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,
3,
6,
6
] |
[
"(3+2)×6-6",
"6×6×2/3",
"(6+2)×(6-3)",
"(6+3)×2+6",
"(6×3-6)×2",
"(6/3+2)×6"
] | true
| 10.81
| 0.921
| 11.24
| 4.42
| 439
|
[
2,
3,
6,
9
] |
[
"(9-3-2)×6",
"(6+2)×9/3",
"6×2+9+3",
"(9-3)×(6-2)",
"(3-2/6)×9",
"9×6/2-3",
"9×3-6/2",
"(9+6-3)×2"
] | true
| 10.29
| 0.933
| 10.78
| 4.23
| 442
|
[
6,
6,
9,
12
] |
[
"12×6/(9-6)",
"12×9/6+6",
"(12-9)×6+6"
] | true
| 7.98
| 0.918
| 8.26
| 3.39
| 1,195
|
[
1,
8,
10,
13
] |
[
"(13-10)×8×1",
"(13-1)×(10-8)"
] | true
| 6.27
| 0.948
| 6.61
| 2.4
| 319
|
[
3,
3,
4,
4
] |
[
"4×3+4×3",
"(4×3-4)×3"
] | true
| 7.05
| 0.945
| 7.41
| 2.63
| 670
|
[
4,
4,
11,
12
] |
[
"4/4+12+11"
] | true
| 5.81
| 0.92
| 6.13
| 2.4
| 939
|
[
1,
1,
2,
7
] |
[
"(7+1)×(2+1)"
] | true
| 6.73
| 0.955
| 6.95
| 2.06
| 5
|
[
1,
2,
7,
11
] |
[
"7×2+11-1"
] | true
| 10.7
| 0.882
| 10.89
| 4.83
| 100
|
[
2,
3,
4,
8
] |
[
"(8-4)×3×2",
"(4+2-3)×8",
"(8/2+4)×3"
] | true
| 8.12
| 0.929
| 8.89
| 4.11
| 424
|
[
3,
6,
7,
10
] |
[
"7×6/3+10"
] | true
| 33.87
| 0.575
| 22.71
| 10.92
| 812
|
[
4,
8,
11,
11
] |
[
"8/4+11+11",
"(4-11/11)×8"
] | true
| 5.77
| 0.953
| 6.09
| 2
| 1,049
|
[
2,
8,
13,
13
] |
[
"(13/13+2)×8"
] | true
| 6.18
| 0.902
| 6.49
| 2.62
| 631
|
[
3,
4,
7,
7
] |
[
"7×3+7-4",
"7×4+3-7",
"(7-3)×7-4",
"(7-4)×7+3"
] | true
| 8.93
| 0.941
| 9.56
| 3.85
| 741
|
[
2,
10,
10,
11
] |
[
"(10/10+11)×2"
] | true
| 7.59
| 0.85
| 7.41
| 3.02
| 643
|
[
5,
6,
8,
8
] |
[
"(6+5-8)×8",
"(5-8/8)×6"
] | true
| 7.42
| 0.924
| 7.86
| 3.05
| 1,112
|
[
3,
3,
3,
3
] |
[
"3×3×3-3"
] | true
| 6.88
| 0.96
| 7.55
| 3.39
| 660
|
[
1,
5,
5,
10
] |
[
"(10-5)×5-1"
] | true
| 16.87
| 0.708
| 12.39
| 7.4
| 227
|
[
7,
7,
12,
13
] |
[
"7×7-13-12",
"13+12-7/7"
] | true
| 6.26
| 0.939
| 6.69
| 2.37
| 1,264
|
[
4,
4,
6,
8
] |
[
"(8+4-6)×4",
"(8+4)×(6-4)"
] | true
| 13.5
| 0.833
| 12.71
| 6.9
| 916
|
[
3,
6,
7,
13
] |
[
"6×3+13-7",
"(13-7)×3+6"
] | true
| 11.65
| 0.824
| 10.94
| 6.02
| 814
|
[
4,
8,
9,
10
] |
[
"(9+4-10)×8"
] | true
| 8.16
| 0.891
| 8.37
| 3.48
| 1,042
|
[
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
| 66
|
[
6,
8,
13,
13
] |
[
"13+13+6-8"
] | true
| 7.5
| 0.933
| 7.95
| 3.12
| 1,236
|
[
4,
7,
9,
10
] |
[
"10×4-9-7",
"(9+7-10)×4",
"(9-7)×10+4"
] | true
| 7.81
| 0.909
| 8.35
| 3.71
| 1,022
|
[
1,
4,
8,
8
] |
[
"(8-4-1)×8",
"(8×4-8)×1",
