name stringlengths 14 134 | problem_type stringclasses 25
values | params dict | prompt stringlengths 167 1k | satisfiable bool 2
classes | solution dict | difficulty dict | partial_assignment dict |
|---|---|---|---|---|---|---|---|
all_interval_n10__v5_h | all_interval | {
"n": 10,
"k": null,
"p": null,
"max_chromatic_number": null,
"min_edges": null,
"min_girth": null,
"vertices": null,
"max_clique": null,
"min_degree": null,
"clique_size": null,
"max_degree": null,
"max_edges": null,
"max_independent_set": null,
"maximal_triangle_free": null,
"min_chroma... | Find an all-interval series of size 10. This is a permutation of 0 to 9 such that the absolute differences between consecutive elements are also a permutation of 1 to 9.
Return a list of 10 integers forming a valid permutation, or state "UNSATISFIABLE" if no solution exists.
Partial assignment (fixed values that must... | true | {
"x": [
0,
9,
1,
8,
2,
7,
3,
6,
4,
5
],
"d": [
9,
8,
7,
6,
5,
4,
3,
2,
1
],
"seq": null,
"c": null,
"edges": null,
"q": null
} | {
"solve_time_ms": 1020.9,
"search_space": 3628800,
"num_variables": 19,
"num_constraints": 13,
"num_edges": -1,
"backend": "pycsp",
"solve_tier": "hard",
"solve_pct_global": 71.99,
"solve_pct_type": 79.17
} | {
"x": {
"0": 0,
"1": null,
"2": null,
"3": 8,
"4": null,
"5": null,
"6": null,
"7": null,
"8": null,
"9": null,
"10": null,
"11": null,
"12": null,
"13": null,
"14": null,
"15": null,
"17": null,
"18": null,
"19": null,
"20": null,
"... |
all_interval_n11__v8_nh | all_interval | {
"n": 11,
"k": null,
"p": null,
"max_chromatic_number": null,
"min_edges": null,
"min_girth": null,
"vertices": null,
"max_clique": null,
"min_degree": null,
"clique_size": null,
"max_degree": null,
"max_edges": null,
"max_independent_set": null,
"maximal_triangle_free": null,
"min_chroma... | Find an all-interval series of size 11. This is a permutation of 0 to 10 such that the absolute differences between consecutive elements are also a permutation of 1 to 10.
Return a list of 11 integers forming a valid permutation, or state "UNSATISFIABLE" if no solution exists. | true | {
"x": [
0,
10,
1,
9,
2,
8,
3,
7,
4,
6,
5
],
"d": [
10,
9,
8,
7,
6,
5,
4,
3,
2,
1
],
"seq": null,
"c": null,
"edges": null,
"q": null
} | {
"solve_time_ms": 1020.3,
"search_space": 39916800,
"num_variables": 21,
"num_constraints": 14,
"num_edges": -1,
"backend": "pycsp",
"solve_tier": "hard",
"solve_pct_global": 71.62,
"solve_pct_type": 70.83
} | null |
all_interval_n12__v9_nh | all_interval | {
"n": 12,
"k": null,
"p": null,
"max_chromatic_number": null,
"min_edges": null,
"min_girth": null,
"vertices": null,
"max_clique": null,
"min_degree": null,
"clique_size": null,
"max_degree": null,
"max_edges": null,
"max_independent_set": null,
"maximal_triangle_free": null,
"min_chroma... | Find an all-interval series of size 12. This is a permutation of 0 to 11 such that the absolute differences between consecutive elements are also a permutation of 1 to 11.
Return a list of 12 integers forming a valid permutation, or state "UNSATISFIABLE" if no solution exists. | true | {
"x": [
0,
11,
1,
10,
2,
9,
3,
8,
4,
7,
5,
6
],
"d": [
11,
10,
9,
8,
7,
6,
5,
4,
3,
2,
1
],
"seq": null,
"c": null,
"edges": null,
"q": null
} | {
"solve_time_ms": 997.3,
"search_space": 479001600,
"num_variables": 23,
"num_constraints": 15,
"num_edges": -1,
"backend": "pycsp",
"solve_tier": "hard",
"solve_pct_global": 70.11,
"solve_pct_type": 54.17
} | null |
all_interval_n13__v6_nh | all_interval | {
"n": 13,
"k": null,
"p": null,
"max_chromatic_number": null,
"min_edges": null,
"min_girth": null,
"vertices": null,
"max_clique": null,
"min_degree": null,
"clique_size": null,
"max_degree": null,
"max_edges": null,
"max_independent_set": null,
"maximal_triangle_free": null,
"min_chroma... | Find an all-interval series of size 13. This is a permutation of 0 to 12 such that the absolute differences between consecutive elements are also a permutation of 1 to 12.
Return a list of 13 integers forming a valid permutation, or state "UNSATISFIABLE" if no solution exists. | true | {
"x": [
0,
12,
1,
11,
2,
10,
3,
9,
4,
8,
5,
7,
6
],
"d": [
12,
11,
10,
9,
8,
7,
6,
5,
4,
3,
2,
1
],
"seq": null,
"c": null,
"edges": null,
"q": null
} | {
"solve_time_ms": 969.3,
"search_space": 6227020800,
"num_variables": 25,
"num_constraints": 16,
"num_edges": -1,
"backend": "pycsp",
"solve_tier": "medium",
"solve_pct_global": 66.35,
"solve_pct_type": 29.17
} | null |
all_interval_n14__v1_h | all_interval | {
"n": 14,
"k": null,
"p": null,
"max_chromatic_number": null,
"min_edges": null,
"min_girth": null,
"vertices": null,
"max_clique": null,
"min_degree": null,
"clique_size": null,
"max_degree": null,
"max_edges": null,
"max_independent_set": null,
"maximal_triangle_free": null,
"min_chroma... | Find an all-interval series of size 14. This is a permutation of 0 to 13 such that the absolute differences between consecutive elements are also a permutation of 1 to 13.
Return a list of 14 integers forming a valid permutation, or state "UNSATISFIABLE" if no solution exists.
Partial assignment (fixed values that mu... | true | {
"x": [
0,
13,
1,
12,
2,
11,
3,
10,
4,
9,
5,
8,
6,
7
],
"d": [
13,
12,
11,
10,
9,
8,
7,
6,
5,
4,
3,
2,
1
],
"seq": null,
"c": null,
"edges": null,
"q": null
} | {
"solve_time_ms": 993.6,
"search_space": 87178291200,
"num_variables": 27,
"num_constraints": 17,
"num_edges": -1,
"backend": "pycsp",
"solve_tier": "hard",
"solve_pct_global": 69.74,
"solve_pct_type": 45.83
} | {
"x": {
"0": null,
"1": null,
"2": null,
"3": null,
"4": null,
"5": null,
"6": 3,
"7": null,
"8": null,
"9": null,
"10": null,
"11": null,
"12": 6,
"13": null,
"14": null,
"15": null,
"17": null,
"18": null,
"19": null,
"20": null,
"... |
all_interval_n2__v0_h | all_interval | {
"n": 2,
"k": null,
"p": null,
"max_chromatic_number": null,
"min_edges": null,
"min_girth": null,
"vertices": null,
"max_clique": null,
"min_degree": null,
"clique_size": null,
"max_degree": null,
"max_edges": null,
"max_independent_set": null,
"maximal_triangle_free": null,
"min_chromat... | Find an all-interval series of size 2. This is a permutation of 0 to 1 such that the absolute differences between consecutive elements are also a permutation of 1 to 1.
Return a list of 2 integers forming a valid permutation, or state "UNSATISFIABLE" if no solution exists.
Partial assignment (fixed values that must b... | true | {
"x": [
0,
1
],
"d": [
1
],
"seq": null,
"c": null,
"edges": null,
"q": null
} | {
"solve_time_ms": 944.5,
"search_space": 2,
"num_variables": 3,
"num_constraints": 2,
"num_edges": -1,
"backend": "pycsp",
"solve_tier": "medium",
"solve_pct_global": 62.22,
"solve_pct_type": 4.17
} | {
"x": {
"0": 0,
"1": null,
"2": null,
"3": null,
"4": null,
"5": null,
"6": null,
"7": null,
"8": null,
"9": null,
"10": null,
"11": null,
"12": null,
"13": null,
"14": null,
"15": null,
"17": null,
"18": null,
"19": null,
"20": null,
... |
all_interval_n3__v10_nh | all_interval | {
"n": 3,
"k": null,
"p": null,
"max_chromatic_number": null,
"min_edges": null,
"min_girth": null,
"vertices": null,
"max_clique": null,
"min_degree": null,
"clique_size": null,
"max_degree": null,
"max_edges": null,
"max_independent_set": null,
"maximal_triangle_free": null,
"min_chromat... | Find an all-interval series of size 3. This is a permutation of 0 to 2 such that the absolute differences between consecutive elements are also a permutation of 1 to 2.
Return a list of 3 integers forming a valid permutation, or state "UNSATISFIABLE" if no solution exists. | true | {
"x": [
0,
2,
1
],
"d": [
2,
1
],
"seq": null,
"c": null,
"edges": null,
"q": null
} | {
"solve_time_ms": 983.9,
"search_space": 6,
"num_variables": 5,
"num_constraints": 6,
"num_edges": -1,
"backend": "pycsp",
"solve_tier": "hard",
"solve_pct_global": 68.23,
"solve_pct_type": 37.5
} | null |
all_interval_n4__v11_nh | all_interval | {
"n": 4,
"k": null,
"p": null,
"max_chromatic_number": null,
"min_edges": null,
"min_girth": null,
"vertices": null,
"max_clique": null,
"min_degree": null,
"clique_size": null,
"max_degree": null,
"max_edges": null,
"max_independent_set": null,
"maximal_triangle_free": null,
"min_chromat... | Find an all-interval series of size 4. This is a permutation of 0 to 3 such that the absolute differences between consecutive elements are also a permutation of 1 to 3.
Return a list of 4 integers forming a valid permutation, or state "UNSATISFIABLE" if no solution exists. | true | {
"x": [
0,
3,
1,
2
],
"d": [
3,
2,
1
],
"seq": null,
"c": null,
"edges": null,
"q": null
} | {
"solve_time_ms": 968.5,
"search_space": 24,
"num_variables": 7,
"num_constraints": 7,
"num_edges": -1,
"backend": "pycsp",
"solve_tier": "medium",
"solve_pct_global": 65.98,
"solve_pct_type": 20.83
} | null |
all_interval_n5__v3_nh | all_interval | {
"n": 5,
"k": null,
"p": null,
"max_chromatic_number": null,
"min_edges": null,
"min_girth": null,
"vertices": null,
"max_clique": null,
"min_degree": null,
"clique_size": null,
"max_degree": null,
"max_edges": null,
"max_independent_set": null,
"maximal_triangle_free": null,
"min_chromat... | Find an all-interval series of size 5. This is a permutation of 0 to 4 such that the absolute differences between consecutive elements are also a permutation of 1 to 4.
Return a list of 5 integers forming a valid permutation, or state "UNSATISFIABLE" if no solution exists. | true | {
"x": [
0,
4,
1,
3,
2
],
"d": [
4,
3,
2,
1
],
"seq": null,
"c": null,
"edges": null,
"q": null
} | {
"solve_time_ms": 1031.3,
"search_space": 120,
"num_variables": 9,
"num_constraints": 8,
"num_edges": -1,
"backend": "pycsp",
"solve_tier": "hard",
"solve_pct_global": 72.74,
"solve_pct_type": 87.5
} | null |
all_interval_n6__v7_nh | all_interval | {
"n": 6,
"k": null,
"p": null,
"max_chromatic_number": null,
"min_edges": null,
"min_girth": null,
"vertices": null,
"max_clique": null,
"min_degree": null,
"clique_size": null,
"max_degree": null,
"max_edges": null,
"max_independent_set": null,
"maximal_triangle_free": null,
"min_chromat... | Find an all-interval series of size 6. This is a permutation of 0 to 5 such that the absolute differences between consecutive elements are also a permutation of 1 to 5.
Return a list of 6 integers forming a valid permutation, or state "UNSATISFIABLE" if no solution exists. | true | {
"x": [
0,
5,
1,
4,
2,
3
],
"d": [
5,
4,
3,
2,
1
],
"seq": null,
"c": null,
"edges": null,
"q": null
} | {
"solve_time_ms": 1045.9,
"search_space": 720,
"num_variables": 11,
"num_constraints": 9,
"num_edges": -1,
"backend": "pycsp",
"solve_tier": "hard",
"solve_pct_global": 75,
"solve_pct_type": 95.83
} | null |
all_interval_n8__v2_h | all_interval | {
"n": 8,
"k": null,
"p": null,
"max_chromatic_number": null,
"min_edges": null,
"min_girth": null,
"vertices": null,
"max_clique": null,
"min_degree": null,
"clique_size": null,
"max_degree": null,
"max_edges": null,
"max_independent_set": null,
"maximal_triangle_free": null,
"min_chromat... | Find an all-interval series of size 8. This is a permutation of 0 to 7 such that the absolute differences between consecutive elements are also a permutation of 1 to 7.
Return a list of 8 integers forming a valid permutation, or state "UNSATISFIABLE" if no solution exists.
Partial assignment (fixed values that must b... | true | {
"x": [
0,
7,
1,
6,
2,
5,
3,
4
],
"d": [
7,
6,
5,
4,
3,
2,
1
],
"seq": null,
"c": null,
"edges": null,
"q": null
} | {
"solve_time_ms": 956.4,
"search_space": 40320,
"num_variables": 15,
"num_constraints": 11,
"num_edges": -1,
"backend": "pycsp",
"solve_tier": "medium",
"solve_pct_global": 64.1,
"solve_pct_type": 12.5
} | {
"x": {
"0": null,
"1": null,
"2": null,
"3": null,
"4": 2,
"5": null,
"6": null,
"7": null,
"8": null,
"9": null,
"10": null,
"11": null,
"12": null,
"13": null,
"14": null,
"15": null,
"17": null,
"18": null,
"19": null,
"20": null,
... |
all_interval_n9__v4_nh | all_interval | {
"n": 9,
"k": null,
"p": null,
"max_chromatic_number": null,
"min_edges": null,
"min_girth": null,
"vertices": null,
"max_clique": null,
"min_degree": null,
"clique_size": null,
"max_degree": null,
"max_edges": null,
"max_independent_set": null,
"maximal_triangle_free": null,
"min_chromat... | Find an all-interval series of size 9. This is a permutation of 0 to 8 such that the absolute differences between consecutive elements are also a permutation of 1 to 8.
Return a list of 9 integers forming a valid permutation, or state "UNSATISFIABLE" if no solution exists. | true | {
"x": [
0,
8,
1,
7,
2,
6,
3,
5,
4
],
"d": [
8,
7,
6,
5,
4,
3,
2,
1
],
"seq": null,
"c": null,
"edges": null,
"q": null
} | {
"solve_time_ms": 1016.2,
"search_space": 362880,
"num_variables": 17,
"num_constraints": 12,
"num_edges": -1,
"backend": "pycsp",
"solve_tier": "hard",
"solve_pct_global": 71.24,
"solve_pct_type": 62.5
} | null |
costas_array_n10__v0_nh | costas_array | {
"n": 10,
"k": null,
"p": null,
"max_chromatic_number": null,
"min_edges": null,
"min_girth": null,
"vertices": null,
"max_clique": null,
"min_degree": null,
"clique_size": null,
"max_degree": null,
"max_edges": null,
"max_independent_set": null,
"maximal_triangle_free": null,
"min_chroma... | Find a Costas array of order 10: place 10 marks on an 10x10 grid, one per row and one per column, such that all 10*(9)/2 displacement vectors (dr, dc) between pairs of marks (with dc > 0) are pairwise distinct.
Return x as a list of 10 integers in 0..9, where x[c] is the row of the mark in column c (permutation), or s... | true | {
"x": [
8,
5,
6,
0,
2,
1,
4,
9,
7,
3
],
"d": null,
"seq": null,
"c": null,
"edges": null,
"q": null
} | {
"solve_time_ms": 1070.6,
"search_space": 3628800,
"num_variables": 10,
"num_constraints": 11,
"num_edges": -1,
"backend": "pycsp",
"solve_tier": "hard",
"solve_pct_global": 75.75,
"solve_pct_type": 72.22
} | null |
costas_array_n11__v1_nh | costas_array | {
"n": 11,
"k": null,
"p": null,
"max_chromatic_number": null,
"min_edges": null,
"min_girth": null,
"vertices": null,
"max_clique": null,
"min_degree": null,
"clique_size": null,
"max_degree": null,
"max_edges": null,
"max_independent_set": null,
"maximal_triangle_free": null,
"min_chroma... | Find a Costas array of order 11: place 11 marks on an 11x11 grid, one per row and one per column, such that all 11*(10)/2 displacement vectors (dr, dc) between pairs of marks (with dc > 0) are pairwise distinct.
