numbers
sequencelengths 4
4
| solutions
sequencelengths 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 |