238
|
[
2,
3,
10,
13
] |
[
"13+10+3-2",
"(13-10/2)×3"
] | true
| 8.63
| 0.936
| 9.12
| 3.96
| 466
|
[
1,
3,
3,
6
] |
[
"(6+3-1)×3",
"(6+1)×3+3"
] | true
| 12.17
| 0.872
| 12.15
| 5.28
| 121
|
[
4,
8,
9,
12
] |
[
"9×8×4/12",
"(8-4)×9-12",
"9×8-12×4"
] | true
| 19.77
| 0.727
| 16.96
| 7.19
| 1,044
|
[
5,
5,
11,
11
] |
[
"5×5-11/11"
] | true
| 7.21
| 0.858
| 7.47
| 3.47
| 1,095
|
[
5,
6,
12,
13
] |
[
"(13-6-5)×12",
"13+12+5-6",
"(12+5-13)×6"
] | true
| 6.1
| 0.975
| 6.51
| 2.17
| 1,130
|
[
8,
8,
8,
11
] |
[
"11×8-8×8"
] | true
| 18.2
| 0.632
| 10.83
| 6.35
| 1,294
|
[
3,
8,
8,
10
] |
[
"(10×8-8)/3"
] | true
| 93.37
| 0.292
| 27.55
| 17.63
| 860
|
[
5,
6,
11,
11
] |
[
"(5-11/11)×6"
] | true
| 7.19
| 0.871
| 7.44
| 3.33
| 1,126
|
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