Return x as a list of 11 integers in 0..10, where x[c] is the row of the mark in column c (permutation), or... | true | {
"x": [
9,
3,
8,
4,
1,
0,
7,
2,
5,
6,
10
],
"d": null,
"seq": null,
"c": null,
"edges": null,
"q": null
} | {
"solve_time_ms": 1035.3,
"search_space": 39916800,
"num_variables": 11,
"num_constraints": 12,
"num_edges": -1,
"backend": "pycsp",
"solve_tier": "hard",
"solve_pct_global": 73.12,
"solve_pct_type": 61.11
} | null |
costas_array_n12__v4_h | costas_array | {
"n": 12,
"k": null,
"p": null,
"max_chromatic_number": null,
"min_edges": null,
"min_girth": null,
"vertices": null,
"max_clique": null,
"min_degree": null,
"clique_size": null,
"max_degree": null,
"max_edges": null,
"max_independent_set": null,
"maximal_triangle_free": null,
"min_chroma... | Find a Costas array of order 12: place 12 marks on an 12x12 grid, one per row and one per column, such that all 12*(11)/2 displacement vectors (dr, dc) between pairs of marks (with dc > 0) are pairwise distinct.
Return x as a list of 12 integers in 0..11, where x[c] is the row of the mark in column c (permutation), or... | true | {
"x": [
6,
1,
10,
8,
9,
5,
11,
3,
2,
4,
7,
0
],
"d": null,
"seq": null,
"c": null,
"edges": null,
"q": null
} | {
"solve_time_ms": 1129.3,
"search_space": 479001600,
"num_variables": 12,
"num_constraints": 13,
"num_edges": -1,
"backend": "pycsp",
"solve_tier": "hard",
"solve_pct_global": 77.63,
"solve_pct_type": 83.33
} | {
"x": {
"0": null,
"1": null,
"2": null,
"3": 8,
"4": null,
"5": null,
"6": null,
"7": null,
"8": 2,
"9": null,
"10": null,
"11": null,
"12": null,
"13": null,
"14": null,
"15": null,
"17": null,
"18": null,
"19": null,
"20": null,
"... |
costas_array_n13__v2_h | costas_array | {
"n": 13,
"k": null,
"p": null,
"max_chromatic_number": null,
"min_edges": null,
"min_girth": null,
"vertices": null,
"max_clique": null,
"min_degree": null,
"clique_size": null,
"max_degree": null,
"max_edges": null,
"max_independent_set": null,
"maximal_triangle_free": null,
"min_chroma... | Find a Costas array of order 13: place 13 marks on an 13x13 grid, one per row and one per column, such that all 13*(12)/2 displacement vectors (dr, dc) between pairs of marks (with dc > 0) are pairwise distinct.
Return x as a list of 13 integers in 0..12, where x[c] is the row of the mark in column c (permutation), or... | true | {
"x": [
8,
7,
5,
10,
3,
0,
4,
12,
6,
1,
2,
9,
11
],
"d": null,
"seq": null,
"c": null,
"edges": null,
"q": null
} | {
"solve_time_ms": 1330,
"search_space": 6227020800,
"num_variables": 13,
"num_constraints": 14,
"num_edges": -1,
"backend": "pycsp",
"solve_tier": "hard",
"solve_pct_global": 82.52,
"solve_pct_type": 94.44
} | {
"x": {
"0": null,
"1": null,
"2": null,
"3": null,
"4": 3,
"5": null,
"6": null,
"7": null,
"8": null,
"9": 1,
"10": null,
"11": null,
"12": null,
"13": null,
"14": null,
"15": null,
"17": null,
"18": null,
"19": null,
"20": null,
"... |
costas_array_n5__v3_h | costas_array | {
"n": 5,
"k": null,
"p": null,
"max_chromatic_number": null,
"min_edges": null,
"min_girth": null,
"vertices": null,
"max_clique": null,
"min_degree": null,
"clique_size": null,
"max_degree": null,
"max_edges": null,
"max_independent_set": null,
"maximal_triangle_free": null,
"min_chromat... | Find a Costas array of order 5: place 5 marks on an 5x5 grid, one per row and one per column, such that all 5*(4)/2 displacement vectors (dr, dc) between pairs of marks (with dc > 0) are pairwise distinct.
Return x as a list of 5 integers in 0..4, where x[c] is the row of the mark in column c (permutation), or state "... | true | {
"x": [
0,
2,
3,
1,
4
],
"d": null,
"seq": null,
"c": null,
"edges": null,
"q": null
} | {
"solve_time_ms": 842.2,
"search_space": 120,
"num_variables": 5,
"num_constraints": 6,
"num_edges": -1,
"backend": "pycsp",
"solve_tier": "medium",
"solve_pct_global": 55.45,
"solve_pct_type": 5.56
} | {
"x": {
"0": null,
"1": null,
"2": 3,
"3": null,
"4": null,
"5": null,
"6": null,
"7": null,
"8": null,
"9": null,
"10": null,
"11": null,
"12": null,
"13": null,
"14": null,
"15": null,
"17": null,
"18": null,
"19": null,
"20": null,
... |
costas_array_n6__v5_nh | costas_array | {
"n": 6,
"k": null,
"p": null,
"max_chromatic_number": null,
"min_edges": null,
"min_girth": null,
"vertices": null,
"max_clique": null,
"min_degree": null,
"clique_size": null,
"max_degree": null,
"max_edges": null,
"max_independent_set": null,
"maximal_triangle_free": null,
"min_chromat... | Find a Costas array of order 6: place 6 marks on an 6x6 grid, one per row and one per column, such that all 6*(5)/2 displacement vectors (dr, dc) between pairs of marks (with dc > 0) are pairwise distinct.
Return x as a list of 6 integers in 0..5, where x[c] is the row of the mark in column c (permutation), or state "... | true | {
"x": [
0,
1,
4,
3,
5,
2
],
"d": null,
"seq": null,
"c": null,
"edges": null,
"q": null
} | {
"solve_time_ms": 863.5,
"search_space": 720,
"num_variables": 6,
"num_constraints": 7,
"num_edges": -1,
"backend": "pycsp",
"solve_tier": "medium",
"solve_pct_global": 56.58,
"solve_pct_type": 16.67
} | null |
costas_array_n7__v8_h | costas_array | {
"n": 7,
"k": null,
"p": null,
"max_chromatic_number": null,
"min_edges": null,
"min_girth": null,
"vertices": null,
"max_clique": null,
"min_degree": null,
"clique_size": null,
"max_degree": null,
"max_edges": null,
"max_independent_set": null,
"maximal_triangle_free": null,
"min_chromat... | Find a Costas array of order 7: place 7 marks on an 7x7 grid, one per row and one per column, such that all 7*(6)/2 displacement vectors (dr, dc) between pairs of marks (with dc > 0) are pairwise distinct.
Return x as a list of 7 integers in 0..6, where x[c] is the row of the mark in column c (permutation), or state "... | true | {
"x": [
0,
1,
6,
4,
3,
5,
2
],
"d": null,
"seq": null,
"c": null,
"edges": null,
"q": null
} | {
"solve_time_ms": 897.2,
"search_space": 5040,
"num_variables": 7,
"num_constraints": 8,
"num_edges": -1,
"backend": "pycsp",
"solve_tier": "medium",
"solve_pct_global": 57.33,
"solve_pct_type": 38.89
} | {
"x": {
"0": null,
"1": 1,
"2": null,
"3": null,
"4": null,
"5": null,
"6": null,
"7": null,
"8": null,
"9": null,
"10": null,
"11": null,
"12": null,
"13": null,
"14": null,
"15": null,
"17": null,
"18": null,
"19": null,
"20": null,
... |
costas_array_n8__v6_nh | costas_array | {
"n": 8,
"k": null,
"p": null,
"max_chromatic_number": null,
"min_edges": null,
"min_girth": null,
"vertices": null,
"max_clique": null,
"min_degree": null,
"clique_size": null,
"max_degree": null,
"max_edges": null,
"max_independent_set": null,
"maximal_triangle_free": null,
"min_chromat... | Find a Costas array of order 8: place 8 marks on an 8x8 grid, one per row and one per column, such that all 8*(7)/2 displacement vectors (dr, dc) between pairs of marks (with dc > 0) are pairwise distinct.
Return x as a list of 8 integers in 0..7, where x[c] is the row of the mark in column c (permutation), or state "... | true | {
"x": [
4,
7,
3,
2,
0,
5,
6,
1
],
"d": null,
"seq": null,
"c": null,
"edges": null,
"q": null
} | {
"solve_time_ms": 880.3,
"search_space": 40320,
"num_variables": 8,
"num_constraints": 9,
"num_edges": -1,
"backend": "pycsp",
"solve_tier": "medium",
"solve_pct_global": 56.95,
"solve_pct_type": 27.78
} | null |
costas_array_n9__v7_nh | costas_array | {
"n": 9,
"k": null,
"p": null,
"max_chromatic_number": null,
"min_edges": null,
"min_girth": null,
"vertices": null,
"max_clique": null,
"min_degree": null,
"clique_size": null,
"max_degree": null,
"max_edges": null,
"max_independent_set": null,
"maximal_triangle_free": null,
"min_chromat... | Find a Costas array of order 9: place 9 marks on an 9x9 grid, one per row and one per column, such that all 9*(8)/2 displacement vectors (dr, dc) between pairs of marks (with dc > 0) are pairwise distinct.
Return x as a list of 9 integers in 0..8, where x[c] is the row of the mark in column c (permutation), or state "... | true | {
"x": [
1,
7,
3,
6,
8,
2,
0,
5,
4
],
"d": null,
"seq": null,
"c": null,
"edges": null,
"q": null
} | {
"solve_time_ms": 932.4,
"search_space": 362880,
"num_variables": 9,
"num_constraints": 10,
"num_edges": -1,
"backend": "pycsp",
"solve_tier": "medium",
"solve_pct_global": 60.71,
"solve_pct_type": 50
} | null |
golomb_n10__v0_nh | golomb | {
"n": 10,
"k": null,
"p": null,
"max_chromatic_number": null,
"min_edges": null,
"min_girth": null,
"vertices": null,
"max_clique": null,
"min_degree": null,
"clique_size": null,
"max_degree": null,
"max_edges": null,
"max_independent_set": null,
"maximal_triangle_free": null,
"min_chroma... | Find a Golomb ruler with 10 marks. A Golomb ruler is a set of 10 integers (marks) such that all pairwise distances between marks are unique. The first mark should be at position 0.
Return a list of 10 integers in increasing order representing the mark positions, or state "UNSATISFIABLE" if no solution exists. | true | {
"x": [
0,
2,
14,
21,
29,
32,
45,
49,
54,
55
],
"d": null,
"seq": null,
"c": null,
"edges": null,
"q": null
} | {
"solve_time_ms": 18872.1,
"search_space": 110462212541120450000,
"num_variables": 10,
"num_constraints": 5,
"num_edges": -1,
"backend": "pycsp",
"solve_tier": "hard",
"solve_pct_global": 99.44,
"solve_pct_type": 91.67
} | null |
golomb_n5__v1_nh | golomb | {
"n": 5,
"k": null,
"p": null,
"max_chromatic_number": null,
"min_edges": null,
"min_girth": null,
"vertices": null,
"max_clique": null,
"min_degree": null,
"clique_size": null,
"max_degree": null,
"max_edges": null,
"max_independent_set": null,
"maximal_triangle_free": null,
"min_chromat... | Find a Golomb ruler with 5 marks. A Golomb ruler is a set of 5 integers (marks) such that all pairwise distances between marks are unique. The first mark should be at position 0.
Return a list of 5 integers in increasing order representing the mark positions, or state "UNSATISFIABLE" if no solution exists. | true | {
"x": [
0,
1,
4,
9,
11
],
"d": null,
"seq": null,
"c": null,
"edges": null,
"q": null
} | {
"solve_time_ms": 1258.9,
"search_space": 11881376,
"num_variables": 5,
"num_constraints": 5,
"num_edges": -1,
"backend": "pycsp",
"solve_tier": "hard",
"solve_pct_global": 80.64,
"solve_pct_type": 8.33
} | null |
golomb_n6__v3_nh | golomb | {
"n": 6,
"k": null,
"p": null,
"max_chromatic_number": null,
"min_edges": null,
"min_girth": null,
"vertices": null,
"max_clique": null,
"min_degree": null,
"clique_size": null,
"max_degree": null,
"max_edges": null,
"max_independent_set": null,
"maximal_triangle_free": null,
"min_chromat... | Find a Golomb ruler with 6 marks. A Golomb ruler is a set of 6 integers (marks) such that all pairwise distances between marks are unique. The first mark should be at position 0.
Return a list of 6 integers in increasing order representing the mark positions, or state "UNSATISFIABLE" if no solution exists. | true | {
"x": [
0,
1,
4,
10,
12,
17
],
"d": null,
"seq": null,
"c": null,
"edges": null,
"q": null
} | {
"solve_time_ms": 1442.1,
"search_space": 2565726409,
"num_variables": 6,
"num_constraints": 5,
"num_edges": -1,
"backend": "pycsp",
"solve_tier": "hard",
"solve_pct_global": 85.9,
"solve_pct_type": 25
} | null |
golomb_n7__v4_h | golomb | {
"n": 7,
"k": null,
"p": null,
"max_chromatic_number": null,
"min_edges": null,
"min_girth": null,
"vertices": null,
"max_clique": null,
"min_degree": null,
"clique_size": null,
"max_degree": null,
"max_edges": null,
"max_independent_set": null,
"maximal_triangle_free": null,
"min_chromat... | Find a Golomb ruler with 7 marks. A Golomb ruler is a set of 7 integers (marks) such that all pairwise distances between marks are unique. The first mark should be at position 0.
Return a list of 7 integers in increasing order representing the mark positions, or state "UNSATISFIABLE" if no solution exists.
Partial as... | true | {
"x": [
0,
2,
6,
9,
14,
24,
25
],
"d": null,
"seq": null,
"c": null,
"edges": null,
"q": null
} | {
"solve_time_ms": 1984.3,
"search_space": 781250000000,
"num_variables": 7,
"num_constraints": 5,
"num_edges": -1,
"backend": "pycsp",
"solve_tier": "hard",
"solve_pct_global": 91.92,
"solve_pct_type": 41.67
} | {
"x": {
"0": null,
"1": 2,
"2": null,
"3": null,
"4": null,
"5": null,
"6": null,
"7": null,
"8": null,
"9": null,
"10": null,
"11": null,
"12": null,
"13": null,
"14": null,
"15": null,
"17": null,
"18": null,
"19": null,
"20": null,
... |
golomb_n8__v5_h | golomb | {
"n": 8,
"k": null,
"p": null,
"max_chromatic_number": null,
"min_edges": null,
"min_girth": null,
"vertices": null,
"max_clique": null,
"min_degree": null,
"clique_size": null,
"max_degree": null,
"max_edges": null,
"max_independent_set": null,
"maximal_triangle_free": null,
"min_chromat... | Find a Golomb ruler with 8 marks. A Golomb ruler is a set of 8 integers (marks) such that all pairwise distances between marks are unique. The first mark should be at position 0.
Return a list of 8 integers in increasing order representing the mark positions, or state "UNSATISFIABLE" if no solution exists.
Partial as... | true | {
"x": [
0,
2,
12,
19,
25,
30,
33,
34
],
"d": null,
"seq": null,
"c": null,
"edges": null,
"q": null
} | {
"solve_time_ms": 2326.3,
"search_space": 318644812890625,
"num_variables": 8,
"num_constraints": 5,
"num_edges": -1,
"backend": "pycsp",
"solve_tier": "hard",
"solve_pct_global": 92.67,
"solve_pct_type": 58.33
} | {
"x": {
"0": null,
"1": 2,
"2": null,
"3": null,
"4": null,
"5": null,
"6": null,
"7": null,
"8": null,
"9": null,
"10": null,
"11": null,
"12": null,
"13": null,
"14": null,
"15": null,
"17": null,
"18": null,
"19": null,
"20": null,
... |
golomb_n9__v2_nh | golomb | {
"n": 9,
"k": null,
"p": null,
"max_chromatic_number": null,
"min_edges": null,
"min_girth": null,
"vertices": null,
"max_clique": null,
"min_degree": null,
"clique_size": null,
"max_degree": null,
"max_edges": null,
"max_independent_set": null,
"maximal_triangle_free": null,
"min_chromat... | Find a Golomb ruler with 9 marks. A Golomb ruler is a set of 9 integers (marks) such that all pairwise distances between marks are unique. The first mark should be at position 0.
