task_id stringlengths 23 52 | subset stringclasses 1
value | family stringclasses 80
values | problem_key stringclasses 75
values | domain stringclasses 8
values | tier stringclasses 2
values | level stringclasses 6
values | source stringclasses 80
values | license stringclasses 3
values | tags listlengths 0 4 | prompt stringlengths 308 37k | instance stringlengths 56 37.8k | direction null | baseline null | best_known null | reference_answer stringlengths 8 198k | reference_reward float64 1 1 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
construct-mc-bibd-l6-s1 | construct | mc_bibd | bibd | combinatorics | competition | 6 | MathConstraint/bibd | CC-BY-4.0 | [
"np_search"
] | A balanced incomplete block design BIBD(31, 15, 7) is a collection of b = 31 blocks, each a set of 15 distinct points from {0, 1, ..., 30}, such that every pair of distinct points is contained in exactly 7 of the blocks (consequently every point lies in exactly r = 15 blocks). The same block may appear more than once.
... | {"v": 31, "k": 15, "lambda": 7, "b": 31, "family": "mc_bibd", "subset": "construct"} | null | null | null | {"blocks": [[1, 2, 4, 5, 7, 8, 9, 10, 14, 16, 18, 19, 20, 25, 28], [2, 3, 5, 6, 8, 9, 10, 11, 15, 17, 19, 20, 21, 26, 29], [3, 4, 6, 7, 9, 10, 11, 12, 16, 18, 20, 21, 22, 27, 30], [0, 4, 5, 7, 8, 10, 11, 12, 13, 17, 19, 21, 22, 23, 28], [1, 5, 6, 8, 9, 11, 12, 13, 14, 18, 20, 22, 23, 24, 29], [2, 6, 7, 9, 10, 12, 13, 1... | 1 |
construct-mc-bibd-l6-s2 | construct | mc_bibd | bibd | combinatorics | competition | 6 | MathConstraint/bibd | CC-BY-4.0 | [
"np_search"
] | A balanced incomplete block design BIBD(49, 7, 1) is a collection of b = 56 blocks, each a set of 7 distinct points from {0, 1, ..., 48}, such that every pair of distinct points is contained in exactly 1 of the blocks (consequently every point lies in exactly r = 8 blocks). The same block may appear more than once.
Co... | {"v": 49, "k": 7, "lambda": 1, "b": 56, "family": "mc_bibd", "subset": "construct"} | null | null | null | {"blocks": [[0, 7, 14, 21, 28, 35, 42], [1, 8, 15, 22, 29, 36, 43], [2, 9, 16, 23, 30, 37, 44], [3, 10, 17, 24, 31, 38, 45], [4, 11, 18, 25, 32, 39, 46], [5, 12, 19, 26, 33, 40, 47], [6, 13, 20, 27, 34, 41, 48], [0, 8, 16, 24, 32, 40, 48], [1, 9, 17, 25, 33, 41, 42], [2, 10, 18, 26, 34, 35, 43], [3, 11, 19, 27, 28, 36,... | 1 |
construct-mc-bibd-l6-s3 | construct | mc_bibd | bibd | combinatorics | competition | 6 | MathConstraint/bibd | CC-BY-4.0 | [
"np_search"
] | A balanced incomplete block design BIBD(43, 21, 10) is a collection of b = 43 blocks, each a set of 21 distinct points from {0, 1, ..., 42}, such that every pair of distinct points is contained in exactly 10 of the blocks (consequently every point lies in exactly r = 21 blocks). The same block may appear more than once... | {"v": 43, "k": 21, "lambda": 10, "b": 43, "family": "mc_bibd", "subset": "construct"} | null | null | null | {"blocks": [[1, 4, 6, 9, 10, 11, 13, 14, 15, 16, 17, 21, 23, 24, 25, 31, 35, 36, 38, 40, 41], [2, 5, 7, 10, 11, 12, 14, 15, 16, 17, 18, 22, 24, 25, 26, 32, 36, 37, 39, 41, 42], [0, 3, 6, 8, 11, 12, 13, 15, 16, 17, 18, 19, 23, 25, 26, 27, 33, 37, 38, 40, 42], [0, 1, 4, 7, 9, 12, 13, 14, 16, 17, 18, 19, 20, 24, 26, 27, 2... | 1 |
construct-mc-costas-array-l1-s0 | construct | mc_costas_array | costas_array | combinatorics | competition | 1 | MathConstraint/costas_array | CC-BY-4.0 | [
"np_search"
] | A Costas array of order 8 is a 8x8 grid with exactly one mark in every row and every column such that the displacement vectors between pairs of marks are all distinct. Encode it as a permutation x[0..7] of 0..7, where x[c] is the row of the mark in column c; the condition is that the vectors (j - i, x[j] - x[i]) over a... | {"n": 8, "fixed": [], "family": "mc_costas_array", "subset": "construct"} | null | null | null | {"x": [4, 7, 3, 2, 0, 5, 6, 1]} | 1 |
construct-mc-costas-array-l1-s1 | construct | mc_costas_array | costas_array | combinatorics | competition | 1 | MathConstraint/costas_array | CC-BY-4.0 | [
"np_search"
] | A Costas array of order 5 is a 5x5 grid with exactly one mark in every row and every column such that the displacement vectors between pairs of marks are all distinct. Encode it as a permutation x[0..4] of 0..4, where x[c] is the row of the mark in column c; the condition is that the vectors (j - i, x[j] - x[i]) over a... | {"n": 5, "fixed": [["x", 2, 3]], "family": "mc_costas_array", "subset": "construct"} | null | null | null | {"x": [0, 2, 3, 1, 4]} | 1 |
construct-mc-costas-array-l1-s2 | construct | mc_costas_array | costas_array | combinatorics | competition | 1 | MathConstraint/costas_array | CC-BY-4.0 | [
"np_search"