"(8/4+1)×8"
] | true
| 6.31
| 0.967
| 6.81
| 2.51
| 211
|
[
11,
12,
13,
13
] |
[
"13/13+12+11",
"(13+11)×(13-12)"
] | true
| 6.26
| 0.953
| 6.74
| 2.49
| 1,356
|
[
4,
5,
5,
5
] |
[
"5×5+4-5",
"(5/5+5)×4"
] | true
| 6.05
| 0.976
| 6.61
| 2.43
| 943
|
[
2,
7,
7,
10
] |
[
"(10/7+2)×7"
] | true
| 90.16
| 0.276
| 28.11
| 13.67
| 594
|
[
5,
6,
9,
9
] |
[
"(9-6)×5+9",
"(5-9/9)×6"
] | true
| 7.01
| 0.908
| 7.33
| 2.8
| 1,117
|
[
4,
5,
8,
12
] |
[
"(12-5-4)×8",
"5×4+12-8",
"8×5-12-4",
"(12-4)×(8-5)",
"(8-5)×4+12",
"(12-8)×5+4"
] | true
| 8.67
| 0.934
| 9.22
| 3.78
| 968
|
[
6,
8,
9,
9
] |
[
"(9+9)×8/6",
"9×8/(9-6)"
] | true
| 10.32
| 0.862
| 10.33
| 4.3
| 1,224
|
[
3,
7,
9,
13
] |
[
"9×7-13×3",
"(7-13/3)×9"
] | true
| 111.27
| 0.26
| 40.42
| 22.14
| 849
|
[
4,
4,
10,
10
] |
[
"(10×10-4)/4"
] | true
| 62.74
| 0.397
| 14.21
| 9.64
| 936
|
[
2,
5,
8,
12
] |
[
"(5×2-8)×12",
"(8+2)×12/5"
] | true
| 34.66
| 0.546
| 18.65
| 10.33
| 549
|
[
6,
8,
9,
10
] |
[
"(10-8)×9+6"
] | true
| 17.26
| 0.711
| 13.34
| 7.45
| 1,225
|
[
3,
8,
9,
13
] |
[
"9/3+13+8",
"(13-8)×3+9"
] | true
| 18.43
| 0.741
| 15.96
| 7.47
| 867
|
[
7,
8,
9,
12
] |
[
"(12+9)×8/7",
"(9+7)×12/8"
] | true
| 43.05
| 0.482
| 16.76
| 10.32
| 1,271
|
[
3,
6,
11,
11
] |
[
"6/3+11+11",
"(11/11+3)×6"
] | true
| 5.74
| 0.946
| 6.04
| 2.08
| 828
|
[
1,
6,
7,
12
] |
[
"12+7+6-1",
"(7+1-6)×12",
"(12-7-1)×6",
"(7-1)×6-12"
] | true
| 5.61
| 0.986
| 6.03
| 2.01
| 273
|
[
4,
6,
6,
8
] |
[
"8+6+6+4",
"8×6-6×4",
"8×6/(6-4)",
"6×6-8-4",
"(6+6)×8/4",
"(6-8/4)×6",
"(4-6/6)×8"
] | true
| 7.15
| 0.974
| 7.64
| 2.63
| 986
|
[
2,
2,
3,
13
] |
[
"(13+2-3)×2"
] | true
| 8.69
| 0.875
| 8.75
| 3.74
| 362
|
[
1,
1,
1,
12
] |
[
"(1+1)×12×1"
] | true
| 4.82
| 0.993
| 5.15
| 1.6
| 2
|
[
1,
1,
2,
8
] |
[
"(2+1)×8×1"
] | true
| 4.97
| 0.978
| 5.33
| 1.74
| 6
|
[
1,
8,
8,
10
] |
[
"(10+1-8)×8"
] | true
| 7.11
| 0.923
| 7.5
| 3.03
| 311
|
[
2,
5,
9,
10
] |
[
"10×2+9-5"
] | true
| 14.94
| 0.781
| 13.46
| 6.36
| 551
|
[
9,
11,
12,
13
] |
[
"(13+9)×12/11"
] | true
| 99.38
| 0.289
| 22.82
| 13.58
| 1,333
|
[
10,
11,
11,
13
] |
[
"(13+11)×(11-10)",
"11/11+13+10"
] | true
| 6.51
| 0.948
| 6.93
| 2.65
| 1,343
|
[
1,
4,
8,
13
] |
[
"13+8+4-1",
"(13+1-8)×4",
"(13-1)×8/4"
] | true
| 6.81
| 0.974
| 7.2
| 2.49
| 215
|
[
4,
8,
8,
12
] |
[
"12+8+8-4",
"12×8/(8-4)",
"(12-8)×4+8"
] | true
| 9.06
| 0.944