Return a list of 9 integers in increasing order representing the mark positions, or state "UNSATISFIABLE" if no solution exists. | true | {
"x": [
0,
1,
5,
12,
25,
27,
35,
41,
44
],
"d": null,
"seq": null,
"c": null,
"edges": null,
"q": null
} | {
"solve_time_ms": 4578.6,
"search_space": 167619550409708030,
"num_variables": 9,
"num_constraints": 5,
"num_edges": -1,
"backend": "pycsp",
"solve_tier": "hard",
"solve_pct_global": 97.18,
"solve_pct_type": 75
} | null |
graceful_graph_k2_p3__v0_h | graceful_graph | {
"n": null,
"k": 2,
"p": 3,
"max_chromatic_number": null,
"min_edges": null,
"min_girth": null,
"vertices": null,
"max_clique": null,
"min_degree": null,
"clique_size": null,
"max_degree": null,
"max_edges": null,
"max_independent_set": null,
"maximal_triangle_free": null,
"min_chromatic_... | Find a graceful labeling for the graph G_{2,3}: 3 disjoint K_2 cliques (numbered 0 through 2), where each pair of consecutive cliques (g, g+1) is connected by 2 edges that link vertex i of clique g to vertex i of clique g+1 for each i in 0..1. The graph has 6 vertices and 7 edges in total.
A graceful labeling assigns ... | true | {
"x": [
0,
2,
7,
3,
1,
6
],
"d": [
2,
4,
5,
7,
1,
6,
3
],
"seq": null,
"c": null,
"edges": null,
"q": null
} | {
"solve_time_ms": 1025.2,
"search_space": 262144,
"num_variables": 13,
"num_constraints": 11,
"num_edges": -1,
"backend": "pycsp",
"solve_tier": "hard",
"solve_pct_global": 72.37,
"solve_pct_type": 18.75
} | {
"x": {
"0": null,
"1": null,
"2": 7,
"3": null,
"4": null,
"5": null,
"6": null,
"7": null,
"8": null,
"9": null,
"10": null,
"11": null,
"12": null,
"13": null,
"14": null,
"15": null,
"17": null,
"18": null,
"19": null,
"20": null,
... |
graceful_graph_k2_p4__v6_nh | graceful_graph | {
"n": null,
"k": 2,
"p": 4,
"max_chromatic_number": null,
"min_edges": null,
"min_girth": null,
"vertices": null,
"max_clique": null,
"min_degree": null,
"clique_size": null,
"max_degree": null,
"max_edges": null,
"max_independent_set": null,
"maximal_triangle_free": null,
"min_chromatic_... | Find a graceful labeling for the graph G_{2,4}: 4 disjoint K_2 cliques (numbered 0 through 3), where each pair of consecutive cliques (g, g+1) is connected by 2 edges that link vertex i of clique g to vertex i of clique g+1 for each i in 0..1. The graph has 8 vertices and 10 edges in total.
A graceful labeling assigns... | true | {
"x": [
0,
2,
10,
3,
1,
7,
9,
4
],
"d": [
2,
7,
6,
5,
10,
1,
9,
4,
8,
3
],
"seq": null,
"c": null,
"edges": null,
"q": null
} | {
"solve_time_ms": 1359.6,
"search_space": 214358881,
"num_variables": 18,
"num_constraints": 14,
"num_edges": -1,
"backend": "pycsp",
"solve_tier": "hard",
"solve_pct_global": 83.65,
"solve_pct_type": 56.25
} | null |
graceful_graph_k2_p5__v1_nh | graceful_graph | {
"n": null,
"k": 2,
"p": 5,
"max_chromatic_number": null,
"min_edges": null,
"min_girth": null,
"vertices": null,
"max_clique": null,
"min_degree": null,
"clique_size": null,
"max_degree": null,
"max_edges": null,
"max_independent_set": null,
"maximal_triangle_free": null,
"min_chromatic_... | Find a graceful labeling for the graph G_{2,5}: 5 disjoint K_2 cliques (numbered 0 through 4), where each pair of consecutive cliques (g, g+1) is connected by 2 edges that link vertex i of clique g to vertex i of clique g+1 for each i in 0..1. The graph has 10 vertices and 13 edges in total.
A graceful labeling assign... | true | {
"x": [
11,
6,
4,
10,
1,
2,
12,
0,
3,
13
],
"d": [
5,
6,
1,
12,
10,
7,
4,
3,
8,
11,
2,
9,
13
],
"seq": null,
"c": null,
"edges": null,
"q": null
} | {
"solve_time_ms": 1003.9,
"search_space": 289254654976,
"num_variables": 23,
"num_constraints": 17,
"num_edges": -1,
"backend": "pycsp",
"solve_tier": "hard",
"solve_pct_global": 70.49,
"solve_pct_type": 6.25
} | null |
graceful_graph_k2_p6__v7_h | graceful_graph | {
"n": null,
"k": 2,
"p": 6,
"max_chromatic_number": null,
"min_edges": null,
"min_girth": null,
"vertices": null,
"max_clique": null,
"min_degree": null,
"clique_size": null,
"max_degree": null,
"max_edges": null,
"max_independent_set": null,
"maximal_triangle_free": null,
"min_chromatic_... | Find a graceful labeling for the graph G_{2,6}: 6 disjoint K_2 cliques (numbered 0 through 5), where each pair of consecutive cliques (g, g+1) is connected by 2 edges that link vertex i of clique g to vertex i of clique g+1 for each i in 0..1. The graph has 12 vertices and 16 edges in total.
A graceful labeling assign... | true | {
"x": [
6,
14,
9,
4,
5,
11,
16,
2,
0,
15,
1,
3
],
"d": [
8,
5,
6,
14,
15,
2,
3,
10,
4,
7,
11,
9,
16,
13,
1,
12
],
"seq": null,
"c": null,
"edges": null,
"q": null
} | {
"solve_time_ms": 1225.8,
"search_space": 582622237229761,
"num_variables": 28,
"num_constraints": 20,
"num_edges": -1,
"backend": "pycsp",
"solve_tier": "hard",
"solve_pct_global": 79.14,
"solve_pct_type": 31.25
} | {
"x": {
"0": 6,
"1": null,
"2": null,
"3": 4,
"4": null,
"5": null,
"6": null,
"7": null,
"8": null,
"9": null,
"10": null,
"11": null,
"12": null,
"13": null,
"14": null,
"15": null,
"17": null,
"18": null,
"19": null,
"20": null,
"... |
graceful_graph_k3_p3__v5_nh | graceful_graph | {
"n": null,
"k": 3,
"p": 3,
"max_chromatic_number": null,
"min_edges": null,
"min_girth": null,
"vertices": null,
"max_clique": null,
"min_degree": null,
"clique_size": null,
"max_degree": null,
"max_edges": null,
"max_independent_set": null,
"maximal_triangle_free": null,
"min_chromatic_... | Find a graceful labeling for the graph G_{3,3}: 3 disjoint K_3 cliques (numbered 0 through 2), where each pair of consecutive cliques (g, g+1) is connected by 3 edges that link vertex i of clique g to vertex i of clique g+1 for each i in 0..2. The graph has 9 vertices and 15 edges in total.
A graceful labeling assigns... | true | {
"x": [
2,
12,
0,
1,
6,
15,
14,
3,
7
],
"d": [
10,
2,
12,
5,
14,
9,
11,
7,
4,
1,
6,
15,
13,
3,
8
],
"seq": null,
"c": null,
"edges": null,
"q": null
} | {
"solve_time_ms": 1302.4,
"search_space": 68719476736,
"num_variables": 24,
"num_constraints": 19,
"num_edges": -1,
"backend": "pycsp",
"solve_tier": "hard",
"solve_pct_global": 81.77,
"solve_pct_type": 43.75
} | null |
graceful_graph_k3_p4__v3_h | graceful_graph | {
"n": null,
"k": 3,
"p": 4,
"max_chromatic_number": null,
"min_edges": null,
"min_girth": null,
"vertices": null,
"max_clique": null,
"min_degree": null,
"clique_size": null,
"max_degree": null,
"max_edges": null,
"max_independent_set": null,
"maximal_triangle_free": null,
"min_chromatic_... | Find a graceful labeling for the graph G_{3,4}: 4 disjoint K_3 cliques (numbered 0 through 3), where each pair of consecutive cliques (g, g+1) is connected by 3 edges that link vertex i of clique g to vertex i of clique g+1 for each i in 0..2. The graph has 12 vertices and 21 edges in total.
A graceful labeling assign... | true | {
"x": [
3,
21,
15,
20,
0,
1,
7,
2,
17,
16,
5,
9
],
"d": [
18,
12,
6,
20,
19,
1,
5,
10,
15,
11,
7,
4,
17,
21,
14,
13,
2,
16,
9,
3,
8
],
"seq": null,
"c": null,
"edges": null,... | {
"solve_time_ms": 1447.9,
"search_space": 12855002631049216,
"num_variables": 33,
"num_constraints": 25,
"num_edges": -1,
"backend": "pycsp",
"solve_tier": "hard",
"solve_pct_global": 86.28,
"solve_pct_type": 68.75
} | {
"x": {
"0": null,
"1": null,
"2": 15,
"3": null,
"4": 0,
"5": null,
"6": null,
"7": null,
"8": null,
"9": null,
"10": null,
"11": null,
"12": null,
"13": null,
"14": null,
"15": null,
"17": null,
"18": null,
"19": null,
"20": null,
... |
graceful_graph_k3_p5__v2_nh | graceful_graph | {
"n": null,
"k": 3,
"p": 5,
"max_chromatic_number": null,
"min_edges": null,
"min_girth": null,
"vertices": null,
"max_clique": null,
"min_degree": null,
"clique_size": null,
"max_degree": null,
"max_edges": null,
"max_independent_set": null,
"maximal_triangle_free": null,
"min_chromatic_... | Find a graceful labeling for the graph G_{3,5}: 5 disjoint K_3 cliques (numbered 0 through 4), where each pair of consecutive cliques (g, g+1) is connected by 3 edges that link vertex i of clique g to vertex i of clique g+1 for each i in 0..2. The graph has 15 vertices and 27 edges in total.
A graceful labeling assign... | true | {
"x": [
5,
24,
14,
23,
3,
7,
1,
6,
18,
25,
12,
26,
2,
27,
0
],
"d": [
19,
9,
10,
20,
16,
4,
5,
17,
12,
13,
1,
14,
25,
2,
27,
18,
21,
7,
22,
3,
11,
24,
6,
8,
... | {
"solve_time_ms": 1655.4,
"search_space": 5.097655355238391e+21,
"num_variables": 42,
"num_constraints": 31,
"num_edges": -1,
"backend": "pycsp",
"solve_tier": "hard",
"solve_pct_global": 88.91,
"solve_pct_type": 81.25
} | null |
graceful_graph_k3_p6__v4_nh | graceful_graph | {
"n": null,
"k": 3,
"p": 6,
"max_chromatic_number": null,
"min_edges": null,
"min_girth": null,
"vertices": null,
"max_clique": null,
"min_degree": null,
"clique_size": null,
"max_degree": null,
"max_edges": null,
"max_independent_set": null,
"maximal_triangle_free": null,
"min_chromatic_... | Find a graceful labeling for the graph G_{3,6}: 6 disjoint K_3 cliques (numbered 0 through 5), where each pair of consecutive cliques (g, g+1) is connected by 3 edges that link vertex i of clique g to vertex i of clique g+1 for each i in 0..2. The graph has 18 vertices and 33 edges in total.