] | A Costas array of order 6 is a 6x6 grid with exactly one mark in every row and every column such that the displacement vectors between pairs of marks are all distinct. Encode it as a permutation x[0..5] of 0..5, where x[c] is the row of the mark in column c; the condition is that the vectors (j - i, x[j] - x[i]) over a... | {"n": 6, "fixed": [], "family": "mc_costas_array", "subset": "construct"} | null | null | null | {"x": [0, 1, 4, 3, 5, 2]} | 1 |
construct-mc-costas-array-l1-s3 | construct | mc_costas_array | costas_array | combinatorics | competition | 1 | MathConstraint/costas_array | CC-BY-4.0 | [
"np_search"
] | A Costas array of order 5 is a 5x5 grid with exactly one mark in every row and every column such that the displacement vectors between pairs of marks are all distinct. Encode it as a permutation x[0..4] of 0..4, where x[c] is the row of the mark in column c; the condition is that the vectors (j - i, x[j] - x[i]) over a... | {"n": 5, "fixed": [], "family": "mc_costas_array", "subset": "construct"} | null | null | null | {"x": [0, 2, 3, 1, 4]} | 1 |
construct-mc-costas-array-l1-s4 | construct | mc_costas_array | costas_array | combinatorics | competition | 1 | MathConstraint/costas_array | CC-BY-4.0 | [
"np_search"
] | A Costas array of order 7 is a 7x7 grid with exactly one mark in every row and every column such that the displacement vectors between pairs of marks are all distinct. Encode it as a permutation x[0..6] of 0..6, where x[c] is the row of the mark in column c; the condition is that the vectors (j - i, x[j] - x[i]) over a... | {"n": 7, "fixed": [["x", 1, 1]], "family": "mc_costas_array", "subset": "construct"} | null | null | null | {"x": [0, 1, 6, 4, 3, 5, 2]} | 1 |
construct-mc-costas-array-l1-s5 | construct | mc_costas_array | costas_array | combinatorics | competition | 1 | MathConstraint/costas_array | CC-BY-4.0 | [
"np_search"
] | A Costas array of order 7 is a 7x7 grid with exactly one mark in every row and every column such that the displacement vectors between pairs of marks are all distinct. Encode it as a permutation x[0..6] of 0..6, where x[c] is the row of the mark in column c; the condition is that the vectors (j - i, x[j] - x[i]) over a... | {"n": 7, "fixed": [], "family": "mc_costas_array", "subset": "construct"} | null | null | null | {"x": [0, 1, 6, 4, 3, 5, 2]} | 1 |
construct-mc-costas-array-l2-s0 | construct | mc_costas_array | costas_array | combinatorics | competition | 2 | MathConstraint/costas_array | CC-BY-4.0 | [
"np_search"
] | A Costas array of order 11 is a 11x11 grid with exactly one mark in every row and every column such that the displacement vectors between pairs of marks are all distinct. Encode it as a permutation x[0..10] of 0..10, where x[c] is the row of the mark in column c; the condition is that the vectors (j - i, x[j] - x[i]) o... | {"n": 11, "fixed": [], "family": "mc_costas_array", "subset": "construct"} | null | null | null | {"x": [9, 3, 8, 4, 1, 0, 7, 2, 5, 6, 10]} | 1 |
construct-mc-costas-array-l2-s1 | construct | mc_costas_array | costas_array | combinatorics | competition | 2 | MathConstraint/costas_array | CC-BY-4.0 | [
"np_search"
] | A Costas array of order 10 is a 10x10 grid with exactly one mark in every row and every column such that the displacement vectors between pairs of marks are all distinct. Encode it as a permutation x[0..9] of 0..9, where x[c] is the row of the mark in column c; the condition is that the vectors (j - i, x[j] - x[i]) ove... | {"n": 10, "fixed": [], "family": "mc_costas_array", "subset": "construct"} | null | null | null | {"x": [8, 5, 6, 0, 2, 1, 4, 9, 7, 3]} | 1 |
construct-mc-costas-array-l2-s2 | construct | mc_costas_array | costas_array | combinatorics | competition | 2 | MathConstraint/costas_array | CC-BY-4.0 | [
"np_search"
] | A Costas array of order 9 is a 9x9 grid with exactly one mark in every row and every column such that the displacement vectors between pairs of marks are all distinct. Encode it as a permutation x[0..8] of 0..8, where x[c] is the row of the mark in column c; the condition is that the vectors (j - i, x[j] - x[i]) over a... | {"n": 9, "fixed": [], "family": "mc_costas_array", "subset": "construct"} | null | null | null | {"x": [1, 7, 3, 6, 8, 2, 0, 5, 4]} | 1 |
construct-mc-costas-array-l3-s0 | construct | mc_costas_array | costas_array | combinatorics | competition | 3 | MathConstraint/costas_array | CC-BY-4.0 | [
"np_search"
] | A Costas array of order 13 is a 13x13 grid with exactly one mark in every row and every column such that the displacement vectors between pairs of marks are all distinct. Encode it as a permutation x[0..12] of 0..12, where x[c] is the row of the mark in column c; the condition is that the vectors (j - i, x[j] - x[i]) o... | {"n": 13, "fixed": [["x", 4, 3], ["x", 9, 1]], "family": "mc_costas_array", "subset": "construct"} | null | null | null | {"x": [8, 7, 5, 10, 3, 0, 4, 12, 6, 1, 2, 9, 11]} | 1 |
