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,
7,
8,
9
] |
[
"(7+5-9)×8",
"8×5-9-7"
] | true
| 9.45
| 0.886
| 9.68
| 4.27
| 1,136
|
[
3,
3,
3,
6
] |
[
"6×3+3+3",
"(3+3)×3+6",
"(3/3+3)×6",
"(6+3)×3-3"
] | true
| 6.24
| 0.977
| 6.79
| 2.6
| 663
|
[
6,
9,
12,
13
] |
[
"(9+6-13)×12",
"(12-6)×(13-9)",
"12/6+13+9"
] | true
| 10.59
| 0.882
| 10.68
| 4.41
| 1,245
|
[
1,
8,
10,
11
] |
[
"(11+1)×(10-8)"
] | true
| 10.18
| 0.873
| 10.17
| 3.5
| 317
|
[
2,
10,
11,
13
] |
[
"(10+2)×(13-11)",
"(13+10-11)×2"
] | true
| 8.6
| 0.897
| 8.66
| 3.42
| 648
|
[
3,
3,
9,
13
] |
[
"(3+3)×(13-9)"
] | true
| 13.29
| 0.741
| 11
| 6.22
| 709
|
[
4,
5,
9,
12
] |
[
"12×5/4+9",
"12×5-9×4"
] | true
| 31.32
| 0.6
| 23.3
| 10.91
| 972
|
[
2,
8,
11,
11
] |
[
"(11/11+2)×8"
] | true
| 6.49
| 0.889
| 6.66
| 2.84
| 627
|
[
2,
9,
9,
11
] |
[
"(9/9+11)×2"
] | true
| 7.09
| 0.875
| 7.12
| 2.81
| 632
|
[
9,
10,
11,
12
] |
[
"12+11+10-9",
"(11+9)×12/10"
] | true
| 6.96
| 0.961
| 7.5
| 2.82
| 1,327
|
[
6,
12,
13,
13
] |
[
"13+13-12/6"
] | true
| 9.95
| 0.873
| 10
| 3.82
| 1,256
|
[
3,
5,
10,
13
] |
[
"(5+3)×(13-10)",
"13×3-10-5",
"(13+5-10)×3"
] | true
| 12
| 0.825
| 11.24
| 5.48
| 795
|
[
2,
10,
10,
13
] |
[
"(10-2)×(13-10)",
"(13-10/10)×2"
] | true
| 7.63
| 0.899
| 7.84
| 3.04
| 645
|
[
4,
7,
7,
7
] |
[
"(7-7/7)×4"
] | true
| 6.86
| 0.888
| 7.08
| 3.04
| 1,012
|
[
2,
5,
10,
12
] |
[
"(12+5)×2-10",
"(12-5)×2+10"
] | true
| 25.59
| 0.647
| 18.56
| 9
| 556
|
[
3,
3,
5,
7
] |
[
"(5×3-7)×3"
] | true
| 108.12
| 0.294
| 30.91
| 19.93
| 681
|
[
2,
6,
8,
10
] |
[
"(10-8)×6×2",
"(10+2-8)×6",
"(8-2)×(10-6)",
"(10+2)×(8-6)",
"(10+8-6)×2",
"(10+6)×2-8",
"8/(2-10/6)"
] | true
| 7.95
| 0.934
| 8.47
| 3.57
| 577
|
[
5,
6,
7,
9
] |
[
"(7-5)×9+6"
] | true
| 27.1
| 0.6
| 16.58
| 9.35
| 1,109
|
[
6,
6,
7,
9
] |
[
"(6+6)×(9-7)",
"(7+6-9)×6"
] | true
| 8.38
| 0.908
| 8.79
| 3.76
| 1,183
|
[
2,
5,
5,
7
] |
[
"7×2+5+5"
] | true
| 12.33
| 0.821
| 11.77
| 4.99
| 524
|
[
4,
9,
10,
13
] |
[
"(10-4)×(13-9)",
"(10+9-13)×4"
] | true
| 11.4
| 0.824
| 10.89
| 4.85
| 1,059
|
[
2,
5,
7,
8
] |
[
"(5×2-7)×8"
] | true
| 87.16
| 0.334
| 28.84
| 16.25
| 540
|
[
6,
6,
9,
11
] |
[
"(6+6)×(11-9)",
"(9+6-11)×6"
] | true
| 8.79
| 0.886
| 9.14
| 4.16
| 1,194
|
[
3,
4,
8,
10
] |
[
"(10-4-3)×8",
"(10-8)×4×3",
"(10+8)×4/3",
"(10-8/4)×3"
] | true
| 7.4
| 0.935
| 7.76
| 3.21
| 748
|
[
7,
7,