A graceful labeling assign... | true | {
"x": [
1,
2,
32,
33,
20,
5,
0,
29,
3,
4,
10,
26,
9,
30,
19,
23,
6,
31
],
"d": [
1,
31,
30,
13,
28,
15,
29,
3,
26,
6,
22,
16,
21,
10,
11,
17,
8,
25,
32,
18,
... | {
"solve_time_ms": 1860.4,
"search_space": 3.6865532106028416e+27,
"num_variables": 51,
"num_constraints": 37,
"num_edges": -1,
"backend": "pycsp",
"solve_tier": "hard",
"solve_pct_global": 90.41,
"solve_pct_type": 93.75
} | null |
knight_tour_n5__v0_h | knight_tour | {
"n": 5,
"k": null,
"p": null,
"max_chromatic_number": null,
"min_edges": null,
"min_girth": null,
"vertices": null,
"max_clique": null,
"min_degree": null,
"clique_size": null,
"max_degree": null,
"max_edges": null,
"max_independent_set": null,
"maximal_triangle_free": null,
"min_chromat... | Find an open knight's tour on an 5x5 chessboard that starts at cell 0 (row 0, column 0). A knight's tour visits every cell exactly once via knight moves; cells are numbered in row-major order so cell k is at row k//5, column k%5. A knight move between cells a and b changes the row by 1 and column by 2, or row by 2 and ... | true | {
"x": [
0,
7,
14,
23,
16,
5,
2,
9,
18,
21,
10,
1,
12,
3,
6,
15,
22,
19,
8,
11,
20,
17,
24,
13,
4
],
"d": null,
"seq": null,
"c": null,
"edges": null,
"q": null
} | {
"solve_time_ms": 1816.3,
"search_space": 1.5511210043330986e+25,
"num_variables": 25,
"num_constraints": 28,
"num_edges": -1,
"backend": "pycsp",
"solve_tier": "hard",
"solve_pct_global": 90.04,
"solve_pct_type": 12.5
} | {
"x": {
"0": null,
"1": null,
"2": null,
"3": 23,
"4": 16,
"5": 5,
"6": null,
"7": null,
"8": null,
"9": null,
"10": null,
"11": null,
"12": null,
"13": null,
"14": null,
"15": 15,
"17": null,
"18": null,
"19": null,
"20": null,
"21"... |
knight_tour_n6__v3_h | knight_tour | {
"n": 6,
"k": null,
"p": null,
"max_chromatic_number": null,
"min_edges": null,
"min_girth": null,
"vertices": null,
"max_clique": null,
"min_degree": null,
"clique_size": null,
"max_degree": null,
"max_edges": null,
"max_independent_set": null,
"maximal_triangle_free": null,
"min_chromat... | Find an open knight's tour on an 6x6 chessboard that starts at cell 0 (row 0, column 0). A knight's tour visits every cell exactly once via knight moves; cells are numbered in row-major order so cell k is at row k//6, column k%6. A knight move between cells a and b changes the row by 1 and column by 2, or row by 2 and ... | true | {
"x": [
0,
8,
4,
17,
28,
32,
24,
20,
7,
18,
31,
27,
35,
22,
11,
15,
26,
30,
19,
6,
2,
13,
9,
5,
16,
3,
14,
1,
12,
25,
33,
29,
21,
34,
23,
10
],
"d": null,
"seq": null,... | {
"solve_time_ms": 6415.9,
"search_space": 3.7199332678990125e+41,
"num_variables": 36,
"num_constraints": 39,
"num_edges": -1,
"backend": "pycsp",
"solve_tier": "hard",
"solve_pct_global": 97.93,
"solve_pct_type": 62.5
} | {
"x": {
"0": null,
"1": null,
"2": null,
"3": 17,
"4": null,
"5": null,
"6": 24,
"7": null,
"8": null,
"9": null,
"10": null,
"11": null,
"12": null,
"13": null,
"14": null,
"15": null,
"17": 30,
"18": null,
"19": 6,
"20": null,
"21"... |
knight_tour_n7__v2_nh | knight_tour | {
"n": 7,
"k": null,
"p": null,
"max_chromatic_number": null,
"min_edges": null,
"min_girth": null,
"vertices": null,
"max_clique": null,
"min_degree": null,
"clique_size": null,
"max_degree": null,
"max_edges": null,
"max_independent_set": null,
"maximal_triangle_free": null,
"min_chromat... | Find an open knight's tour on an 7x7 chessboard that starts at cell 0 (row 0, column 0). A knight's tour visits every cell exactly once via knight moves; cells are numbered in row-major order so cell k is at row k//7, column k%7. A knight move between cells a and b changes the row by 1 and column by 2, or row by 2 and ... | true | {
"x": [
0,
15,
30,
17,
2,
7,
16,
3,
18,
5,
20,
11,
6,
19,
24,
9,
4,
13,
26,
39,
48,
33,
46,
41,
32,
27,
12,
25,
10,
1,
14,
23,
8,
21,
36,
45,
40,
31,
22,
35,... | {
"solve_time_ms": 2845.5,
"search_space": 6.082818640342675e+62,
"num_variables": 49,
"num_constraints": 52,
"num_edges": -1,
"backend": "pycsp",
"solve_tier": "hard",
"solve_pct_global": 95.68,
"solve_pct_type": 37.5
} | null |
knight_tour_n8__v1_h | knight_tour | {
"n": 8,
"k": null,
"p": null,
"max_chromatic_number": null,
"min_edges": null,
"min_girth": null,
"vertices": null,
"max_clique": null,
"min_degree": null,
"clique_size": null,
"max_degree": null,
"max_edges": null,
"max_independent_set": null,
"maximal_triangle_free": null,
"min_chromat... | Find an open knight's tour on an 8x8 chessboard that starts at cell 0 (row 0, column 0). A knight's tour visits every cell exactly once via knight moves; cells are numbered in row-major order so cell k is at row k//8, column k%8. A knight move between cells a and b changes the row by 1 and column by 2, or row by 2 and ... | true | {
"x": [
0,
17,
27,
21,
6,
12,
2,
19,
4,
10,
16,
1,
18,
8,
25,
35,
50,
56,
41,
24,
9,
3,
20,
5,
15,
30,
36,
51,
34,
49,
32,
26,
11,
28,
22,
7,
13,
23,
38,
44,... | {
"solve_time_ms": 56542.2,
"search_space": 1.2688693218588417e+89,
"num_variables": 64,
"num_constraints": 67,
"num_edges": -1,
"backend": "pycsp",
"solve_tier": "hard",
"solve_pct_global": 99.81,
"solve_pct_type": 87.5
} | {
"x": {
"0": null,
"1": null,
"2": 27,
"3": 21,
"4": null,
"5": null,
"6": null,
"7": null,
"8": null,
"9": null,
"10": 16,
"11": 1,
"12": null,
"13": null,
"14": null,
"15": null,
"17": null,
"18": null,
"19": 24,
"20": null,
"21": ... |
langford_n11__v4_nh | langford | {
"n": 11,
"k": null,
"p": null,
"max_chromatic_number": null,
"min_edges": null,
"min_girth": null,
"vertices": null,
"max_clique": null,
"min_degree": null,
"clique_size": null,
"max_degree": null,
"max_edges": null,
"max_independent_set": null,
"maximal_triangle_free": null,
"min_chroma... | Construct a Langford sequence L(2,11): a sequence of length 22 containing exactly 2 copies of each integer from 1 to 11, such that the two occurrences of each value v are exactly v+1 positions apart (so copies of 1 are 1 position apart, copies of 2 are 2 positions apart, etc.). Example: L(2,3) has solution [2, 3, 1, 2,... | true | {
"x": null,
"d": null,
"seq": [
6,
2,
3,
11,
2,
10,
3,
6,
9,
1,
8,
1,
4,
7,
5,
11,
10,
4,
9,
8,
5,
7
],
"c": null,
"edges": null,
"q": null
} | {
"solve_time_ms": 1587,
"search_space": 1.1240007277776077e+21,
"num_variables": 22,
"num_constraints": 258,
"num_edges": -1,
"backend": "pycsp",
"solve_tier": "hard",
"solve_pct_global": 87.78,
"solve_pct_type": 31.25
} | null |
langford_n12__v6_nh | langford | {
"n": 12,
"k": null,
"p": null,
"max_chromatic_number": null,
"min_edges": null,
"min_girth": null,
"vertices": null,
"max_clique": null,
"min_degree": null,
"clique_size": null,
"max_degree": null,
"max_edges": null,
"max_independent_set": null,
"maximal_triangle_free": null,
"min_chroma... | Construct a Langford sequence L(2,12): a sequence of length 24 containing exactly 2 copies of each integer from 1 to 12, such that the two occurrences of each value v are exactly v+1 positions apart (so copies of 1 are 1 position apart, copies of 2 are 2 positions apart, etc.). Example: L(2,3) has solution [2, 3, 1, 2,... | true | {
"x": null,
"d": null,
"seq": [
4,
2,
7,
11,
2,
4,
5,
10,
8,
12,
7,
9,
5,
6,
1,
11,
1,
8,
10,
3,
6,
9,
12,
3
],
"c": null,
"edges": null,
"q": null
} | {
"solve_time_ms": 1602,
"search_space": 6.204484017332394e+23,
"num_variables": 24,
"num_constraints": 305,
"num_edges": -1,
"backend": "pycsp",
"solve_tier": "hard",
"solve_pct_global": 88.16,
"solve_pct_type": 43.75
} | null |
langford_n15__v3_h | langford | {
"n": 15,
"k": null,
"p": null,
"max_chromatic_number": null,
"min_edges": null,
"min_girth": null,
"vertices": null,
"max_clique": null,
"min_degree": null,
"clique_size": null,
"max_degree": null,
"max_edges": null,
"max_independent_set": null,
"maximal_triangle_free": null,
"min_chroma... | Construct a Langford sequence L(2,15): a sequence of length 30 containing exactly 2 copies of each integer from 1 to 15, such that the two occurrences of each value v are exactly v+1 positions apart (so copies of 1 are 1 position apart, copies of 2 are 2 positions apart, etc.). Example: L(2,3) has solution [2, 3, 1, 2,... | true | {
"x": null,
"d": null,
"seq": [
2,
6,
3,
2,
4,
12,
3,
15,
6,
4,
13,
14,
9,
11,
1,
5,
1,
10,
12,
7,
8,
5,
9,
15,
13,
11,
14,
7,
10,
8
],
"c": null,
"edges": null,
"q": null
} | {
"solve_time_ms": 2620.2,
"search_space": 2.6525285981219107e+32,
"num_variables": 30,
"num_constraints": 470,
"num_edges": -1,
"backend": "pycsp",
"solve_tier": "hard",
"solve_pct_global": 94.17,
"solve_pct_type": 68.75
} | {
"x": null,
"d": null,
"seq": {
"0": null,
"1": null,
"3": 2,
"4": null,
"5": null,
"6": null,
"8": null,
"9": null,
"10": null,
"11": 14,
"12": null,
"13": 11,
"14": null,
"15": null,
"17": null,
"19": null,
"20": null,
"21": null,
"22"... |
langford_n16__v1_h | langford | {
"n": 16,
"k": null,
"p": null,
"max_chromatic_number": null,
"min_edges": null,
"min_girth": null,
"vertices": null,
"max_clique": null,
"min_degree": null,
"clique_size": null,
"max_degree": null,
"max_edges": null,
"max_independent_set": null,
"maximal_triangle_free": null,
"min_chroma... | Construct a Langford sequence L(2,16): a sequence of length 32 containing exactly 2 copies of each integer from 1 to 16, such that the two occurrences of each value v are exactly v+1 positions apart (so copies of 1 are 1 position apart, copies of 2 are 2 positions apart, etc.). Example: L(2,3) has solution [2, 3, 1, 2,... | true | {
"x": null,
"d": null,
"seq": [
2,
6,
3,
2,
4,
14,
3,
11,
6,
4,
5,
15,
13,
16,
8,
12,
5,
7,
10,
11,
14,
9,
1,
8,
1,
7,
13,
15,
12,
10,
16,
9
],
"c": null,
"edges": null,
"q": nu... | {
"solve_time_ms": 2795.9,
"search_space": 2.631308369336935e+35,
"num_variables": 32,
"num_constraints": 533,
"num_edges": -1,
"backend": "pycsp",
"solve_tier": "hard",
"solve_pct_global": 94.92,
"solve_pct_type": 81.25
} | {
"x": null,
"d": null,
"seq": {
"0": null,
"1": null,
"3": null,
"4": null,
"5": 14,
"6": null,
"8": null,
"9": 4,
"10": null,
"11": 15,
"12": null,
"13": null,
"14": null,
"15": null,
"17": null,
"19": null,
"20": null,
"21": 9,
"22": n... |
langford_n6__v8 | langford | {
"n": 6,
"k": null,
"p": null,
"max_chromatic_number": null,
"min_edges": null,
"min_girth": null,
"vertices": null,
"max_clique": null,
"min_degree": null,
"clique_size": null,
"max_degree": null,
"max_edges": null,
"max_independent_set": null,
"maximal_triangle_free": null,
"min_chromat... | Construct a Langford sequence L(2,6): a sequence of length 12 containing exactly 2 copies of each integer from 1 to 6, such that the two occurrences of each value v are exactly v+1 positions apart (so copies of 1 are 1 position apart, copies of 2 are 2 positions apart, etc.). Example: L(2,3) has solution [2, 3, 1, 2, 1... | false | null | {
"solve_time_ms": 1434.5,
"search_space": 479001600,
"num_variables": 12,
"num_constraints": 83,
"num_edges": -1,
"backend": "pycsp",
"solve_tier": "hard",
"solve_pct_global": 85.53,
"solve_pct_type": 18.75
} | null |
langford_n7__v11_nh | langford | {
"n": 7,
"k": null,
"p": null,
"max_chromatic_number": null,
"min_edges": null,
"min_girth": null,
"vertices": null,
"max_clique": null,
"min_degree": null,
"clique_size": null,
"max_degree": null,
"max_edges": null,
"max_independent_set": null,
"maximal_triangle_free": null,
"min_chromat... | Construct a Langford sequence L(2,7): a sequence of length 14 containing exactly 2 copies of each integer from 1 to 7, such that the two occurrences of each value v are exactly v+1 positions apart (so copies of 1 are 1 position apart, copies of 2 are 2 positions apart, etc.). Example: L(2,3) has solution [2, 3, 1, 2, 1... | true | {
"x": null,
"d": null,
"seq": [
1,
7,
1,
2,
5,
6,
2,
3,
4,
7,
5,
3,
6,
4
],
"c": null,
"edges": null,
"q": null
} | {
"solve_time_ms": 1875,
"search_space": 87178291200,
"num_variables": 14,
"num_constraints": 110,
"num_edges": -1,
"backend": "pycsp",
"solve_tier": "hard",
"solve_pct_global": 90.79,
"solve_pct_type": 56.25
} | null |
langford_n8__v5_h | langford | {
"n": 8,
"k": null,
"p": null,
"max_chromatic_number": null,
"min_edges": null,
"min_girth": null,
"vertices": null,
"max_clique": null,
"min_degree": null,
"clique_size": null,
"max_degree": null,
"max_edges": null,
"max_independent_set": null,
"maximal_triangle_free": null,
"min_chromat... | Construct a Langford sequence L(2,8): a sequence of length 16 containing exactly 2 copies of each integer from 1 to 8, such that the two occurrences of each value v are exactly v+1 positions apart (so copies of 1 are 1 position apart, copies of 2 are 2 positions apart, etc.). Example: L(2,3) has solution [2, 3, 1, 2, 1... | true | {
"x": null,
"d": null,
"seq": [
2,
3,
8,
2,
7,
3,
6,
1,
5,
1,
4,
8,
7,
6,
5,
4
],
"c": null,
"edges": null,
"q": null
} | {
"solve_time_ms": 1339.8,
"search_space": 20922789888000,
"num_variables": 16,
"num_constraints": 141,
"num_edges": -1,
"backend": "pycsp",
"solve_tier": "hard",
"solve_pct_global": 82.89,
"solve_pct_type": 6.25
} | {
"x": null,
"d": null,
"seq": {
"0": null,
"1": null,
"3": null,
"4": 7,
"5": null,
"6": null,
"8": 5,
"9": null,
"10": 4,
"11": null,
"12": null,
"13": null,
"14": null,
"15": null,
"17": null,
"19": null,
"20": null,
"21": null,
"22": ... |
langford_n9__v7 | langford | {
"n": 9,
"k": null,
"p": null,
"max_chromatic_number": null,
"min_edges": null,
"min_girth": null,
"vertices": null,
"max_clique": null,
"min_degree": null,
"clique_size": null,
"max_degree": null,
"max_edges": null,
"max_independent_set": null,
"maximal_triangle_free": null,
"min_chromat... | Construct a Langford sequence L(2,9): a sequence of length 18 containing exactly 2 copies of each integer from 1 to 9, such that the two occurrences of each value v are exactly v+1 positions apart (so copies of 1 are 1 position apart, copies of 2 are 2 positions apart, etc.). Example: L(2,3) has solution [2, 3, 1, 2, 1... | false | null | {
"solve_time_ms": 2919.6,
"search_space": 6402373705728000,
"num_variables": 18,
"num_constraints": 176,
"num_edges": -1,
"backend": "pycsp",
"solve_tier": "hard",
"solve_pct_global": 96.05,
"solve_pct_type": 93.75
} | null |
low_autocorrelation_n10__v9_h | low_autocorrelation | {
"n": 10,
"k": null,
"p": null,
"max_chromatic_number": null,
"min_edges": null,
"min_girth": null,
"vertices": null,
"max_clique": null,
"min_degree": null,
"clique_size": null,
"max_degree": null,
"max_edges": null,
"max_independent_set": null,
"maximal_triangle_free": null,
"min_chroma... | Find a binary sequence of length 10 over the alphabet {-1, +1} with low aperiodic autocorrelation: specifically, the sum over k=1..9 of C_k^2, where C_k = sum_{i=0}^{n-k-1} seq[i]*seq[i+k], must be at most 20.
Return seq as a list of 10 integers, each -1 or +1, or state "UNSATISFIABLE" if no such sequence exists.
Par... | true | {
"x": null,
"d": null,
"seq": [
-1,
-1,
1,
1,
-1,
1,
-1,
1,
1,
1
],
"c": [
-1,
0,
-1,
0,
1,
2,
-1,
-2,
-1
],
"edges": null,
"q": null
} | {
"solve_time_ms": 1343.9,
"search_space": 1024,
"num_variables": 19,
"num_constraints": 16,
"num_edges": -1,
"backend": "pycsp",
"solve_tier": "hard",
"solve_pct_global": 83.27,
"solve_pct_type": 20.83
} | {
"x": null,
"d": null,
"seq": {
"0": -1,
"1": null,
"3": null,
"4": null,
"5": null,
"6": null,
"8": 1,
"9": null,
"10": null,
"11": null,
"12": null,
"13": null,
"14": null,
"15": null,
"17": null,
"19": null,
"20": null,
"21": null,
"2... |
low_autocorrelation_n11__v3_h | low_autocorrelation | {
"n": 11,
"k": null,
"p": null,
"max_chromatic_number": null,
"min_edges": null,
"min_girth": null,
"vertices": null,
"max_clique": null,
"min_degree": null,
"clique_size": null,
"max_degree": null,
"max_edges": null,
"max_independent_set": null,
"maximal_triangle_free": null,
"min_chroma... | Find a binary sequence of length 11 over the alphabet {-1, +1} with low aperiodic autocorrelation: specifically, the sum over k=1..10 of C_k^2, where C_k = sum_{i=0}^{n-k-1} seq[i]*seq[i+k], must be at most 23.
Return seq as a list of 11 integers, each -1 or +1, or state "UNSATISFIABLE" if no such sequence exists.
Pa... | true | {
"x": null,
"d": null,
"seq": [
-1,
1,
-1,
1,
1,
-1,
1,
1,
1,
-1,
-1
],
"c": [
-2,
-1,
0,
-1,
2,
-3,
0,
-1,
0,
1
],
"edges": null,
"q": null
} | {
"solve_time_ms": 974.3,
"search_space": 2048,
"num_variables": 21,
"num_constraints": 17,
"num_edges": -1,
"backend": "pycsp",
"solve_tier": "hard",
"solve_pct_global": 66.73,
"solve_pct_type": 4.17
} | {
"x": null,
"d": null,
"seq": {
"0": null,
"1": 1,
"3": null,
"4": null,
"5": null,
"6": null,
"8": 1,
"9": null,
"10": null,
"11": null,
"12": null,
"13": null,
"14": null,
"15": null,
"17": null,
"19": null,
"20": null,
"21": null,
"22... |
low_autocorrelation_n12__v11_nh | low_autocorrelation | {
"n": 12,
"k": null,
"p": null,
"max_chromatic_number": null,
"min_edges": null,
"min_girth": null,
"vertices": null,
"max_clique": null,
"min_degree": null,
"clique_size": null,
"max_degree": null,
"max_edges": null,
"max_independent_set": null,
"maximal_triangle_free": null,
"min_chroma... | Find a binary sequence of length 12 over the alphabet {-1, +1} with low aperiodic autocorrelation: specifically, the sum over k=1..11 of C_k^2, where C_k = sum_{i=0}^{n-k-1} seq[i]*seq[i+k], must be at most 25.