construct-mc-costas-array-l3-s1 | construct | mc_costas_array | costas_array | combinatorics | competition | 3 | MathConstraint/costas_array | CC-BY-4.0 | [
"np_search"
] | A Costas array of order 15 is a 15x15 grid with exactly one mark in every row and every column such that the displacement vectors between pairs of marks are all distinct. Encode it as a permutation x[0..14] of 0..14, where x[c] is the row of the mark in column c; the condition is that the vectors (j - i, x[j] - x[i]) o... | {"n": 15, "fixed": [], "family": "mc_costas_array", "subset": "construct"} | null | null | null | {"x": [6, 12, 2, 3, 10, 14, 8, 11, 13, 0, 5, 1, 9, 7, 4]} | 1 |
construct-mc-costas-array-l3-s2 | construct | mc_costas_array | costas_array | combinatorics | competition | 3 | MathConstraint/costas_array | CC-BY-4.0 | [
"np_search"
] | A Costas array of order 13 is a 13x13 grid with exactly one mark in every row and every column such that the displacement vectors between pairs of marks are all distinct. Encode it as a permutation x[0..12] of 0..12, where x[c] is the row of the mark in column c; the condition is that the vectors (j - i, x[j] - x[i]) o... | {"n": 13, "fixed": [], "family": "mc_costas_array", "subset": "construct"} | null | null | null | {"x": [8, 7, 5, 10, 3, 0, 4, 12, 6, 1, 2, 9, 11]} | 1 |
construct-mc-costas-array-l3-s3 | construct | mc_costas_array | costas_array | combinatorics | competition | 3 | MathConstraint/costas_array | CC-BY-4.0 | [
"np_search"
] | A Costas array of order 12 is a 12x12 grid with exactly one mark in every row and every column such that the displacement vectors between pairs of marks are all distinct. Encode it as a permutation x[0..11] of 0..11, where x[c] is the row of the mark in column c; the condition is that the vectors (j - i, x[j] - x[i]) o... | {"n": 12, "fixed": [["x", 3, 8], ["x", 8, 2]], "family": "mc_costas_array", "subset": "construct"} | null | null | null | {"x": [6, 1, 10, 8, 9, 5, 11, 3, 2, 4, 7, 0]} | 1 |
construct-mc-costas-array-l3-s4 | construct | mc_costas_array | costas_array | combinatorics | competition | 3 | MathConstraint/costas_array | CC-BY-4.0 | [
"np_search"
] | A Costas array of order 12 is a 12x12 grid with exactly one mark in every row and every column such that the displacement vectors between pairs of marks are all distinct. Encode it as a permutation x[0..11] of 0..11, where x[c] is the row of the mark in column c; the condition is that the vectors (j - i, x[j] - x[i]) o... | {"n": 12, "fixed": [], "family": "mc_costas_array", "subset": "construct"} | null | null | null | {"x": [0, 10, 3, 4, 2, 6, 11, 1, 8, 7, 9, 5]} | 1 |
construct-mc-costas-array-l4-s0 | construct | mc_costas_array | costas_array | combinatorics | competition | 4 | MathConstraint/costas_array | CC-BY-4.0 | [
"np_search"
] | A Costas array of order 16 is a 16x16 grid with exactly one mark in every row and every column such that the displacement vectors between pairs of marks are all distinct. Encode it as a permutation x[0..15] of 0..15, where x[c] is the row of the mark in column c; the condition is that the vectors (j - i, x[j] - x[i]) o... | {"n": 16, "fixed": [], "family": "mc_costas_array", "subset": "construct"} | null | null | null | {"x": [14, 8, 7, 10, 2, 4, 11, 12, 3, 15, 0, 6, 1, 5, 13, 9]} | 1 |
construct-mc-costas-array-l4-s1 | construct | mc_costas_array | costas_array | combinatorics | competition | 4 | MathConstraint/costas_array | CC-BY-4.0 | [
"np_search"
] | A Costas array of order 17 is a 17x17 grid with exactly one mark in every row and every column such that the displacement vectors between pairs of marks are all distinct. Encode it as a permutation x[0..16] of 0..16, where x[c] is the row of the mark in column c; the condition is that the vectors (j - i, x[j] - x[i]) o... | {"n": 17, "fixed": [], "family": "mc_costas_array", "subset": "construct"} | null | null | null | {"x": [5, 4, 2, 15, 1, 11, 6, 12, 13, 10, 0, 14, 8, 16, 3, 7, 9]} | 1 |
construct-mc-costas-array-l4-s2 | construct | mc_costas_array | costas_array | combinatorics | competition | 4 | MathConstraint/costas_array | CC-BY-4.0 | [
"np_search"
] | A Costas array of order 18 is a 18x18 grid with exactly one mark in every row and every column such that the displacement vectors between pairs of marks are all distinct. Encode it as a permutation x[0..17] of 0..17, where x[c] is the row of the mark in column c; the condition is that the vectors (j - i, x[j] - x[i]) o... | {"n": 18, "fixed": [], "family": "mc_costas_array", "subset": "construct"} | null | null | null | {"x": [0, 13, 5, 7, 16, 9, 6, 2, 3, 17, 4, 12, 10, 1, 8, 11, 15, 14]} | 1 |