9,
10
] |
[
"(9-7)×7+10"
] | true
| 13
| 0.757
| 11.52
| 5.28
| 1,259
|
[
2,
4,
5,
6
] |
[
"6×5-4-2",
"(4+2)×5-6",
"5×4+6-2",
"(6-2)×5+4",
"(5+4)×2+6"
] | true
| 11.29
| 0.911
| 11.75
| 4.52
| 484
|
[
1,
2,
6,
13
] |
[
"6×2+13-1"
] | true
| 8.53
| 0.912
| 9.06
| 3.98
| 95
|
[
4,
7,
8,
13
] |
[
"13+8+7-4",
"(13-7)×(8-4)"
] | true
| 9.72
| 0.909
| 10.22
| 4.41
| 1,020
|
[
2,
6,
6,
8
] |
[
"(8-6)×6×2",
"(6×2-8)×6",
"(8+2-6)×6",
"(6-6/2)×8",
"(6/6+2)×8"
] | true
| 6.88
| 0.957
| 7.49
| 3.02
| 563
|
[
3,
4,
7,
8
] |
[
"(7-3)×4+8"
] | true
| 27.11
| 0.603
| 15.33
| 8.86
| 742
|
[
3,
8,
9,
9
] |
[
"8×3+9-9"
] | true
| 5.43
| 0.969
| 5.79
| 1.95
| 863
|
[
3,
10,
10,
12
] |
[
"12/3+10+10",
"(10+10-12)×3",
"(3-10/10)×12"
] | true
| 6.6
| 0.945
| 6.98
| 2.37
| 891
|
[
4,
8,
8,
11
] |
[
"(11×8+8)/4"
] | true
| 94.44
| 0.298
| 24.47
| 14.91
| 1,038
|
[
1,
4,
7,
8
] |
[
"8×4-7-1",
"(7+1)×4-8",
"(7-1)×(8-4)",
"(7-4)×8×1"
] | true
| 6.25
| 0.966
| 6.78
| 2.73
| 206
|
[
2,
2,
7,
12
] |
[
"7×2+12-2"
] | true
| 10.6
| 0.836
| 10.24
| 4.65
| 392
|
[
3,
5,
10,
12
] |
[
"(10-5-3)×12",
"12+10+5-3"
] | true
| 7.54
| 0.948
| 8.1
| 3.18
| 794
|
[
3,
8,
10,
12
] |
[
"12×10/(8-3)"
] | true
| 35.54
| 0.54
| 21.25
| 11.09
| 870
|
[
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
| 397
|
[
3,
5,
5,
9
] |
[
"(9-5/5)×3",
"(9/5+3)×5"
] | true
| 9.48
| 0.833
| 9.06
| 4.16
| 766
|
[
6,
10,
12,
12
] |
[
"12/6+12+10",
"(12-10)×6+12"
] | true
| 10.08
| 0.887
| 10.37
| 4.61
| 1,249
|
[
4,
7,
10,
12
] |
[
"(10+4)×12/7",
"(12-4)×(10-7)",
"(10-7)×4+12"
] | true
| 13.36
| 0.792
| 11.83
| 5.79
| 1,028
|
[
2,
9,
13,
13
] |
[
"(13+9)/2+13"
] | true
| 111.17
| 0.251
| 32.13
| 19.96
| 642
|
[
2,
8,
8,
8
] |
[
"8×8/2-8",
"(8+8)×2-8",
"(8/8+2)×8"
] | true
| 7.25
| 0.938
| 7.83
| 3.39
| 612
|
[
4,
5,
7,
10
] |
[
"(7-5)×10+4"
] | true
| 23.06
| 0.634
| 15.23
| 8.36
| 960
|
[
3,
4,
5,
5
] |
[
"5×5+3-4",
"5×3+5+4"
] | true
| 8.09
| 0.94
| 8.78
| 3.79
| 725
|
[
3,
3,
5,
10
] |
[
"3×3+10+5",
"(10+3-5)×3",
"(3-3/5)×10"
] | true
| 13.28
| 0.83
| 12.36
| 5.42
| 683
|
[
1,
2,
7,
9
] |
[
"9×2+7-1",
"7×2+9+1"
] | true
| 9.52
| 0.934
| 10.01
| 3.92
| 98
|
[
3,
6,
6,
9
] |
[
"9+6+6+3",
"9×6/3+6",
"6×6-9-3",
"(9-6/6)×3"
] | true
| 7.87
| 0.963
| 8.38
| 3.06
| 804
|
[
2,
2,
11,
13
] |
[
"13+11+2-2"
] | true
| 6.05
| 0.981
| 6.62
| 2.43
| 406
|
[
2,
4,
7,
9
] |
[