Return seq as a list of 12 integers, each -1 or +1, or state "UNSATISFIABLE" if no such sequence exists. | true | {
"x": null,
"d": null,
"seq": [
-1,
1,
1,
-1,
1,
1,
1,
1,
-1,
-1,
-1,
1
],
"c": [
1,
-2,
-1,
-2,
1,
0,
-1,
-2,
1,
2,
-1
],
"edges": null,
"q": null
} | {
"solve_time_ms": 1544.4,
"search_space": 4096,
"num_variables": 23,
"num_constraints": 18,
"num_edges": -1,
"backend": "pycsp",
"solve_tier": "hard",
"solve_pct_global": 87.41,
"solve_pct_type": 45.83
} | null |
low_autocorrelation_n13__v6_h | low_autocorrelation | {
"n": 13,
"k": null,
"p": null,
"max_chromatic_number": null,
"min_edges": null,
"min_girth": null,
"vertices": null,
"max_clique": null,
"min_degree": null,
"clique_size": null,
"max_degree": null,
"max_edges": null,
"max_independent_set": null,
"maximal_triangle_free": null,
"min_chroma... | Find a binary sequence of length 13 over the alphabet {-1, +1} with low aperiodic autocorrelation: specifically, the sum over k=1..12 of C_k^2, where C_k = sum_{i=0}^{n-k-1} seq[i]*seq[i+k], must be at most 28.
Return seq as a list of 13 integers, each -1 or +1, or state "UNSATISFIABLE" if no such sequence exists.
Pa... | true | {
"x": null,
"d": null,
"seq": [
1,
-1,
1,
-1,
-1,
-1,
-1,
1,
1,
-1,
-1,
1,
1
],
"c": [
0,
-3,
-2,
1,
2,
-1,
-2,
-1,
0,
-1,
0,
1
],
"edges": null,
"q": null
} | {
"solve_time_ms": 1102.3,
"search_space": 8192,
"num_variables": 25,
"num_constraints": 19,
"num_edges": -1,
"backend": "pycsp",
"solve_tier": "hard",
"solve_pct_global": 76.5,
"solve_pct_type": 12.5
} | {
"x": null,
"d": null,
"seq": {
"0": null,
"1": null,
"3": null,
"4": null,
"5": null,
"6": null,
"8": 1,
"9": null,
"10": -1,
"11": null,
"12": null,
"13": null,
"14": null,
"15": null,
"17": null,
"19": null,
"20": null,
"21": null,
"2... |
low_autocorrelation_n16__v5_nh | low_autocorrelation | {
"n": 16,
"k": null,
"p": null,
"max_chromatic_number": null,
"min_edges": null,
"min_girth": null,
"vertices": null,
"max_clique": null,
"min_degree": null,
"clique_size": null,
"max_degree": null,
"max_edges": null,
"max_independent_set": null,
"maximal_triangle_free": null,
"min_chroma... | Find a binary sequence of length 16 over the alphabet {-1, +1} with low aperiodic autocorrelation: specifically, the sum over k=1..15 of C_k^2, where C_k = sum_{i=0}^{n-k-1} seq[i]*seq[i+k], must be at most 37.
Return seq as a list of 16 integers, each -1 or +1, or state "UNSATISFIABLE" if no such sequence exists. | true | {
"x": null,
"d": null,
"seq": [
1,
1,
-1,
-1,
-1,
-1,
-1,
-1,
1,
1,
-1,
-1,
1,
-1,
1,
-1
],
"c": [
1,
0,
-1,
0,
-1,
-2,
-1,
4,
1,
-2,
1,
0,
1,
0,
-1
],
"edges": null,
"q": null
} | {
"solve_time_ms": 1391.4,
"search_space": 65536,
"num_variables": 31,
"num_constraints": 22,
"num_edges": -1,
"backend": "pycsp",
"solve_tier": "hard",
"solve_pct_global": 84.02,
"solve_pct_type": 29.17
} | null |
low_autocorrelation_n17__v8_h | low_autocorrelation | {
"n": 17,
"k": null,
"p": null,
"max_chromatic_number": null,
"min_edges": null,
"min_girth": null,
"vertices": null,
"max_clique": null,
"min_degree": null,
"clique_size": null,
"max_degree": null,
"max_edges": null,
"max_independent_set": null,
"maximal_triangle_free": null,
"min_chroma... | Find a binary sequence of length 17 over the alphabet {-1, +1} with low aperiodic autocorrelation: specifically, the sum over k=1..16 of C_k^2, where C_k = sum_{i=0}^{n-k-1} seq[i]*seq[i+k], must be at most 40.
Return seq as a list of 17 integers, each -1 or +1, or state "UNSATISFIABLE" if no such sequence exists.
Pa... | true | {
"x": null,
"d": null,
"seq": [
-1,
-1,
-1,
-1,
1,
-1,
1,
-1,
-1,
-1,
1,
1,
1,
-1,
1,
1,
-1
],
"c": [
0,
1,
-2,
1,
0,
1,
0,
3,
-2,
-3,
0,
-3,
0,
-1,
0,
1
],
"edges": null,
... | {
"solve_time_ms": 1407.7,
"search_space": 131072,
"num_variables": 33,
"num_constraints": 23,
"num_edges": -1,
"backend": "pycsp",
"solve_tier": "hard",
"solve_pct_global": 84.4,
"solve_pct_type": 37.5
} | {
"x": null,
"d": null,
"seq": {
"0": null,
"1": -1,
"3": null,
"4": null,
"5": null,
"6": 1,
"8": null,
"9": -1,
"10": null,
"11": null,
"12": null,
"13": null,
"14": null,
"15": null,
"17": null,
"19": null,
"20": null,
"21": null,
"22"... |
low_autocorrelation_n19__v10_h | low_autocorrelation | {
"n": 19,
"k": null,
"p": null,
"max_chromatic_number": null,
"min_edges": null,
"min_girth": null,
"vertices": null,
"max_clique": null,
"min_degree": null,
"clique_size": null,
"max_degree": null,
"max_edges": null,
"max_independent_set": null,
"maximal_triangle_free": null,
"min_chroma... | Find a binary sequence of length 19 over the alphabet {-1, +1} with low aperiodic autocorrelation: specifically, the sum over k=1..18 of C_k^2, where C_k = sum_{i=0}^{n-k-1} seq[i]*seq[i+k], must be at most 46.
Return seq as a list of 19 integers, each -1 or +1, or state "UNSATISFIABLE" if no such sequence exists.
Pa... | true | {
"x": null,
"d": null,
"seq": [
1,
-1,
-1,
1,
-1,
-1,
1,
1,
-1,
-1,
-1,
-1,
1,
-1,
1,
-1,
1,
1,
1
],
"c": [
-2,
-1,
0,
1,
-2,
1,
0,
-3,
0,
-1,
2,
-1,
-2,
1,
-2,
-1,
... | {
"solve_time_ms": 2829.7,
"search_space": 524288,
"num_variables": 37,
"num_constraints": 25,
"num_edges": -1,
"backend": "pycsp",
"solve_tier": "hard",
"solve_pct_global": 95.3,
"solve_pct_type": 79.17
} | {
"x": null,
"d": null,
"seq": {
"0": null,
"1": null,
"3": null,
"4": -1,
"5": null,
"6": null,
"8": null,
"9": null,
"10": null,
"11": null,
"12": 1,
"13": -1,
"14": null,
"15": null,
"17": null,
"19": null,
"20": null,
"21": null,
"22"... |
low_autocorrelation_n20__v2_nh | low_autocorrelation | {
"n": 20,
"k": null,
"p": null,
"max_chromatic_number": null,
"min_edges": null,
"min_girth": null,
"vertices": null,
"max_clique": null,
"min_degree": null,
"clique_size": null,
"max_degree": null,
"max_edges": null,
"max_independent_set": null,
"maximal_triangle_free": null,
"min_chroma... | Find a binary sequence of length 20 over the alphabet {-1, +1} with low aperiodic autocorrelation: specifically, the sum over k=1..19 of C_k^2, where C_k = sum_{i=0}^{n-k-1} seq[i]*seq[i+k], must be at most 49.
Return seq as a list of 20 integers, each -1 or +1, or state "UNSATISFIABLE" if no such sequence exists. | true | {
"x": null,
"d": null,
"seq": [
-1,
-1,
-1,
-1,
-1,
1,
1,
-1,
-1,
-1,
1,
-1,
1,
-1,
1,
1,
-1,
1,
1,
-1
],
"c": [
-1,
0,
1,
0,
1,
0,
1,
2,
1,
-2,
-1,
2,
-1,
-4,
-1,
0... | {
"solve_time_ms": 3389.3,
"search_space": 1048576,
"num_variables": 39,
"num_constraints": 26,
"num_edges": -1,
"backend": "pycsp",
"solve_tier": "hard",
"solve_pct_global": 96.43,
"solve_pct_type": 87.5
} | null |
low_autocorrelation_n21__v1_h | low_autocorrelation | {
"n": 21,
"k": null,
"p": null,
"max_chromatic_number": null,
"min_edges": null,
"min_girth": null,
"vertices": null,
"max_clique": null,
"min_degree": null,
"clique_size": null,
"max_degree": null,
"max_edges": null,
"max_independent_set": null,
"maximal_triangle_free": null,
"min_chroma... | Find a binary sequence of length 21 over the alphabet {-1, +1} with low aperiodic autocorrelation: specifically, the sum over k=1..20 of C_k^2, where C_k = sum_{i=0}^{n-k-1} seq[i]*seq[i+k], must be at most 52.
Return seq as a list of 21 integers, each -1 or +1, or state "UNSATISFIABLE" if no such sequence exists.
Pa... | true | {
"x": null,
"d": null,
"seq": [
-1,
1,
1,
-1,
-1,
-1,
1,
1,
1,
-1,
1,
-1,
-1,
-1,
-1,
-1,
-1,
1,
-1,
-1,
1
],
"c": [
2,
-1,
0,
1,
0,
-1,
0,
-3,
2,
1,
0,
-1,
0,
1,
2,... | {
"solve_time_ms": 1603.4,
"search_space": 2097152,
"num_variables": 41,
"num_constraints": 27,
"num_edges": -1,
"backend": "pycsp",
"solve_tier": "hard",
"solve_pct_global": 88.53,
"solve_pct_type": 54.17
} | {
"x": null,
"d": null,
"seq": {
"0": null,
"1": null,
"3": null,
"4": null,
"5": -1,
"6": null,
"8": null,
"9": null,
"10": null,
"11": null,
"12": -1,
"13": null,
"14": null,
"15": null,
"17": 1,
"19": null,
"20": 1,
"21": null,
"22": n... |
low_autocorrelation_n22__v7_nh | low_autocorrelation | {
"n": 22,
"k": null,
"p": null,
"max_chromatic_number": null,
"min_edges": null,
"min_girth": null,
"vertices": null,
"max_clique": null,
"min_degree": null,
"clique_size": null,
"max_degree": null,
"max_edges": null,
"max_independent_set": null,
"maximal_triangle_free": null,
"min_chroma... | Find a binary sequence of length 22 over the alphabet {-1, +1} with low aperiodic autocorrelation: specifically, the sum over k=1..21 of C_k^2, where C_k = sum_{i=0}^{n-k-1} seq[i]*seq[i+k], must be at most 56.
Return seq as a list of 22 integers, each -1 or +1, or state "UNSATISFIABLE" if no such sequence exists. | true | {
"x": null,
"d": null,
"seq": [
1,
-1,
1,
-1,
1,
1,
-1,
-1,
1,
-1,
-1,
1,
1,
1,
-1,
-1,
-1,
-1,
1,
-1,
-1,
-1
],
"c": [
-1,
-2,
-1,
0,
1,
2,
1,
0,
-1,
0,
1,
-2,
3,
2... | {
"solve_time_ms": 2577.9,
"search_space": 4194304,
"num_variables": 43,
"num_constraints": 28,
"num_edges": -1,
"backend": "pycsp",
"solve_tier": "hard",
"solve_pct_global": 93.8,
"solve_pct_type": 70.83
} | null |
low_autocorrelation_n23__v4_h | low_autocorrelation | {
"n": 23,
"k": null,
"p": null,
"max_chromatic_number": null,
"min_edges": null,
"min_girth": null,
"vertices": null,
"max_clique": null,
"min_degree": null,
"clique_size": null,
"max_degree": null,
"max_edges": null,
"max_independent_set": null,
"maximal_triangle_free": null,
"min_chroma... | Find a binary sequence of length 23 over the alphabet {-1, +1} with low aperiodic autocorrelation: specifically, the sum over k=1..22 of C_k^2, where C_k = sum_{i=0}^{n-k-1} seq[i]*seq[i+k], must be at most 59.
Return seq as a list of 23 integers, each -1 or +1, or state "UNSATISFIABLE" if no such sequence exists.
Pa... | true | {
"x": null,
"d": null,
"seq": [
-1,
1,
-1,
1,
-1,
-1,
-1,
-1,
-1,
-1,
-1,
1,
1,
1,
-1,
-1,
1,
-1,
1,
1,
-1,
-1,
1
],
"c": [
0,
1,
0,
-1,
0,
3,
0,
-1,
-2,
3,
0,
-1,
0... | {
"solve_time_ms": 2252.8,
"search_space": 8388608,
"num_variables": 45,
"num_constraints": 29,
"num_edges": -1,
"backend": "pycsp",
"solve_tier": "hard",
"solve_pct_global": 92.29,
"solve_pct_type": 62.5
} | {
"x": null,
"d": null,
"seq": {
"0": null,
"1": null,
"3": null,
"4": null,
"5": -1,
"6": null,
"8": null,
"9": null,
"10": -1,
"11": null,
"12": null,
"13": 1,
"14": null,
"15": null,
"17": null,
"19": 1,
"20": null,
"21": null,
"22": n... |
low_autocorrelation_n24__v0_h | low_autocorrelation | {
"n": 24,
"k": null,
"p": null,
"max_chromatic_number": null,
"min_edges": null,
"min_girth": null,
"vertices": null,
"max_clique": null,
"min_degree": null,
"clique_size": null,
"max_degree": null,
"max_edges": null,
"max_independent_set": null,
"maximal_triangle_free": null,
"min_chroma... | Find a binary sequence of length 24 over the alphabet {-1, +1} with low aperiodic autocorrelation: specifically, the sum over k=1..23 of C_k^2, where C_k = sum_{i=0}^{n-k-1} seq[i]*seq[i+k], must be at most 62.
Return seq as a list of 24 integers, each -1 or +1, or state "UNSATISFIABLE" if no such sequence exists.
Pa... | true | {
"x": null,
"d": null,
"seq": [
-1,
1,
1,
-1,
-1,
1,
1,
-1,
1,
-1,
1,
1,
1,
-1,
1,
-1,
1,
1,
1,
1,
-1,
-1,
-1,
-1
],
"c": [
-1,
0,
-3,
0,
-3,
4,
-1,
0,
1,
-2,
-1,
-2... | {
"solve_time_ms": 11665.1,
"search_space": 16777216,
"num_variables": 47,
"num_constraints": 30,
"num_edges": -1,
"backend": "pycsp",
"solve_tier": "hard",
"solve_pct_global": 98.68,
"solve_pct_type": 95.83
} | {
"x": null,
"d": null,
"seq": {
"0": null,
"1": null,
"3": null,
"4": null,
"5": null,
"6": null,
"8": null,
"9": -1,
"10": null,
"11": null,
"12": null,
"13": null,
"14": 1,
"15": -1,
"17": null,
"19": null,
"20": null,
"21": null,
"22"... |
magic_sequence_n11__v1_h | magic_sequence | {
"n": 11,
"k": null,
"p": null,
"max_chromatic_number": null,
"min_edges": null,
"min_girth": null,
"vertices": null,
"max_clique": null,
"min_degree": null,
"clique_size": null,
"max_degree": null,
"max_edges": null,
"max_independent_set": null,
"maximal_triangle_free": null,
"min_chroma... | Find a magic sequence of length 11. A magic sequence is a sequence x[0], x[1], ..., x[10] where each x[i] equals the count of how many times i appears in the sequence.
Return a list of 11 integers, or state "UNSATISFIABLE" if no solution exists.