construct-mc-costas-array-l5-s0 | construct | mc_costas_array | costas_array | combinatorics | competition | 5 | MathConstraint/costas_array | CC-BY-4.0 | [
"np_search"
] | A Costas array of order 21 is a 21x21 grid with exactly one mark in every row and every column such that the displacement vectors between pairs of marks are all distinct. Encode it as a permutation x[0..20] of 0..20, where x[c] is the row of the mark in column c; the condition is that the vectors (j - i, x[j] - x[i]) o... | {"n": 21, "fixed": [], "family": "mc_costas_array", "subset": "construct"} | null | null | null | {"x": [12, 10, 5, 4, 13, 1, 17, 11, 19, 16, 20, 7, 9, 14, 15, 6, 18, 2, 8, 0, 3]} | 1 |
construct-mc-costas-array-l5-s1 | construct | mc_costas_array | costas_array | combinatorics | competition | 5 | MathConstraint/costas_array | CC-BY-4.0 | [
"np_search"
] | A Costas array of order 22 is a 22x22 grid with exactly one mark in every row and every column such that the displacement vectors between pairs of marks are all distinct. Encode it as a permutation x[0..21] of 0..21, where x[c] is the row of the mark in column c; the condition is that the vectors (j - i, x[j] - x[i]) o... | {"n": 22, "fixed": [], "family": "mc_costas_array", "subset": "construct"} | null | null | null | {"x": [0, 14, 17, 16, 1, 6, 12, 10, 3, 13, 2, 21, 7, 4, 5, 20, 15, 9, 11, 18, 8, 19]} | 1 |
construct-mc-costas-array-l6-s0 | construct | mc_costas_array | costas_array | combinatorics | competition | 6 | MathConstraint/costas_array | CC-BY-4.0 | [
"np_search"
] | A Costas array of order 28 is a 28x28 grid with exactly one mark in every row and every column such that the displacement vectors between pairs of marks are all distinct. Encode it as a permutation x[0..27] of 0..27, where x[c] is the row of the mark in column c; the condition is that the vectors (j - i, x[j] - x[i]) o... | {"n": 28, "fixed": [], "family": "mc_costas_array", "subset": "construct"} | null | null | null | {"x": [0, 1, 3, 7, 15, 2, 5, 11, 23, 18, 8, 17, 6, 13, 27, 26, 24, 20, 12, 25, 22, 16, 4, 9, 19, 10, 21, 14]} | 1 |
construct-mc-costas-array-l6-s1 | construct | mc_costas_array | costas_array | combinatorics | competition | 6 | MathConstraint/costas_array | CC-BY-4.0 | [
"np_search"
] | A Costas array of order 30 is a 30x30 grid with exactly one mark in every row and every column such that the displacement vectors between pairs of marks are all distinct. Encode it as a permutation x[0..29] of 0..29, where x[c] is the row of the mark in column c; the condition is that the vectors (j - i, x[j] - x[i]) o... | {"n": 30, "fixed": [], "family": "mc_costas_array", "subset": "construct"} | null | null | null | {"x": [0, 23, 17, 28, 13, 25, 3, 2, 9, 22, 24, 10, 15, 11, 8, 29, 6, 12, 1, 16, 4, 26, 27, 20, 7, 5, 19, 14, 18, 21]} | 1 |
construct-mc-costas-array-l6-s2 | construct | mc_costas_array | costas_array | combinatorics | competition | 6 | MathConstraint/costas_array | CC-BY-4.0 | [
"np_search"
] | A Costas array of order 29 is a 29x29 grid with exactly one mark in every row and every column such that the displacement vectors between pairs of marks are all distinct. Encode it as a permutation x[0..28] of 0..28, where x[c] is the row of the mark in column c; the condition is that the vectors (j - i, x[j] - x[i]) o... | {"n": 29, "fixed": [], "family": "mc_costas_array", "subset": "construct"} | null | null | null | {"x": [19, 5, 21, 16, 4, 0, 9, 12, 13, 3, 10, 2, 20, 26, 28, 8, 22, 6, 11, 23, 27, 18, 15, 14, 24, 17, 25, 7, 1]} | 1 |
construct-mc-costas-array-l6-s3 | construct | mc_costas_array | costas_array | combinatorics | competition | 6 | MathConstraint/costas_array | CC-BY-4.0 | [
"np_search"
] | A Costas array of order 27 is a 27x27 grid with exactly one mark in every row and every column such that the displacement vectors between pairs of marks are all distinct. Encode it as a permutation x[0..26] of 0..26, where x[c] is the row of the mark in column c; the condition is that the vectors (j - i, x[j] - x[i]) o... | {"n": 27, "fixed": [], "family": "mc_costas_array", "subset": "construct"} | null | null | null | {"x": [12, 20, 16, 18, 17, 3, 10, 21, 1, 11, 6, 23, 0, 26, 13, 5, 9, 7, 8, 22, 15, 4, 24, 14, 19, 2, 25]} | 1 |
construct-mc-debruijn-l1-s0 | construct | mc_debruijn | de_bruijn_sequence | combinatorics | competition | 1 | MathConstraint/debruijn | CC-BY-4.0 | [
"agentic_trivial"
] | A De Bruijn sequence B(2, 4) is a cyclic sequence x[0..15] of length 2^4 = 16 over the alphabet {0, ..., 1} in which every word of length 4 over that alphabet appears exactly once as a window x[i], x[i+1], ..., x[i+3] (indices taken modulo 16).