| 9.57
| 3.94
| 1,039
|
[
1,
1,
4,
9
] |
[
"(9-1)×(4-1)"
] | true
| 6.9
| 0.935
| 7.12
| 2.35
| 27
|
[
8,
8,
12,
13
] |
[
"13+12-8/8"
] | true
| 7.07
| 0.922
| 7.4
| 2.7
| 1,305
|
[
3,
4,
4,
7
] |
[
"(7+3-4)×4",
"(4/4+7)×3"
] | true
| 7.64
| 0.904
| 8.09
| 3.53
| 718
|
[
4,
4,
8,
13
] |
[
"(4×4-13)×8",
"(13-8)×4+4"
] | true
| 9.15
| 0.865
| 9.05
| 4.33
| 933
|
[
5,
7,
7,
11
] |
[
"(5-11/7)×7"
] | true
| 90.39
| 0.275
| 26.22
| 13.42
| 1,134
|
[
9,
9,
12,
13
] |
[
"13+12-9/9",
"(13-9)×9-12"
] | true
| 6.34
| 0.94
| 6.7
| 2.24
| 1,325
|
[
4,
5,
11,
12
] |
[
"(11-5-4)×12",
"12+11+5-4",
"(12+5-11)×4"
] | true
| 5.68
| 0.975
| 6.09
| 2.09
| 979
|
[
1,
5,
10,
10
] |
[
"10+10+5-1"
] | true
| 6.28
| 0.974
| 6.68
| 2.3
| 256
|
[
1,
1,
4,
7
] |
[
"(7-1)×4×1",
"(7+1)×(4-1)"
] | true
| 5.59
| 0.972
| 5.94
| 2.07
| 25
|
[
1,
11,
12,
12
] |
[
"(12+1-11)×12"
] | true
| 7.04
| 0.943
| 7.62
| 3.19
| 336
|
[
1,
1,
12,
13
] |
[
"(13+12-1)×1"
] | true
| 5.45
| 0.988
| 5.84
| 1.85
| 47
|
[
1,
2,
9,
11
] |
[
"(2+1)×11-9"
] | true
| 48.09
| 0.448
| 23.76
| 13.21
| 106
|
[
2,
2,
2,
11
] |
[
"(2/2+11)×2",
"(11+2)×2-2"
] | true
| 6.62
| 0.923
| 6.97
| 2.8
| 349
|
[
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
| 55
|
[
3,
3,
4,
6
] |
[
"6×4+3-3"
] | true
| 5.69
| 0.978
| 6.13
| 2.08
| 672
|
[
1,
4,
8,
11
] |
[
"11+8+4+1",
"(11+1)×8/4"
] | true
| 7.89
| 0.957
| 8.34
| 2.9
| 213
|
[
1,
3,
3,
5
] |
[
"(5+3)×3×1",
"(3+3)×(5-1)"
] | true
| 6.6
| 0.952
| 6.91
| 2.52
| 120
|
[
3,
4,
4,
10
] |
[
"(10-3)×4-4"
] | true
| 15.03
| 0.769
| 12.54
| 6.93
| 721
|
[
2,
8,
8,
9
] |
[
"(9+2-8)×8"
] | true
| 8.16
| 0.904
| 8.5
| 3.44
| 613
|
[
1,
2,
4,
6
] |
[
"(2-1)×6×4",
"(6+2)×(4-1)"
] | true
| 6.5
| 0.96
| 6.92
| 2.54
| 72
|
[
2,
11,
11,
11
] |
[
"(11/11+11)×2"
] | true
| 6.21
| 0.897
| 6.28
| 2.49
| 650
|
[
2,
7,
8,
8
] |
[
"(8+2-7)×8",
"(7-8/2)×8",
"(8×7-8)/2"
] | true
| 7.78
| 0.926
| 8.16
| 3.19
| 598
|
[
1,
1,
11,
13
] |
[
"13+11+1-1"
] | true
| 5.23
| 0.991
| 5.64
| 1.81
| 45
|
[
4,
6,
10,
11
] |
[
"(11-10)×6×4"
] | true
| 5.94
| 0.946
| 6.34
| 2.41
| 1,005
|
[
2,
4,
13,
13
] |
[
"13+13+2-4",
"13+13-4/2"
] | true
| 6.94
| 0.959
| 7.48
| 2.76
| 523
|
[
3,
4,
4,
9
] |
[
"9×4-4×3",
"(4-4/3)×9",
"(4+4)×9/3",
"(9-4/4)×3"
] | true
| 7.79
| 0.908
| 8.34
| 3.4
| 720
|
[
3,
4,
4,
4
] |
[
"(4+3)×4-4"
] | true
| 26.36
| 0.672