"4×2+9+7",
"(9+7-4)×2"
] | true
| 14.33
| 0.804
| 13.43
| 6.37
| 502
|
[
5,
5,
5,
5
] |
[
"5×5-5/5"
] | true
| 6.03
| 0.952
| 6.48
| 2.23
| 1,071
|
[
4,
9,
9,
12
] |
[
"(9+9-12)×4",
"(4-12/9)×9"
] | true
| 17.15
| 0.711
| 13.83
| 6.78
| 1,056
|
[
4,
4,
8,
9
] |
[
"9×4-8-4"
] | true
| 21.4
| 0.697
| 17.26
| 8.52
| 929
|
[
3,
5,
7,
10
] |
[
"(5+3)×(10-7)",
"(5-3)×7+10",
"(10+5-7)×3"
] | true
| 11.37
| 0.846
| 11.02
| 5.28
| 779
|
[
1,
4,
6,
9
] |
[
"(9-4-1)×6"
] | true
| 9.05
| 0.862
| 9
| 4.15
| 200
|
[
1,
3,
4,
10
] |
[
"(10-4)×(3+1)",
"(10-3-1)×4",
"(3-1)×10+4"
] | true
| 8.65
| 0.931
| 8.96
| 3.43
| 134
|
[
4,
8,
11,
13
] |
[
"(8+4)×(13-11)",
"(11+8-13)×4"
] | true
| 11.65
| 0.825
| 10.89
| 5.3
| 1,051
|
[
1,
1,
9,
13
] |
[
"13+9+1+1"
] | true
| 6.18
| 0.973
| 6.64
| 2.53
| 40
|
[
4,
7,
8,
10
] |
[
"8×7/4+10"
] | true
| 27.29
| 0.623
| 19.27
| 9.38
| 1,017
|
[
1,
5,
5,
13
] |
[
"13+5+5+1"
] | true
| 8.31
| 0.93
| 8.49
| 3.27
| 230
|
[
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
| 378
|
[
1,
6,
12,
12
] |
[
"12×12×1/6",
"12/(1-6/12)"
] | true
| 6.06
| 0.945
| 6.44
| 2.43
| 288
|
[
2,
3,
3,
12
] |
[
"12×2+3-3",
"(3+3)×2+12"
] | true
| 5.48
| 0.986
| 5.96
| 2.06
| 418
|
[
2,
2,
7,
10
] |
[
"(10/2+7)×2"
] | true
| 32.81
| 0.532
| 17.19
| 9.45
| 391
|
[
2,
6,
12,
13
] |
[
"13×2-12/6",
"12/(13/2-6)",
"13×12/6-2"
] | true
| 15.13
| 0.785
| 13.77
| 6.11
| 592
|
[
5,
9,
9,
11
] |
[
"11+9+9-5"
] | true
| 9.55
| 0.895
| 9.81
| 3.88
| 1,162
|
[
5,
5,
8,
11
] |
[
"8×5-11-5"
] | true
| 39.63
| 0.468
| 25.02
| 11.4
| 1,086
|
[
2,
10,
11,
12
] |
[
"11×2+12-10",
"(11-10)×12×2",
"(12-10)×11+2"
] | true
| 6.62
| 0.958
| 6.95
| 2.42
| 647
|
[
5,
8,
8,
10
] |
[
"(8+5-10)×8",
"10×8/5+8"
] | true
| 7.51
| 0.916
| 7.97
| 3.42
| 1,152
|
[
2,
4,
11,
11
] |
[
"11+11+4-2",
"4/2+11+11"
] | true
| 5.94
| 0.962
| 6.36
| 2.34
| 520
|
[
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
| 64
|
[
1,
1,
3,
6
] |
[
"(6+1+1)×3",
"(3+1)×6×1"
] | true
| 5.2
| 0.979
| 5.56
| 1.79
| 14
|
[
6,
6,
6,
10
] |
[
"10×6-6×6"
] | true
| 17.77
| 0.657
| 11.82
| 6.68
| 1,180
|
[
4,
10,
10,
12
] |
[
"(12-10)×10+4"
] | true
| 13.97
| 0.778
| 12.43
| 6.44
| 1,064
|
[
2,
4,
6,
6
] |
[
"(6+2-4)×6",
"(6+6)×(4-2)",
"(6+6)×4/2",
"(6-4/2)×6",
"(6-4)×6×2",
"(6×2-6)×4"
] | true
| 8.65
| 0.943
| 9.33
| 3.92
| 492
|
[
2,
2,
5,
11
] |
[
"(11-5)×(2+2)",
"(11-5)×2×2"