Find a De Bruijn sequence B(2, 4).
Answer format: {"seq": [x_0, x_1, ...,... | {"b": 2, "n": 4, "family": "mc_debruijn", "subset": "construct"} | null | null | null | {"seq": [0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 1, 1, 1, 1]} | 1 |
construct-mc-debruijn-l1-s1 | construct | mc_debruijn | de_bruijn_sequence | combinatorics | competition | 1 | MathConstraint/debruijn | CC-BY-4.0 | [
"agentic_trivial"
] | A De Bruijn sequence B(2, 3) is a cyclic sequence x[0..7] of length 2^3 = 8 over the alphabet {0, ..., 1} in which every word of length 3 over that alphabet appears exactly once as a window x[i], x[i+1], ..., x[i+2] (indices taken modulo 8).
Find a De Bruijn sequence B(2, 3).
Answer format: {"seq": [x_0, x_1, ..., x_... | {"b": 2, "n": 3, "family": "mc_debruijn", "subset": "construct"} | null | null | null | {"seq": [0, 0, 0, 1, 0, 1, 1, 1]} | 1 |
construct-mc-debruijn-l1-s2 | construct | mc_debruijn | de_bruijn_sequence | combinatorics | competition | 1 | MathConstraint/debruijn | CC-BY-4.0 | [
"agentic_trivial"
] | A De Bruijn sequence B(3, 2) is a cyclic sequence x[0..8] of length 3^2 = 9 over the alphabet {0, ..., 2} in which every word of length 2 over that alphabet appears exactly once as a window x[i], x[i+1], ..., x[i+1] (indices taken modulo 9).
Find a De Bruijn sequence B(3, 2).
Answer format: {"seq": [x_0, x_1, ..., x_... | {"b": 3, "n": 2, "family": "mc_debruijn", "subset": "construct"} | null | null | null | {"seq": [0, 0, 1, 0, 2, 1, 1, 2, 2]} | 1 |
construct-mc-debruijn-l2-s0 | construct | mc_debruijn | de_bruijn_sequence | combinatorics | competition | 2 | MathConstraint/debruijn | CC-BY-4.0 | [
"agentic_trivial"
] | A De Bruijn sequence B(2, 5) is a cyclic sequence x[0..31] of length 2^5 = 32 over the alphabet {0, ..., 1} in which every word of length 5 over that alphabet appears exactly once as a window x[i], x[i+1], ..., x[i+4] (indices taken modulo 32).
Find a De Bruijn sequence B(2, 5).
Answer format: {"seq": [x_0, x_1, ...,... | {"b": 2, "n": 5, "family": "mc_debruijn", "subset": "construct"} | null | null | null | {"seq": [0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0, 1, 1, 0, 1, 1, 1, 1, 1]} | 1 |
construct-mc-debruijn-l2-s1 | construct | mc_debruijn | de_bruijn_sequence | combinatorics | competition | 2 | MathConstraint/debruijn | CC-BY-4.0 | [
"agentic_trivial"
] | A De Bruijn sequence B(3, 3) is a cyclic sequence x[0..26] of length 3^3 = 27 over the alphabet {0, ..., 2} in which every word of length 3 over that alphabet appears exactly once as a window x[i], x[i+1], ..., x[i+2] (indices taken modulo 27).
Find a De Bruijn sequence B(3, 3).
Answer format: {"seq": [x_0, x_1, ...,... | {"b": 3, "n": 3, "family": "mc_debruijn", "subset": "construct"} | null | null | null | {"seq": [0, 0, 0, 1, 0, 0, 2, 0, 1, 1, 0, 1, 2, 0, 2, 1, 0, 2, 2, 1, 1, 1, 2, 1, 2, 2, 2]} | 1 |
construct-mc-debruijn-l2-s2 | construct | mc_debruijn | de_bruijn_sequence | combinatorics | competition | 2 | MathConstraint/debruijn | CC-BY-4.0 | [
"agentic_trivial"
] | A De Bruijn sequence B(4, 2) is a cyclic sequence x[0..15] of length 4^2 = 16 over the alphabet {0, ..., 3} in which every word of length 2 over that alphabet appears exactly once as a window x[i], x[i+1], ..., x[i+1] (indices taken modulo 16).