Partial assignment (fixed values that must be respected):
- x[4]=0, x[10... | true | {
"x": [
7,
2,
1,
0,
0,
0,
0,
1,
0,
0,
0
],
"d": null,
"seq": null,
"c": null,
"edges": null,
"q": null
} | {
"solve_time_ms": 991.8,
"search_space": 285311670611,
"num_variables": 11,
"num_constraints": 23,
"num_edges": -1,
"backend": "pycsp",
"solve_tier": "hard",
"solve_pct_global": 69.36,
"solve_pct_type": 54.17
} | {
"x": {
"0": null,
"1": null,
"2": null,
"3": null,
"4": 0,
"5": null,
"6": null,
"7": null,
"8": null,
"9": null,
"10": 0,
"11": null,
"12": null,
"13": null,
"14": null,
"15": null,
"17": null,
"18": null,
"19": null,
"20": null,
"... |
magic_sequence_n12__v0_h | magic_sequence | {
"n": 12,
"k": null,
"p": null,
"max_chromatic_number": null,
"min_edges": null,
"min_girth": null,
"vertices": null,
"max_clique": null,
"min_degree": null,
"clique_size": null,
"max_degree": null,
"max_edges": null,
"max_independent_set": null,
"maximal_triangle_free": null,
"min_chroma... | Find a magic sequence of length 12. A magic sequence is a sequence x[0], x[1], ..., x[11] where each x[i] equals the count of how many times i appears in the sequence.
Return a list of 12 integers, or state "UNSATISFIABLE" if no solution exists.
Partial assignment (fixed values that must be respected):
- x[7]=0, x[8]... | true | {
"x": [
8,
2,
1,
0,
0,
0,
0,
0,
1,
0,
0,
0
],
"d": null,
"seq": null,
"c": null,
"edges": null,
"q": null
} | {
"solve_time_ms": 1063,
"search_space": 8916100448256,
"num_variables": 12,
"num_constraints": 24,
"num_edges": -1,
"backend": "pycsp",
"solve_tier": "hard",
"solve_pct_global": 75.38,
"solve_pct_type": 95.83
} | {
"x": {
"0": null,
"1": null,
"2": null,
"3": null,
"4": null,
"5": null,
"6": null,
"7": 0,
"8": 1,
"9": null,
"10": null,
"11": null,
"12": null,
"13": null,
"14": null,
"15": null,
"17": null,
"18": null,
"19": null,
"20": null,
"... |
magic_sequence_n13__v3_h | magic_sequence | {
"n": 13,
"k": null,
"p": null,
"max_chromatic_number": null,
"min_edges": null,
"min_girth": null,
"vertices": null,
"max_clique": null,
"min_degree": null,
"clique_size": null,
"max_degree": null,
"max_edges": null,
"max_independent_set": null,
"maximal_triangle_free": null,
"min_chroma... | Find a magic sequence of length 13. A magic sequence is a sequence x[0], x[1], ..., x[12] where each x[i] equals the count of how many times i appears in the sequence.
Return a list of 13 integers, or state "UNSATISFIABLE" if no solution exists.
Partial assignment (fixed values that must be respected):
- x[7]=0, x[11... | true | {
"x": [
9,
2,
1,
0,
0,
0,
0,
0,
0,
1,
0,
0,
0
],
"d": null,
"seq": null,
"c": null,
"edges": null,
"q": null
} | {
"solve_time_ms": 1045.4,
"search_space": 302875106592253,
"num_variables": 13,
"num_constraints": 25,
"num_edges": -1,
"backend": "pycsp",
"solve_tier": "hard",
"solve_pct_global": 74.25,
"solve_pct_type": 79.17
} | {
"x": {
"0": null,
"1": null,
"2": null,
"3": null,
"4": null,
"5": null,
"6": null,
"7": 0,
"8": null,
"9": null,
"10": null,
"11": 0,
"12": null,
"13": null,
"14": null,
"15": null,
"17": null,
"18": null,
"19": null,
"20": null,
"... |
magic_sequence_n14__v4_h | magic_sequence | {
"n": 14,
"k": null,
"p": null,
"max_chromatic_number": null,
"min_edges": null,
"min_girth": null,
"vertices": null,
"max_clique": null,
"min_degree": null,
"clique_size": null,
"max_degree": null,
"max_edges": null,
"max_independent_set": null,
"maximal_triangle_free": null,
"min_chroma... | Find a magic sequence of length 14. A magic sequence is a sequence x[0], x[1], ..., x[13] where each x[i] equals the count of how many times i appears in the sequence.
Return a list of 14 integers, or state "UNSATISFIABLE" if no solution exists.
Partial assignment (fixed values that must be respected):
- x[11]=0, x[1... | true | {
"x": [
10,
2,
1,
0,
0,
0,
0,
0,
0,
0,
1,
0,
0,
0
],
"d": null,
"seq": null,
"c": null,
"edges": null,
"q": null
} | {
"solve_time_ms": 978.1,
"search_space": 11112006825558016,
"num_variables": 14,
"num_constraints": 26,
"num_edges": -1,
"backend": "pycsp",
"solve_tier": "hard",
"solve_pct_global": 67.11,
"solve_pct_type": 37.5
} | {
"x": {
"0": null,
"1": null,
"2": null,
"3": null,
"4": null,
"5": null,
"6": null,
"7": null,
"8": null,
"9": null,
"10": null,
"11": 0,
"12": 0,
"13": null,
"14": null,
"15": null,
"17": null,
"18": null,
"19": null,
"20": null,
"... |
magic_sequence_n15__v9_nh | magic_sequence | {
"n": 15,
"k": null,
"p": null,
"max_chromatic_number": null,
"min_edges": null,
"min_girth": null,
"vertices": null,
"max_clique": null,
"min_degree": null,
"clique_size": null,
"max_degree": null,
"max_edges": null,
"max_independent_set": null,
"maximal_triangle_free": null,
"min_chroma... | Find a magic sequence of length 15. A magic sequence is a sequence x[0], x[1], ..., x[14] where each x[i] equals the count of how many times i appears in the sequence.
Return a list of 15 integers, or state "UNSATISFIABLE" if no solution exists. | true | {
"x": [
11,
2,
1,
0,
0,
0,
0,
0,
0,
0,
0,
1,
0,
0,
0
],
"d": null,
"seq": null,
"c": null,
"edges": null,
"q": null
} | {
"solve_time_ms": 1045.5,
"search_space": 437893890380859400,
"num_variables": 15,
"num_constraints": 27,
"num_edges": -1,
"backend": "pycsp",
"solve_tier": "hard",
"solve_pct_global": 74.62,
"solve_pct_type": 87.5
} | null |
magic_sequence_n16__v6_nh | magic_sequence | {
"n": 16,
"k": null,
"p": null,
"max_chromatic_number": null,
"min_edges": null,
"min_girth": null,
"vertices": null,
"max_clique": null,
"min_degree": null,
"clique_size": null,
"max_degree": null,
"max_edges": null,
"max_independent_set": null,
"maximal_triangle_free": null,
"min_chroma... | Find a magic sequence of length 16. A magic sequence is a sequence x[0], x[1], ..., x[15] where each x[i] equals the count of how many times i appears in the sequence.
Return a list of 16 integers, or state "UNSATISFIABLE" if no solution exists. | true | {
"x": [
12,
2,
1,
0,
0,
0,
0,
0,
0,
0,
0,
0,
1,
0,
0,
0
],
"d": null,
"seq": null,
"c": null,
"edges": null,
"q": null
} | {
"solve_time_ms": 980.4,
"search_space": 18446744073709552000,
"num_variables": 16,
"num_constraints": 28,
"num_edges": -1,
"backend": "pycsp",
"solve_tier": "hard",
"solve_pct_global": 67.86,
"solve_pct_type": 45.83
} | null |
magic_sequence_n3__v10 | magic_sequence | {
"n": 3,
"k": null,
"p": null,
"max_chromatic_number": null,
"min_edges": null,
"min_girth": null,
"vertices": null,
"max_clique": null,
"min_degree": null,
"clique_size": null,
"max_degree": null,
"max_edges": null,
"max_independent_set": null,
"maximal_triangle_free": null,
"min_chromat... | Find a magic sequence of length 3. A magic sequence is a sequence x[0], x[1], ..., x[2] where each x[i] equals the count of how many times i appears in the sequence.
Return a list of 3 integers, or state "UNSATISFIABLE" if no solution exists. | false | null | {
"solve_time_ms": 951.8,
"search_space": 27,
"num_variables": 3,
"num_constraints": 15,
"num_edges": -1,
"backend": "pycsp",
"solve_tier": "medium",
"solve_pct_global": 63.35,
"solve_pct_type": 4.17
} | null |
magic_sequence_n4__v11_nh | magic_sequence | {
"n": 4,
"k": null,
"p": null,
"max_chromatic_number": null,
"min_edges": null,
"min_girth": null,
"vertices": null,
"max_clique": null,
"min_degree": null,
"clique_size": null,
"max_degree": null,
"max_edges": null,
"max_independent_set": null,
"maximal_triangle_free": null,
"min_chromat... | Find a magic sequence of length 4. A magic sequence is a sequence x[0], x[1], ..., x[3] where each x[i] equals the count of how many times i appears in the sequence.
Return a list of 4 integers, or state "UNSATISFIABLE" if no solution exists. | true | {
"x": [
1,
2,
1,
0
],
"d": null,
"seq": null,
"c": null,
"edges": null,
"q": null
} | {
"solve_time_ms": 1040.6,
"search_space": 256,
"num_variables": 4,
"num_constraints": 16,
"num_edges": -1,
"backend": "pycsp",
"solve_tier": "hard",
"solve_pct_global": 73.87,
"solve_pct_type": 70.83
} | null |
magic_sequence_n5__v2_h | magic_sequence | {
"n": 5,
"k": null,
"p": null,
"max_chromatic_number": null,
"min_edges": null,
"min_girth": null,
"vertices": null,
"max_clique": null,
"min_degree": null,
"clique_size": null,
"max_degree": null,
"max_edges": null,
"max_independent_set": null,
"maximal_triangle_free": null,
"min_chromat... | Find a magic sequence of length 5. A magic sequence is a sequence x[0], x[1], ..., x[4] where each x[i] equals the count of how many times i appears in the sequence.
Return a list of 5 integers, or state "UNSATISFIABLE" if no solution exists.
Partial assignment (fixed values that must be respected):
- x[2]=2
Return a... | true | {
"x": [
2,
1,
2,
0,
0
],
"d": null,
"seq": null,
"c": null,
"edges": null,
"q": null
} | {
"solve_time_ms": 955.1,
"search_space": 3125,
"num_variables": 5,
"num_constraints": 17,
"num_edges": -1,
"backend": "pycsp",
"solve_tier": "medium",
"solve_pct_global": 63.72,
"solve_pct_type": 12.5
} | {
"x": {
"0": null,
"1": null,
"2": 2,
"3": null,
"4": null,
"5": null,
"6": null,
"7": null,
"8": null,
"9": null,
"10": null,
"11": null,
"12": null,
"13": null,
"14": null,
"15": null,
"17": null,
"18": null,
"19": null,
"20": null,
... |
magic_sequence_n6__v5 | magic_sequence | {
"n": 6,
"k": null,
"p": null,
"max_chromatic_number": null,
"min_edges": null,
"min_girth": null,
"vertices": null,
"max_clique": null,
"min_degree": null,
"clique_size": null,
"max_degree": null,
"max_edges": null,
"max_independent_set": null,
"maximal_triangle_free": null,
"min_chromat... | Find a magic sequence of length 6. A magic sequence is a sequence x[0], x[1], ..., x[5] where each x[i] equals the count of how many times i appears in the sequence.
Return a list of 6 integers, or state "UNSATISFIABLE" if no solution exists. | false | null | {
"solve_time_ms": 962.6,
"search_space": 46656,
"num_variables": 6,
"num_constraints": 18,
"num_edges": -1,
"backend": "pycsp",
"solve_tier": "medium",
"solve_pct_global": 65.23,
"solve_pct_type": 29.17
} | null |
magic_sequence_n7__v8_nh | magic_sequence | {
"n": 7,
"k": null,
"p": null,
"max_chromatic_number": null,
"min_edges": null,
"min_girth": null,
"vertices": null,
"max_clique": null,
"min_degree": null,
"clique_size": null,
"max_degree": null,
"max_edges": null,
"max_independent_set": null,
"maximal_triangle_free": null,
"min_chromat... | Find a magic sequence of length 7. A magic sequence is a sequence x[0], x[1], ..., x[6] where each x[i] equals the count of how many times i appears in the sequence.
Return a list of 7 integers, or state "UNSATISFIABLE" if no solution exists. | true | {
"x": [
3,
2,
1,
1,
0,
0,
0
],
"d": null,
"seq": null,
"c": null,
"edges": null,
"q": null
} | {
"solve_time_ms": 961.5,
"search_space": 823543,
"num_variables": 7,
"num_constraints": 19,
"num_edges": -1,
"backend": "pycsp",
"solve_tier": "medium",
"solve_pct_global": 64.47,
"solve_pct_type": 20.83
} | null |
magic_sequence_n9__v7_h | magic_sequence | {
"n": 9,
"k": null,
"p": null,
"max_chromatic_number": null,
"min_edges": null,
"min_girth": null,
"vertices": null,
"max_clique": null,
"min_degree": null,
"clique_size": null,
"max_degree": null,
"max_edges": null,
"max_independent_set": null,
"maximal_triangle_free": null,
"min_chromat... | Find a magic sequence of length 9. A magic sequence is a sequence x[0], x[1], ..., x[8] where each x[i] equals the count of how many times i appears in the sequence.
Return a list of 9 integers, or state "UNSATISFIABLE" if no solution exists.
Partial assignment (fixed values that must be respected):
- x[4]=0
Return a... | true | {
"x": [
5,
2,
1,
0,
0,
1,
0,
0,
0
],
"d": null,
"seq": null,
"c": null,
"edges": null,
"q": null
} | {
"solve_time_ms": 1010.1,
"search_space": 387420489,
"num_variables": 9,
"num_constraints": 21,
"num_edges": -1,
"backend": "pycsp",
"solve_tier": "hard",
"solve_pct_global": 70.86,
"solve_pct_type": 62.5
} | {
"x": {
"0": null,
"1": null,
"2": null,
"3": null,
"4": 0,
"5": null,
"6": null,
"7": null,
"8": null,
"9": null,
"10": null,
"11": null,
"12": null,
"13": null,
"14": null,
"15": null,
"17": null,
"18": null,
"19": null,
"20": null,
... |
pigeons_n11__v4 | pigeons | {
"n": 11,
"k": null,
"p": null,
"max_chromatic_number": null,
"min_edges": null,
"min_girth": null,
"vertices": null,
"max_clique": null,
"min_degree": null,
"clique_size": null,
"max_degree": null,
"max_edges": null,
"max_independent_set": null,
"maximal_triangle_free": null,
"min_chroma... | Place 11 pigeons into 10 holes such that each hole contains at most one pigeon. Each pigeon must be assigned to exactly one hole (numbered 0 to 9).
Return a list of 11 integers where the i-th integer is the hole assigned to pigeon i, or state "UNSATISFIABLE" if no solution exists. | false | null | {
"solve_time_ms": 850,
"search_space": 100000000000,
"num_variables": 11,
"num_constraints": 1,
"num_edges": -1,
"backend": "pycsp",
"solve_tier": "medium",
"solve_pct_global": 55.83,
"solve_pct_type": 4.17
} | null |
pigeons_n12__v6 | pigeons | {
"n": 12,
"k": null,
"p": null,
"max_chromatic_number": null,
"min_edges": null,
"min_girth": null,
"vertices": null,
"max_clique": null,
"min_degree": null,
"clique_size": null,
"max_degree": null,
"max_edges": null,
"max_independent_set": null,
"maximal_triangle_free": null,
"min_chroma... | Place 12 pigeons into 11 holes such that each hole contains at most one pigeon. Each pigeon must be assigned to exactly one hole (numbered 0 to 10).
Return a list of 12 integers where the i-th integer is the hole assigned to pigeon i, or state "UNSATISFIABLE" if no solution exists. | false | null | {
"solve_time_ms": 909.5,
"search_space": 3138428376721,
"num_variables": 12,
"num_constraints": 1,
"num_edges": -1,
"backend": "pycsp",
"solve_tier": "medium",
"solve_pct_global": 58.46,
"solve_pct_type": 29.17
} | null |
pigeons_n15__v5 | pigeons | {
"n": 15,
"k": null,
"p": null,
"max_chromatic_number": null,
"min_edges": null,
"min_girth": null,
"vertices": null,
"max_clique": null,
"min_degree": null,
"clique_size": null,
"max_degree": null,
"max_edges": null,
"max_independent_set": null,
"maximal_triangle_free": null,
"min_chroma... | Place 15 pigeons into 14 holes such that each hole contains at most one pigeon. Each pigeon must be assigned to exactly one hole (numbered 0 to 13).