| 19.02
| 10.56
| 715
|
[
3,
3,
3,
4
] |
[
"(3×3-3)×4",
"(4+3)×3+3"
] | true
| 12.83
| 0.82
| 11.78
| 5.94
| 661
|
[
2,
5,
6,
8
] |
[
"5×2+8+6",
"(6+2-5)×8",
"(6+2)×(8-5)",
"6×5+2-8",
"(8-2)×5-6"
] | true
| 7.54
| 0.955
| 8.03
| 3.05
| 533
|
[
2,
3,
10,
12
] |
[
"12×10/(3+2)",
"12×3-10-2",
"(10+2)×3-12",
"10×2+12/3",
"(10×2-12)×3",
"(10/2-3)×12",
"10×3-12/2"
] | true
| 11.33
| 0.867
| 11.45
| 4.21
| 465
|
[
3,
3,
4,
13
] |
[
"(13-4)×3-3"
] | true
| 15.11
| 0.765
| 12.74
| 7.08
| 678
|
[
5,
9,
10,
10
] |
[
"10+10+9-5"
] | true
| 7.32
| 0.929
| 7.75
| 3.15
| 1,164
|
[
3,
7,
8,
12
] |
[
"(7+3-8)×12",
"12+8+7-3",
"12×8/(7-3)",
"(7-12/3)×8"
] | true
| 8.24
| 0.951
| 8.77
| 3.27
| 843
|
[
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
| 60
|
[
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
| 92
|
[
2,
6,
10,
10
] |
[
"10+10+6-2",
"10×2+10-6"
] | true
| 7.25
| 0.959
| 7.78
| 3.05
| 585
|
[
1,
4,
5,
11
] |
[
"(11-5)×4×1"
] | true
| 8.35
| 0.907
| 8.63
| 4
| 194
|
[
1,
6,
9,
9
] |
[
"(9-1)×(9-6)",
"(9+9+6)×1"
] | true
| 6.5
| 0.975
| 6.94
| 2.51
| 280
|
[
2,
2,
3,
10
] |
[
"(10+3)×2-2"
] | true
| 36.04
| 0.547
| 18.71
| 10.73
| 359
|
[
2,
4,
10,
13
] |
[
"(13-10)×4×2",
"(13+4)×2-10"
] | true
| 8.89
| 0.892
| 9.31
| 4.55
| 519
|
[
3,
3,
4,
11
] |
[
"3×3+11+4",
"(11-4)×3+3"
] | true
| 11.13
| 0.885
| 11.18
| 5.5
| 676
|
[
6,
6,
8,
12
] |
[
"8×6×6/12",
"12×6-8×6",
"(8-6)×6+12",
"(12+6)×8/6"
] | true
| 9.86
| 0.907
| 10.17
| 4.36
| 1,191
|
[
1,
4,
4,
7
] |
[
"4×4+7+1",
"(7×4-4)×1"
] | true
| 6.66
| 0.962
| 7.37
| 3.22
| 182
|
[
1,
2,
10,
12
] |
[
"(12+10+2)×1"
] | true
| 6.06
| 0.974
| 6.57
| 2.4
| 110
|
[
4,
4,
4,
9
] |
[
"(9-4)×4+4"
] | true
| 8.61
| 0.881
| 8.62
| 4.06
| 904
|
[
3,
8,
11,
12
] |
[
"(12-11)×8×3"
] | true
| 6.18
| 0.942
| 6.7
| 2.72
| 872
|
[
1,
4,
6,
13
] |
[
"13+6+4+1",
"(13-6-1)×4",
"(13-1)×(6-4)"
] | true
| 6.58
| 0.977
| 7
| 2.35
| 204
|
[
3,
3,
5,
9
] |
[
"(3+3)×(9-5)",
"(5+3)×9/3",
"(9+3)×(5-3)",
"(9/3+5)×3"
] | true
| 9.77
| 0.873
| 9.76
| 4.06
| 682
|
[
1,
2,
2,
7
] |
[
"(7-1)×(2+2)",
"(7-1)×2×2"
] | true
| 8.47
| 0.918
| 8.8
| 3.37
| 52
|
[
2,
5,
8,
8
] |
[
"8×5-8×2",
"(8×5+8)/2"
] | true
| 15.74
| 0.716
| 12.2
| 6.91
| 545
|
[
3,
9,
10,
11
] |
[
"9/3+11+10",
"(10+9-11)×3"
] | true
| 7.29
| 0.93
| 7.68
| 2.95
| 882
|
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