Find a De Bruijn sequence B(4, 2).
Answer format: {"seq": [x_0, x_1, ...,... | {"b": 4, "n": 2, "family": "mc_debruijn", "subset": "construct"} | null | null | null | {"seq": [0, 0, 1, 0, 2, 0, 3, 1, 1, 2, 1, 3, 2, 2, 3, 3]} | 1 |
construct-mc-debruijn-l3-s0 | construct | mc_debruijn | de_bruijn_sequence | combinatorics | competition | 3 | MathConstraint/debruijn | CC-BY-4.0 | [
"agentic_trivial"
] | A De Bruijn sequence B(4, 3) is a cyclic sequence x[0..63] of length 4^3 = 64 over the alphabet {0, ..., 3} in which every word of length 3 over that alphabet appears exactly once as a window x[i], x[i+1], ..., x[i+2] (indices taken modulo 64).
Find a De Bruijn sequence B(4, 3).
Answer format: {"seq": [x_0, x_1, ...,... | {"b": 4, "n": 3, "family": "mc_debruijn", "subset": "construct"} | null | null | null | {"seq": [0, 0, 0, 1, 0, 0, 2, 0, 0, 3, 0, 1, 1, 0, 1, 2, 0, 1, 3, 0, 2, 1, 0, 2, 2, 0, 2, 3, 0, 3, 1, 0, 3, 2, 0, 3, 3, 1, 1, 1, 2, 1, 1, 3, 1, 2, 2, 1, 2, 3, 1, 3, 2, 1, 3, 3, 2, 2, 2, 3, 2, 3, 3, 3]} | 1 |
construct-mc-debruijn-l3-s1 | construct | mc_debruijn | de_bruijn_sequence | combinatorics | competition | 3 | MathConstraint/debruijn | CC-BY-4.0 | [
"agentic_trivial"
] | A De Bruijn sequence B(5, 2) is a cyclic sequence x[0..24] of length 5^2 = 25 over the alphabet {0, ..., 4} in which every word of length 2 over that alphabet appears exactly once as a window x[i], x[i+1], ..., x[i+1] (indices taken modulo 25).
Find a De Bruijn sequence B(5, 2).
Answer format: {"seq": [x_0, x_1, ...,... | {"b": 5, "n": 2, "family": "mc_debruijn", "subset": "construct"} | null | null | null | {"seq": [0, 0, 1, 0, 2, 0, 3, 0, 4, 1, 1, 2, 1, 3, 1, 4, 2, 2, 3, 2, 4, 3, 3, 4, 4]} | 1 |
construct-mc-debruijn-l3-s2 | construct | mc_debruijn | de_bruijn_sequence | combinatorics | competition | 3 | MathConstraint/debruijn | CC-BY-4.0 | [
"agentic_trivial"
] | A De Bruijn sequence B(3, 4) is a cyclic sequence x[0..80] of length 3^4 = 81 over the alphabet {0, ..., 2} in which every word of length 4 over that alphabet appears exactly once as a window x[i], x[i+1], ..., x[i+3] (indices taken modulo 81).
Find a De Bruijn sequence B(3, 4).
Answer format: {"seq": [x_0, x_1, ...,... | {"b": 3, "n": 4, "family": "mc_debruijn", "subset": "construct"} | null | null | null | {"seq": [0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 1, 1, 0, 0, 1, 2, 0, 0, 2, 1, 0, 0, 2, 2, 0, 1, 0, 1, 0, 2, 0, 1, 1, 1, 0, 1, 1, 2, 0, 1, 2, 1, 0, 1, 2, 2, 0, 2, 0, 2, 1, 1, 0, 2, 1, 2, 0, 2, 2, 1, 0, 2, 2, 2, 1, 1, 1, 1, 2, 1, 1, 2, 2, 1, 2, 1, 2, 2, 2, 2]} | 1 |
construct-mc-debruijn-l3-s3 | construct | mc_debruijn | de_bruijn_sequence | combinatorics | competition | 3 | MathConstraint/debruijn | CC-BY-4.0 | [
"agentic_trivial"
] | A De Bruijn sequence B(2, 7) is a cyclic sequence x[0..127] of length 2^7 = 128 over the alphabet {0, ..., 1} in which every word of length 7 over that alphabet appears exactly once as a window x[i], x[i+1], ..., x[i+6] (indices taken modulo 128).
Find a De Bruijn sequence B(2, 7).
Answer format: {"seq": [x_0, x_1, .... | {"b": 2, "n": 7, "family": "mc_debruijn", "subset": "construct"} | null | null | null | {"seq": [0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 1, 1, 1, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 1, 1, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 1, 1, 0, 1, 0, 1, 0,... | 1 |
construct-mc-debruijn-l4-s0 | construct | mc_debruijn | de_bruijn_sequence | combinatorics | competition | 4 | MathConstraint/debruijn | CC-BY-4.0 | [
"agentic_trivial"
] | A De Bruijn sequence B(2, 9) is a cyclic sequence x[0..511] of length 2^9 = 512 over the alphabet {0, ..., 1} in which every word of length 9 over that alphabet appears exactly once as a window x[i], x[i+1], ..., x[i+8] (indices taken modulo 512).