Return a list of 15 integers where the i-th integer is the hole assigned to pigeon i, or state "UNSATISFIABLE" if no solution exists. | false | null | {
"solve_time_ms": 961.6,
"search_space": 155568095557812220,
"num_variables": 15,
"num_constraints": 1,
"num_edges": -1,
"backend": "pycsp",
"solve_tier": "medium",
"solve_pct_global": 64.85,
"solve_pct_type": 87.5
} | null |
pigeons_n17__v0 | pigeons | {
"n": 17,
"k": null,
"p": null,
"max_chromatic_number": null,
"min_edges": null,
"min_girth": null,
"vertices": null,
"max_clique": null,
"min_degree": null,
"clique_size": null,
"max_degree": null,
"max_edges": null,
"max_independent_set": null,
"maximal_triangle_free": null,
"min_chroma... | Place 17 pigeons into 16 holes such that each hole contains at most one pigeon. Each pigeon must be assigned to exactly one hole (numbered 0 to 15).
Return a list of 17 integers where the i-th integer is the hole assigned to pigeon i, or state "UNSATISFIABLE" if no solution exists. | false | null | {
"solve_time_ms": 929.3,
"search_space": 295147905179352830000,
"num_variables": 17,
"num_constraints": 1,
"num_edges": -1,
"backend": "pycsp",
"solve_tier": "medium",
"solve_pct_global": 59.96,
"solve_pct_type": 54.17
} | null |
pigeons_n18__v7 | pigeons | {
"n": 18,
"k": null,
"p": null,
"max_chromatic_number": null,
"min_edges": null,
"min_girth": null,
"vertices": null,
"max_clique": null,
"min_degree": null,
"clique_size": null,
"max_degree": null,
"max_edges": null,
"max_independent_set": null,
"maximal_triangle_free": null,
"min_chroma... | Place 18 pigeons into 17 holes such that each hole contains at most one pigeon. Each pigeon must be assigned to exactly one hole (numbered 0 to 16).
Return a list of 18 integers where the i-th integer is the hole assigned to pigeon i, or state "UNSATISFIABLE" if no solution exists. | false | null | {
"solve_time_ms": 926.4,
"search_space": 1.4063084452067724e+22,
"num_variables": 18,
"num_constraints": 1,
"num_edges": -1,
"backend": "pycsp",
"solve_tier": "medium",
"solve_pct_global": 59.59,
"solve_pct_type": 45.83
} | null |
pigeons_n19__v9 | pigeons | {
"n": 19,
"k": null,
"p": null,
"max_chromatic_number": null,
"min_edges": null,
"min_girth": null,
"vertices": null,
"max_clique": null,
"min_degree": null,
"clique_size": null,
"max_degree": null,
"max_edges": null,
"max_independent_set": null,
"maximal_triangle_free": null,
"min_chroma... | Place 19 pigeons into 18 holes such that each hole contains at most one pigeon. Each pigeon must be assigned to exactly one hole (numbered 0 to 17).
Return a list of 19 integers where the i-th integer is the hole assigned to pigeon i, or state "UNSATISFIABLE" if no solution exists. | false | null | {
"solve_time_ms": 942.9,
"search_space": 7.082353453553376e+23,
"num_variables": 19,
"num_constraints": 1,
"num_edges": -1,
"backend": "pycsp",
"solve_tier": "medium",
"solve_pct_global": 61.84,
"solve_pct_type": 70.83
} | null |
pigeons_n20__v1 | pigeons | {
"n": 20,
"k": null,
"p": null,
"max_chromatic_number": null,
"min_edges": null,
"min_girth": null,
"vertices": null,
"max_clique": null,
"min_degree": null,
"clique_size": null,
"max_degree": null,
"max_edges": null,
"max_independent_set": null,
"maximal_triangle_free": null,
"min_chroma... | Place 20 pigeons into 19 holes such that each hole contains at most one pigeon. Each pigeon must be assigned to exactly one hole (numbered 0 to 18).
Return a list of 20 integers where the i-th integer is the hole assigned to pigeon i, or state "UNSATISFIABLE" if no solution exists. | false | null | {
"solve_time_ms": 951.6,
"search_space": 3.758997345754596e+25,
"num_variables": 20,
"num_constraints": 1,
"num_edges": -1,
"backend": "pycsp",
"solve_tier": "medium",
"solve_pct_global": 62.97,
"solve_pct_type": 79.17
} | null |
pigeons_n21__v8 | pigeons | {
"n": 21,
"k": null,
"p": null,
"max_chromatic_number": null,
"min_edges": null,
"min_girth": null,
"vertices": null,
"max_clique": null,
"min_degree": null,
"clique_size": null,
"max_degree": null,
"max_edges": null,
"max_independent_set": null,
"maximal_triangle_free": null,
"min_chroma... | Place 21 pigeons into 20 holes such that each hole contains at most one pigeon. Each pigeon must be assigned to exactly one hole (numbered 0 to 19).
Return a list of 21 integers where the i-th integer is the hole assigned to pigeon i, or state "UNSATISFIABLE" if no solution exists. | false | null | {
"solve_time_ms": 901.4,
"search_space": 2.097152e+27,
"num_variables": 21,
"num_constraints": 1,
"num_edges": -1,
"backend": "pycsp",
"solve_tier": "medium",
"solve_pct_global": 57.71,
"solve_pct_type": 12.5
} | null |
pigeons_n24__v11 | pigeons | {
"n": 24,
"k": null,
"p": null,
"max_chromatic_number": null,
"min_edges": null,
"min_girth": null,
"vertices": null,
"max_clique": null,
"min_degree": null,
"clique_size": null,
"max_degree": null,
"max_edges": null,
"max_independent_set": null,
"maximal_triangle_free": null,
"min_chroma... | Place 24 pigeons into 23 holes such that each hole contains at most one pigeon. Each pigeon must be assigned to exactly one hole (numbered 0 to 22).
Return a list of 24 integers where the i-th integer is the hole assigned to pigeon i, or state "UNSATISFIABLE" if no solution exists. | false | null | {
"solve_time_ms": 940,
"search_space": 4.8025076399650196e+32,
"num_variables": 24,
"num_constraints": 1,
"num_edges": -1,
"backend": "pycsp",
"solve_tier": "medium",
"solve_pct_global": 61.47,
"solve_pct_type": 62.5
} | null |
pigeons_n4__v10 | pigeons | {
"n": 4,
"k": null,
"p": null,
"max_chromatic_number": null,
"min_edges": null,
"min_girth": null,
"vertices": null,
"max_clique": null,
"min_degree": null,
"clique_size": null,
"max_degree": null,
"max_edges": null,
"max_independent_set": null,
"maximal_triangle_free": null,
"min_chromat... | Place 4 pigeons into 3 holes such that each hole contains at most one pigeon. Each pigeon must be assigned to exactly one hole (numbered 0 to 2).
Return a list of 4 integers where the i-th integer is the hole assigned to pigeon i, or state "UNSATISFIABLE" if no solution exists. | false | null | {
"solve_time_ms": 966,
"search_space": 81,
"num_variables": 4,
"num_constraints": 1,
"num_edges": -1,
"backend": "pycsp",
"solve_tier": "medium",
"solve_pct_global": 65.6,
"solve_pct_type": 95.83
} | null |
pigeons_n5__v2 | pigeons | {
"n": 5,
"k": null,
"p": null,
"max_chromatic_number": null,
"min_edges": null,
"min_girth": null,
"vertices": null,
"max_clique": null,
"min_degree": null,
"clique_size": null,
"max_degree": null,
"max_edges": null,
"max_independent_set": null,
"maximal_triangle_free": null,
"min_chromat... | Place 5 pigeons into 4 holes such that each hole contains at most one pigeon. Each pigeon must be assigned to exactly one hole (numbered 0 to 3).
Return a list of 5 integers where the i-th integer is the hole assigned to pigeon i, or state "UNSATISFIABLE" if no solution exists. | false | null | {
"solve_time_ms": 921.3,
"search_space": 1024,
"num_variables": 5,
"num_constraints": 1,
"num_edges": -1,
"backend": "pycsp",
"solve_tier": "medium",
"solve_pct_global": 59.21,
"solve_pct_type": 37.5
} | null |
pigeons_n7__v3 | pigeons | {
"n": 7,
"k": null,
"p": null,
"max_chromatic_number": null,
"min_edges": null,
"min_girth": null,
"vertices": null,
"max_clique": null,
"min_degree": null,
"clique_size": null,
"max_degree": null,
"max_edges": null,
"max_independent_set": null,
"maximal_triangle_free": null,
"min_chromat... | Place 7 pigeons into 6 holes such that each hole contains at most one pigeon. Each pigeon must be assigned to exactly one hole (numbered 0 to 5).
Return a list of 7 integers where the i-th integer is the hole assigned to pigeon i, or state "UNSATISFIABLE" if no solution exists. | false | null | {
"solve_time_ms": 907.4,
"search_space": 279936,
"num_variables": 7,
"num_constraints": 1,
"num_edges": -1,
"backend": "pycsp",
"solve_tier": "medium",
"solve_pct_global": 58.08,
"solve_pct_type": 20.83
} | null |
pysms_chromatic_girth_max_chromatic_number2_min_edges16_min_girth6_vertices15__v10_nh | pysms_chromatic_girth | {
"n": null,
"k": null,
"p": null,
"max_chromatic_number": 2,
"min_edges": 16,
"min_girth": 6,
"vertices": 15,
"max_clique": null,
"min_degree": null,
"clique_size": null,
"max_degree": null,
"max_edges": null,
"max_independent_set": null,
"maximal_triangle_free": null,
"min_chromatic_numb... | Generate a graph with 15 vertices that is colorable with at most 2 colors, has girth (shortest cycle) at least 6, and has at least 16 edges.
Return the graph as a list of edges (u, v) with 0 <= u < v < 15, or state "UNSATISFIABLE" if no graph exists. | true | {
"x": null,
"d": null,
"seq": null,
"c": null,
"edges": [
[
0,
13
],
[
0,
14
],
[
1,
11
],
[
1,
12
],
[
2,
10
],
[
2,
12
],
[
2,
14
],
[
3,
9
],
... | {
"solve_time_ms": 217.9,
"search_space": -1,
"num_variables": -1,
"num_constraints": -1,
"num_edges": 21,
"backend": "pysms",
"solve_tier": "medium",
"solve_pct_global": 50.56,
"solve_pct_type": 54.17
} | null |
pysms_chromatic_girth_max_chromatic_number2_min_edges19_min_girth4_vertices15__v8_nh | pysms_chromatic_girth | {
"n": null,
"k": null,
"p": null,
"max_chromatic_number": 2,
"min_edges": 19,
"min_girth": 4,
"vertices": 15,
"max_clique": null,
"min_degree": null,
"clique_size": null,
"max_degree": null,
"max_edges": null,
"max_independent_set": null,
"maximal_triangle_free": null,
"min_chromatic_numb... | Generate a graph with 15 vertices that is colorable with at most 2 colors, has girth (shortest cycle) at least 4, and has at least 19 edges.
Return the graph as a list of edges (u, v) with 0 <= u < v < 15, or state "UNSATISFIABLE" if no graph exists. | true | {
"x": null,
"d": null,
"seq": null,
"c": null,
"edges": [
[
0,
2
],
[
0,
3
],
[
0,
4
],
[
0,
5
],
[
0,
6
],
[
0,
7
],
[
0,
8
],
[
0,
9
],
[
... | {
"solve_time_ms": 99.4,
"search_space": -1,
"num_variables": -1,
"num_constraints": -1,
"num_edges": 26,
"backend": "pysms",
"solve_tier": "medium",
"solve_pct_global": 41.17,
"solve_pct_type": 45.83
} | null |
pysms_chromatic_girth_max_chromatic_number2_min_edges8_min_girth5_vertices13__v2_h | pysms_chromatic_girth | {
"n": null,
"k": null,
"p": null,
"max_chromatic_number": 2,
"min_edges": 8,
"min_girth": 5,
"vertices": 13,
"max_clique": null,
"min_degree": null,
"clique_size": null,
"max_degree": null,
"max_edges": null,
"max_independent_set": null,
"maximal_triangle_free": null,
"min_chromatic_numbe... | Generate a graph with 13 vertices that is colorable with at most 2 colors, has girth (shortest cycle) at least 5, and has at least 8 edges.
Return the graph as a list of edges (u, v) with 0 <= u < v < 13, or state "UNSATISFIABLE" if no graph exists.
Partial assignment (fixed values that must be respected):
- Known pr... | true | {
"x": null,
"d": null,
"seq": null,
"c": null,
"edges": [
[
0,
1
],
[
0,
2
],
[
0,
3
],
[
0,
4
],
[
0,
5
],
[
0,
6
],
[
0,
7
],
[
0,
8
],
[
... | {
"solve_time_ms": 91.3,
"search_space": -1,
"num_variables": -1,
"num_constraints": -1,
"num_edges": 12,
"backend": "pysms",
"solve_tier": "easy",
"solve_pct_global": 32.89,
"solve_pct_type": 20.83
} | {
"x": null,
"d": null,
"seq": null,
"c": null,
"edges": [
[
0,
1
],
[
0,
8
]
],
"q": null
} |
pysms_chromatic_girth_max_chromatic_number3_min_edges19_min_girth7_vertices14__v7 | pysms_chromatic_girth | {
"n": null,
"k": null,
"p": null,
"max_chromatic_number": 3,
"min_edges": 19,
"min_girth": 7,
"vertices": 14,
"max_clique": null,
"min_degree": null,
"clique_size": null,
"max_degree": null,
"max_edges": null,
"max_independent_set": null,
"maximal_triangle_free": null,
"min_chromatic_numb... | Generate a graph with 14 vertices that is colorable with at most 3 colors, has girth (shortest cycle) at least 7, and has at least 19 edges.
Return the graph as a list of edges (u, v) with 0 <= u < v < 14, or state "UNSATISFIABLE" if no graph exists. | false | null | {
"solve_time_ms": 1766.3,
"search_space": -1,
"num_variables": -1,
"num_constraints": -1,
"num_edges": -1,
"backend": "pysms",
"solve_tier": "hard",
"solve_pct_global": 89.66,
"solve_pct_type": 95.83
} | null |
pysms_chromatic_girth_max_chromatic_number3_min_edges20_min_girth6_vertices14__v1_nh | pysms_chromatic_girth | {
"n": null,
"k": null,
"p": null,
"max_chromatic_number": 3,
"min_edges": 20,
"min_girth": 6,
"vertices": 14,
"max_clique": null,
"min_degree": null,
"clique_size": null,
"max_degree": null,
"max_edges": null,
"max_independent_set": null,
"maximal_triangle_free": null,
"min_chromatic_numb... | Generate a graph with 14 vertices that is colorable with at most 3 colors, has girth (shortest cycle) at least 6, and has at least 20 edges.
Return the graph as a list of edges (u, v) with 0 <= u < v < 14, or state "UNSATISFIABLE" if no graph exists. | true | {
"x": null,
"d": null,
"seq": null,
"c": null,
"edges": [
[
0,
11
],
[
0,
12
],
[
0,
13
],
[
1,
9
],
[
1,
10
],
[
1,
13
],
[
2,
8
],
[
2,
10
],
[... | {
"solve_time_ms": 276,
"search_space": -1,
"num_variables": -1,
"num_constraints": -1,
"num_edges": 21,
"backend": "pysms",
"solve_tier": "medium",
"solve_pct_global": 52.07,
"solve_pct_type": 70.83
} | null |
pysms_chromatic_girth_max_chromatic_number4_min_edges16_min_girth4_vertices14__v3_nh | pysms_chromatic_girth | {
"n": null,
"k": null,
"p": null,
"max_chromatic_number": 4,
"min_edges": 16,
"min_girth": 4,
"vertices": 14,
"max_clique": null,
"min_degree": null,
"clique_size": null,
"max_degree": null,
"max_edges": null,
"max_independent_set": null,
"maximal_triangle_free": null,
"min_chromatic_numb... | Generate a graph with 14 vertices that is colorable with at most 4 colors, has girth (shortest cycle) at least 4, and has at least 16 edges.