] | true
| 9.36
| 0.877
| 9.67
| 4.57
| 379
|
[
1,
4,
4,
12
] |
[
"(12-4)×(4-1)",
"(4-1)×4+12",
"(4/4+1)×12"
] | true
| 5.84
| 0.958
| 6.33
| 2.33
| 187
|
[
3,
5,
5,
6
] |
[
"(5+5)×3-6",
"(5/5+3)×6"
] | true
| 7.18
| 0.892
| 7.48
| 3.3
| 763
|
[
1,
4,
9,
10
] |
[
"10+9+4+1"
] | true
| 8.66
| 0.937
| 9.08
| 3.72
| 216
|
[
3,
5,
9,
13
] |
[
"13+9+5-3",
"(13-5)×9/3",
"(13×9+3)/5"
] | true
| 9.91
| 0.914
| 10.25
| 4.2
| 791
|
[
5,
5,
6,
7
] |
[
"5×5+6-7",
"7×5-6-5"
] | true
| 9.07
| 0.91
| 9.51
| 4.08
| 1,076
|
[
3,
9,
9,
11
] |
[
"(9+3)×(11-9)",
"11×9/3-9"
] | true
| 18.75
| 0.698
| 14.37
| 7.84
| 878
|
[
1,
11,
12,
13
] |
[
"(13-11)×12×1"
] | true
| 7.44
| 0.943
| 7.87
| 3.18
| 337
|
[
3,
4,
4,
8
] |
[
"4×3+8+4",
"8×3+4-4",
"(8-3)×4+4",
"(4×4-8)×3"
] | true
| 5.47
| 0.984
| 5.9
| 1.96
| 719
|
[
1,
7,
8,
9
] |
[
"(9+1-7)×8",
"(9+8+7)×1"
] | true
| 6.02
| 0.972
| 6.46
| 2.29
| 295
|
[
4,
7,
8,
9
] |
[
"9×8/(7-4)",
"(8+4)×(9-7)",
"(8+7-9)×4"
] | true
| 8.55
| 0.919
| 8.93
| 3.78
| 1,016
|
[
7,
8,
10,
13
] |
[
"13+10+8-7"
] | true
| 8.96
| 0.922
| 9.51
| 4.18
| 1,275
|
[
2,
3,
8,
9
] |
[
"(9-3×2)×8",
"(9-3)×8/2"
] | true
| 14.34
| 0.809
| 13.17
| 6.4
| 455
|
[
3,
6,
8,
8
] |
[
"8×6/3+8",
"8×6-8×3",
"(8/8+3)×6"
] | true
| 7.44
| 0.927
| 7.77
| 2.97
| 815
|
[
1,
6,
6,
13
] |
[
"13+6+6-1",
"6×6+1-13"
] | true
| 6.47
| 0.974
| 6.87
| 2.48
| 269
|
[
4,
6,
8,
8
] |
[
"6×4+8-8",
"(6-4)×8+8",
"(8+8)×6/4",
"(8+4)×(8-6)"
] | true
| 5.93
| 0.969
| 6.38
| 2.28
| 995
|
[
1,
4,
6,
10
] |
[
"(4-1)×10-6"
] | true
| 33.87
| 0.556
| 20.04
| 10.17
| 201
|
[
1,
3,
8,
9
] |
[
"9×8×1/3",
"3/(9/8-1)"
] | true
| 6.44
| 0.922
| 7.03
| 3.37
| 161
|
[
3,
4,
5,
9
] |
[
"(5×3-9)×4",
"(9+4-5)×3"
] | true
| 9.65
| 0.849
| 9.47
| 4.64
| 729
|
[
2,
2,
10,
10
] |
[
"10+10+2+2",
"2×2+10+10"
] | true
| 4.81
| 0.982
| 5.11
| 1.61
| 401
|
[
3,
3,
8,
10
] |
[
"10+8+3+3",
"8/(10/3-3)"
] | true
| 14.47
| 0.815
| 13.81
| 5.74
| 702
|
[
5,
6,
12,
12
] |
[
"(12+12)×(6-5)",
"(5-12/12)×6"
] | true
| 5.42
| 0.972
| 5.8
| 1.81
| 1,129
|
[
2,
6,
6,
10
] |
[
"10+6+6+2",
"10×6/2-6",
"6×6-10-2"
] | true
| 8.66
| 0.94
| 9.12
| 3.63
| 565
|
[
4,
7,
9,
9
] |
[
"(7-9/9)×4"
] | true
| 7.55
| 0.866
| 7.68
| 3.24
| 1,021
|
[
4,
7,
9,
13
] |
[
"7×4+9-13",
"(13-9)×7-4"
] | true
| 10.5
| 0.845
| 10.62
| 5.92
| 1,025
|
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