Find a De Bruijn sequence B(2, 9).
Answer format: {"seq": [x_0, x_1, .... | {"b": 2, "n": 9, "family": "mc_debruijn", "subset": "construct"} | null | null | null | {"seq": [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0,... | 1 |
construct-mc-debruijn-l4-s1 | construct | mc_debruijn | de_bruijn_sequence | combinatorics | competition | 4 | MathConstraint/debruijn | CC-BY-4.0 | [
"agentic_trivial"
] | A De Bruijn sequence B(3, 5) is a cyclic sequence x[0..242] of length 3^5 = 243 over the alphabet {0, ..., 2} in which every word of length 5 over that alphabet appears exactly once as a window x[i], x[i+1], ..., x[i+4] (indices taken modulo 243).
Find a De Bruijn sequence B(3, 5).
Answer format: {"seq": [x_0, x_1, .... | {"b": 3, "n": 5, "family": "mc_debruijn", "subset": "construct"} | null | null | null | {"seq": [0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 0, 0, 0, 1, 1, 0, 0, 0, 1, 2, 0, 0, 0, 2, 1, 0, 0, 0, 2, 2, 0, 0, 1, 0, 1, 0, 0, 1, 0, 2, 0, 0, 1, 1, 1, 0, 0, 1, 1, 2, 0, 0, 1, 2, 1, 0, 0, 1, 2, 2, 0, 0, 2, 0, 1, 0, 0, 2, 0, 2, 0, 0, 2, 1, 1, 0, 0, 2, 1, 2, 0, 0, 2, 2, 1, 0, 0, 2, 2, 2, 0, 1, 0, 1, 1, 0, 1, 0, 1, 2, 0, 1, 0,... | 1 |
construct-mc-debruijn-l4-s2 | construct | mc_debruijn | de_bruijn_sequence | combinatorics | competition | 4 | MathConstraint/debruijn | CC-BY-4.0 | [
"agentic_trivial"
] | A De Bruijn sequence B(4, 4) is a cyclic sequence x[0..255] of length 4^4 = 256 over the alphabet {0, ..., 3} in which every word of length 4 over that alphabet appears exactly once as a window x[i], x[i+1], ..., x[i+3] (indices taken modulo 256).
Find a De Bruijn sequence B(4, 4).
Answer format: {"seq": [x_0, x_1, .... | {"b": 4, "n": 4, "family": "mc_debruijn", "subset": "construct"} | null | null | null | {"seq": [0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 0, 3, 0, 0, 1, 1, 0, 0, 1, 2, 0, 0, 1, 3, 0, 0, 2, 1, 0, 0, 2, 2, 0, 0, 2, 3, 0, 0, 3, 1, 0, 0, 3, 2, 0, 0, 3, 3, 0, 1, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 1, 1, 0, 1, 1, 2, 0, 1, 1, 3, 0, 1, 2, 1, 0, 1, 2, 2, 0, 1, 2, 3, 0, 1, 3, 1, 0, 1, 3, 2, 0, 1, 3, 3, 0, 2, 0, 2, 0, 3, 0, 2, 1,... | 1 |
construct-mc-debruijn-l4-s3 | construct | mc_debruijn | de_bruijn_sequence | combinatorics | competition | 4 | MathConstraint/debruijn | CC-BY-4.0 | [
"agentic_trivial"
] | A De Bruijn sequence B(6, 3) is a cyclic sequence x[0..215] of length 6^3 = 216 over the alphabet {0, ..., 5} in which every word of length 3 over that alphabet appears exactly once as a window x[i], x[i+1], ..., x[i+2] (indices taken modulo 216).
Find a De Bruijn sequence B(6, 3).
Answer format: {"seq": [x_0, x_1, .... | {"b": 6, "n": 3, "family": "mc_debruijn", "subset": "construct"} | null | null | null | {"seq": [0, 0, 0, 1, 0, 0, 2, 0, 0, 3, 0, 0, 4, 0, 0, 5, 0, 1, 1, 0, 1, 2, 0, 1, 3, 0, 1, 4, 0, 1, 5, 0, 2, 1, 0, 2, 2, 0, 2, 3, 0, 2, 4, 0, 2, 5, 0, 3, 1, 0, 3, 2, 0, 3, 3, 0, 3, 4, 0, 3, 5, 0, 4, 1, 0, 4, 2, 0, 4, 3, 0, 4, 4, 0, 4, 5, 0, 5, 1, 0, 5, 2, 0, 5, 3, 0, 5, 4, 0, 5, 5, 1, 1, 1, 2, 1, 1, 3, 1, 1, 4, 1, 1, 5,... | 1 |
construct-mc-debruijn-l5-s0 | construct | mc_debruijn | de_bruijn_sequence | combinatorics | competition | 5 | MathConstraint/debruijn | CC-BY-4.0 | [
"agentic_trivial"
] | A De Bruijn sequence B(3, 6) is a cyclic sequence x[0..728] of length 3^6 = 729 over the alphabet {0, ..., 2} in which every word of length 6 over that alphabet appears exactly once as a window x[i], x[i+1], ..., x[i+5] (indices taken modulo 729).