Return the graph as a list of edges (u, v) with 0 <= u < v < 14, or state "UNSATISFIABLE" if no graph exists. | true | {
"x": null,
"d": null,
"seq": null,
"c": null,
"edges": [
[
0,
2
],
[
0,
3
],
[
0,
4
],
[
0,
5
],
[
0,
6
],
[
0,
7
],
[
0,
8
],
[
0,
9
],
[
... | {
"solve_time_ms": 94.5,
"search_space": -1,
"num_variables": -1,
"num_constraints": -1,
"num_edges": 24,
"backend": "pysms",
"solve_tier": "medium",
"solve_pct_global": 35.53,
"solve_pct_type": 29.17
} | null |
pysms_chromatic_girth_max_chromatic_number4_min_edges19_min_girth7_vertices14__v0 | pysms_chromatic_girth | {
"n": null,
"k": null,
"p": null,
"max_chromatic_number": 4,
"min_edges": 19,
"min_girth": 7,
"vertices": 14,
"max_clique": null,
"min_degree": null,
"clique_size": null,
"max_degree": null,
"max_edges": null,
"max_independent_set": null,
"maximal_triangle_free": null,
"min_chromatic_numb... | Generate a graph with 14 vertices that is colorable with at most 4 colors, has girth (shortest cycle) at least 7, and has at least 19 edges.
Return the graph as a list of edges (u, v) with 0 <= u < v < 14, or state "UNSATISFIABLE" if no graph exists. | false | null | {
"solve_time_ms": 1743.5,
"search_space": -1,
"num_variables": -1,
"num_constraints": -1,
"num_edges": -1,
"backend": "pysms",
"solve_tier": "hard",
"solve_pct_global": 89.29,
"solve_pct_type": 87.5
} | null |
pysms_chromatic_girth_max_chromatic_number4_min_edges22_min_girth7_vertices13__v4 | pysms_chromatic_girth | {
"n": null,
"k": null,
"p": null,
"max_chromatic_number": 4,
"min_edges": 22,
"min_girth": 7,
"vertices": 13,
"max_clique": null,
"min_degree": null,
"clique_size": null,
"max_degree": null,
"max_edges": null,
"max_independent_set": null,
"maximal_triangle_free": null,
"min_chromatic_numb... | Generate a graph with 13 vertices that is colorable with at most 4 colors, has girth (shortest cycle) at least 7, and has at least 22 edges.
Return the graph as a list of edges (u, v) with 0 <= u < v < 13, or state "UNSATISFIABLE" if no graph exists. | false | null | {
"solve_time_ms": 603.7,
"search_space": -1,
"num_variables": -1,
"num_constraints": -1,
"num_edges": -1,
"backend": "pysms",
"solve_tier": "medium",
"solve_pct_global": 54.7,
"solve_pct_type": 79.17
} | null |
pysms_chromatic_girth_max_chromatic_number5_min_edges10_min_girth5_vertices13__v5_h | pysms_chromatic_girth | {
"n": null,
"k": null,
"p": null,
"max_chromatic_number": 5,
"min_edges": 10,
"min_girth": 5,
"vertices": 13,
"max_clique": null,
"min_degree": null,
"clique_size": null,
"max_degree": null,
"max_edges": null,
"max_independent_set": null,
"maximal_triangle_free": null,
"min_chromatic_numb... | Generate a graph with 13 vertices that is colorable with at most 5 colors, has girth (shortest cycle) at least 5, and has at least 10 edges.
Return the graph as a list of edges (u, v) with 0 <= u < v < 13, or state "UNSATISFIABLE" if no graph exists.
Partial assignment (fixed values that must be respected):
- Known p... | true | {
"x": null,
"d": null,
"seq": null,
"c": null,
"edges": [
[
0,
1
],
[
0,
2
],
[
0,
3
],
[
0,
4
],
[
0,
5
],
[
0,
6
],
[
0,
7
],
[
0,
8
],
[
... | {
"solve_time_ms": 90.7,
"search_space": -1,
"num_variables": -1,
"num_constraints": -1,
"num_edges": 12,
"backend": "pysms",
"solve_tier": "easy",
"solve_pct_global": 32.52,
"solve_pct_type": 12.5
} | {
"x": null,
"d": null,
"seq": null,
"c": null,
"edges": [
[
0,
2
],
[
0,
4
]
],
"q": null
} |
pysms_chromatic_girth_max_chromatic_number5_min_edges10_min_girth7_vertices15__v6_nh | pysms_chromatic_girth | {
"n": null,
"k": null,
"p": null,
"max_chromatic_number": 5,
"min_edges": 10,
"min_girth": 7,
"vertices": 15,
"max_clique": null,
"min_degree": null,
"clique_size": null,
"max_degree": null,
"max_edges": null,
"max_independent_set": null,
"maximal_triangle_free": null,
"min_chromatic_numb... | Generate a graph with 15 vertices that is colorable with at most 5 colors, has girth (shortest cycle) at least 7, and has at least 10 edges.
Return the graph as a list of edges (u, v) with 0 <= u < v < 15, or state "UNSATISFIABLE" if no graph exists. | true | {
"x": null,
"d": null,
"seq": null,
"c": null,
"edges": [
[
0,
1
],
[
0,
2
],
[
0,
3
],
[
0,
4
],
[
0,
5
],
[
0,
6
],
[
0,
7
],
[
0,
8
],
[
... | {
"solve_time_ms": 262.9,
"search_space": -1,
"num_variables": -1,
"num_constraints": -1,
"num_edges": 14,
"backend": "pysms",
"solve_tier": "medium",
"solve_pct_global": 51.69,
"solve_pct_type": 62.5
} | null |
pysms_chromatic_girth_max_chromatic_number5_min_edges16_min_girth5_vertices14__v11_nh | pysms_chromatic_girth | {
"n": null,
"k": null,
"p": null,
"max_chromatic_number": 5,
"min_edges": 16,
"min_girth": 5,
"vertices": 14,
"max_clique": null,
"min_degree": null,
"clique_size": null,
"max_degree": null,
"max_edges": null,
"max_independent_set": null,
"maximal_triangle_free": null,
"min_chromatic_numb... | Generate a graph with 14 vertices that is colorable with at most 5 colors, has girth (shortest cycle) at least 5, and has at least 16 edges.
Return the graph as a list of edges (u, v) with 0 <= u < v < 14, or state "UNSATISFIABLE" if no graph exists. | true | {
"x": null,
"d": null,
"seq": null,
"c": null,
"edges": [
[
0,
11
],
[
0,
12
],
[
0,
13
],
[
1,
9
],
[
1,
10
],
[
1,
13
],
[
2,
8
],
[
2,
10
],
[... | {
"solve_time_ms": 99,
"search_space": -1,
"num_variables": -1,
"num_constraints": -1,
"num_edges": 21,
"backend": "pysms",
"solve_tier": "medium",
"solve_pct_global": 40.41,
"solve_pct_type": 37.5
} | null |
pysms_chromatic_girth_max_chromatic_number5_min_edges9_min_girth5_vertices9__v9_h | pysms_chromatic_girth | {
"n": null,
"k": null,
"p": null,
"max_chromatic_number": 5,
"min_edges": 9,
"min_girth": 5,
"vertices": 9,
"max_clique": null,
"min_degree": null,
"clique_size": null,
"max_degree": null,
"max_edges": null,
"max_independent_set": null,
"maximal_triangle_free": null,
"min_chromatic_number... | Generate a graph with 9 vertices that is colorable with at most 5 colors, has girth (shortest cycle) at least 5, and has at least 9 edges.
Return the graph as a list of edges (u, v) with 0 <= u < v < 9, or state "UNSATISFIABLE" if no graph exists.
Partial assignment (fixed values that must be respected):
- Known pres... | true | {
"x": null,
"d": null,
"seq": null,
"c": null,
"edges": [
[
0,
8
],
[
1,
8
],
[
2,
7
],
[
3,
6
],
[
3,
8
],
[
4,
5
],
[
4,
8
],
[
5,
6
],
[
... | {
"solve_time_ms": 13.6,
"search_space": -1,
"num_variables": -1,
"num_constraints": -1,
"num_edges": 9,
"backend": "pysms",
"solve_tier": "easy",
"solve_pct_global": 7.52,
"solve_pct_type": 4.17
} | {
"x": null,
"d": null,
"seq": null,
"c": null,
"edges": [
[
4,
8
]
],
"q": null
} |
pysms_clique_coloring_max_chromatic_number2_max_clique2_min_degree1_vertices16__v6_nh | pysms_clique_coloring | {
"n": null,
"k": null,
"p": null,
"max_chromatic_number": 2,
"min_edges": null,
"min_girth": null,
"vertices": 16,
"max_clique": 2,
"min_degree": 1,
"clique_size": null,
"max_degree": null,
"max_edges": null,
"max_independent_set": null,
"maximal_triangle_free": null,
"min_chromatic_numbe... | Generate a graph with 16 vertices where the maximum clique size is at most 2, the chromatic number is at most 2, and every vertex has degree at least 1.
Return the graph as a list of edges (u, v) with 0 <= u < v < 16, or state "UNSATISFIABLE" if no graph exists. | true | {
"x": null,
"d": null,
"seq": null,
"c": null,
"edges": [
[
0,
2
],
[
0,
3
],
[
0,
4
],
[
0,
5
],
[
0,
6
],
[
0,
7
],
[
0,
8
],
[
0,
9
],
[
... | {
"solve_time_ms": 96.7,
"search_space": -1,
"num_variables": -1,
"num_constraints": -1,
"num_edges": 28,
"backend": "pysms",
"solve_tier": "medium",
"solve_pct_global": 37.78,
"solve_pct_type": 79.17
} | null |
pysms_clique_coloring_max_chromatic_number2_max_clique2_min_degree4_vertices12__v3_h | pysms_clique_coloring | {
"n": null,
"k": null,
"p": null,
"max_chromatic_number": 2,
"min_edges": null,
"min_girth": null,
"vertices": 12,
"max_clique": 2,
"min_degree": 4,
"clique_size": null,
"max_degree": null,
"max_edges": null,
"max_independent_set": null,
"maximal_triangle_free": null,
"min_chromatic_numbe... | Generate a graph with 12 vertices where the maximum clique size is at most 2, the chromatic number is at most 2, and every vertex has degree at least 4.
Return the graph as a list of edges (u, v) with 0 <= u < v < 12, or state "UNSATISFIABLE" if no graph exists.
Partial assignment (fixed values that must be respected... | true | {
"x": null,
"d": null,
"seq": null,
"c": null,
"edges": [
[
0,
4
],
[
0,
5
],
[
0,
6
],
[
0,
7
],
[
0,
8
],
[
0,
9
],
[
0,
10
],
[
0,
11
],
[
... | {
"solve_time_ms": 87.7,
"search_space": -1,
"num_variables": -1,
"num_constraints": -1,
"num_edges": 32,
"backend": "pysms",
"solve_tier": "easy",
"solve_pct_global": 29.14,
"solve_pct_type": 29.17
} | {
"x": null,
"d": null,
"seq": null,
"c": null,
"edges": [
[
2,
8
],
[
1,
9
],
[
0,
6
],
[
3,
10
],
[
0,
9
],
[
3,
9
]
],
"q": null
} |
pysms_clique_coloring_max_chromatic_number2_max_clique4_min_degree1_vertices8__v2_h | pysms_clique_coloring | {
"n": null,
"k": null,
"p": null,
"max_chromatic_number": 2,
"min_edges": null,
"min_girth": null,
"vertices": 8,
"max_clique": 4,
"min_degree": 1,
"clique_size": null,
"max_degree": null,
"max_edges": null,
"max_independent_set": null,
"maximal_triangle_free": null,
"min_chromatic_number... | Generate a graph with 8 vertices where the maximum clique size is at most 4, the chromatic number is at most 2, and every vertex has degree at least 1.
Return the graph as a list of edges (u, v) with 0 <= u < v < 8, or state "UNSATISFIABLE" if no graph exists.
Partial assignment (fixed values that must be respected):... | true | {
"x": null,
"d": null,
"seq": null,
"c": null,
"edges": [
[
0,
5
],
[
0,
6
],
[
0,
7
],
[
1,
4
],
[
1,
6
],
[
1,
7
],
[
2,
4
],
[
2,
5
],
[
... | {
"solve_time_ms": 13.6,
"search_space": -1,
"num_variables": -1,
"num_constraints": -1,
"num_edges": 14,
"backend": "pysms",
"solve_tier": "easy",
"solve_pct_global": 7.52,
"solve_pct_type": 4.17
} | {
"x": null,
"d": null,
"seq": null,
"c": null,
"edges": [
[
2,
7
],
[
0,
5
]
],
"q": null
} |
pysms_clique_coloring_max_chromatic_number2_max_clique4_min_degree3_vertices11__v1_h | pysms_clique_coloring | {
"n": null,
"k": null,
"p": null,
"max_chromatic_number": 2,
"min_edges": null,
"min_girth": null,
"vertices": 11,
"max_clique": 4,
"min_degree": 3,
"clique_size": null,
"max_degree": null,
"max_edges": null,
"max_independent_set": null,
"maximal_triangle_free": null,
"min_chromatic_numbe... | Generate a graph with 11 vertices where the maximum clique size is at most 4, the chromatic number is at most 2, and every vertex has degree at least 3.
Return the graph as a list of edges (u, v) with 0 <= u < v < 11, or state "UNSATISFIABLE" if no graph exists.
Partial assignment (fixed values that must be respected... | true | {
"x": null,
"d": null,
"seq": null,
"c": null,
"edges": [
[
0,
3
],
[
0,
4
],
[
0,
5
],
[
0,
6
],
[
0,
7
],
[
0,
8
],
[
0,
9
],
[
0,
10
],
[
... | {
"solve_time_ms": 85.3,
"search_space": -1,
"num_variables": -1,
"num_constraints": -1,
"num_edges": 24,
"backend": "pysms",
"solve_tier": "easy",
"solve_pct_global": 28.01,
"solve_pct_type": 20.83
} | {
"x": null,
"d": null,
"seq": null,
"c": null,
"edges": [
[
1,
10
],
[
0,
4
],
[
0,
8
],
[
2,
9
]
],
"q": null
} |
pysms_clique_coloring_max_chromatic_number3_max_clique5_min_degree3_vertices12__v8_h | pysms_clique_coloring | {
"n": null,
"k": null,
"p": null,
"max_chromatic_number": 3,
"min_edges": null,
"min_girth": null,
"vertices": 12,
"max_clique": 5,
"min_degree": 3,
"clique_size": null,
"max_degree": null,
"max_edges": null,
"max_independent_set": null,
"maximal_triangle_free": null,
"min_chromatic_numbe... | Generate a graph with 12 vertices where the maximum clique size is at most 5, the chromatic number is at most 3, and every vertex has degree at least 3.
Return the graph as a list of edges (u, v) with 0 <= u < v < 12, or state "UNSATISFIABLE" if no graph exists.
Partial assignment (fixed values that must be respected... | true | {
"x": null,
"d": null,
"seq": null,
"c": null,
"edges": [
[
0,
2
],
[
0,
3
],
[
0,
4
],
[
0,
5
],
[
0,
6
],
[
0,
7
],
[
0,
8
],
[
0,
9
],
[
... | {
"solve_time_ms": 88.2,
"search_space": -1,
"num_variables": -1,
"num_constraints": -1,
"num_edges": 29,
"backend": "pysms",
"solve_tier": "easy",
"solve_pct_global": 29.89,
"solve_pct_type": 37.5
} | {
"x": null,
"d": null,
"seq": null,
"c": null,
"edges": [
[
1,
2
],
[
0,
2
],
[
1,
4
],
[
2,
9
],
[
2,
7
]
],
"q": null
} |
End of preview. Expand in Data Studio
MathConstraint-Easy
A 266-instance benchmark of natural-language combinatorial constraint-satisfaction problems with solver-verified ground truth. 25 problem types drawn from constraint programming (PyCSP3) and SAT-modulo-symmetries on graphs (pysms). 206 SAT / 60 UNSAT; SAT instances split 103 / 103 into hinted and unhinted. A harder companion split is at MathConstraint.
Files
problems.jsonl— canonical data file; one JSON record per lineinstances/<name>.json— same data, one file per instancemanifest.json— schema, type / SAT / wall-time stats, generation provenance_raw/<name>.{xml,cnf}— solver model file (XCSP3 for pycsp problems, CNF DIMACS for pysms graph problems)_raw/<name>.out.json— solver stdout / stderr / command for the reference verdict
The _raw/ files let any external SAT/CSP solver independently verify the labels.
License
CC-BY-4.0
Citation
Anonymous. Citation provided in camera-ready.
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