Find a De Bruijn sequence B(3, 6).
Answer format: {"seq": [x_0, x_1, .... | {"b": 3, "n": 6, "family": "mc_debruijn", "subset": "construct"} | null | null | null | {"seq": [0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 2, 0, 0, 0, 0, 2, 1, 0, 0, 0, 0, 2, 2, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 2, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 2, 0, 0, 0, 1, 2, 1, 0, 0, 0, 1, 2, 2, 0, 0, 0, 2, 0, 1, 0, 0, 0, 2, 0, 2, 0, 0, 0, 2, 1, 1, 0, 0, 0, 2, 1, 2, 0, 0, 0, 2, 2, 1, 0,... | 1 |
construct-mc-debruijn-l5-s1 | construct | mc_debruijn | de_bruijn_sequence | combinatorics | competition | 5 | MathConstraint/debruijn | CC-BY-4.0 | [
"agentic_trivial"
] | A De Bruijn sequence B(2, 11) is a cyclic sequence x[0..2047] of length 2^11 = 2048 over the alphabet {0, ..., 1} in which every word of length 11 over that alphabet appears exactly once as a window x[i], x[i+1], ..., x[i+10] (indices taken modulo 2048).
Find a De Bruijn sequence B(2, 11).
Answer format: {"seq": [x_0... | {"b": 2, "n": 11, "family": "mc_debruijn", "subset": "construct"} | null | null | null | {"seq": [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0,... | 1 |
construct-mc-debruijn-l5-s2 | construct | mc_debruijn | de_bruijn_sequence | combinatorics | competition | 5 | MathConstraint/debruijn | CC-BY-4.0 | [
"agentic_trivial"
] | A De Bruijn sequence B(4, 5) is a cyclic sequence x[0..1023] of length 4^5 = 1024 over the alphabet {0, ..., 3} in which every word of length 5 over that alphabet appears exactly once as a window x[i], x[i+1], ..., x[i+4] (indices taken modulo 1024).
Find a De Bruijn sequence B(4, 5).
Answer format: {"seq": [x_0, x_1... | {"b": 4, "n": 5, "family": "mc_debruijn", "subset": "construct"} | null | null | null | {"seq": [0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 0, 0, 0, 0, 3, 0, 0, 0, 1, 1, 0, 0, 0, 1, 2, 0, 0, 0, 1, 3, 0, 0, 0, 2, 1, 0, 0, 0, 2, 2, 0, 0, 0, 2, 3, 0, 0, 0, 3, 1, 0, 0, 0, 3, 2, 0, 0, 0, 3, 3, 0, 0, 1, 0, 1, 0, 0, 1, 0, 2, 0, 0, 1, 0, 3, 0, 0, 1, 1, 1, 0, 0, 1, 1, 2, 0, 0, 1, 1, 3, 0, 0, 1, 2, 1, 0, 0, 1, 2, 2, 0, 0, 1,... | 1 |
construct-mc-debruijn-l5-s3 | construct | mc_debruijn | de_bruijn_sequence | combinatorics | competition | 5 | MathConstraint/debruijn | CC-BY-4.0 | [
"agentic_trivial"
] | A De Bruijn sequence B(5, 4) is a cyclic sequence x[0..624] of length 5^4 = 625 over the alphabet {0, ..., 4} in which every word of length 4 over that alphabet appears exactly once as a window x[i], x[i+1], ..., x[i+3] (indices taken modulo 625).
Find a De Bruijn sequence B(5, 4).
Answer format: {"seq": [x_0, x_1, .... | {"b": 5, "n": 4, "family": "mc_debruijn", "subset": "construct"} | null | null | null | {"seq": [0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 0, 3, 0, 0, 0, 4, 0, 0, 1, 1, 0, 0, 1, 2, 0, 0, 1, 3, 0, 0, 1, 4, 0, 0, 2, 1, 0, 0, 2, 2, 0, 0, 2, 3, 0, 0, 2, 4, 0, 0, 3, 1, 0, 0, 3, 2, 0, 0, 3, 3, 0, 0, 3, 4, 0, 0, 4, 1, 0, 0, 4, 2, 0, 0, 4, 3, 0, 0, 4, 4, 0, 1, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 4, 0, 1, 1, 1, 0, 1, 1, 2, 0,... | 1 |
construct-mc-debruijn-l6-s0 | construct | mc_debruijn | de_bruijn_sequence | combinatorics | competition | 6 | MathConstraint/debruijn | CC-BY-4.0 | [
"agentic_trivial"
] | A De Bruijn sequence B(7, 4) is a cyclic sequence x[0..2400] of length 7^4 = 2401 over the alphabet {0, ..., 6} in which every word of length 4 over that alphabet appears exactly once as a window x[i], x[i+1], ..., x[i+3] (indices taken modulo 2401).
Find a De Bruijn sequence B(7, 4).
Answer format: {"seq": [x_0, x_1... | {"b": 7, "n": 4, "family": "mc_debruijn", "subset": "construct"} | null | null | null | {"seq": [0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 0, 3, 0, 0, 0, 4, 0, 0, 0, 5, 0, 0, 0, 6, 0, 0, 1, 1, 0, 0, 1, 2, 0, 0, 1, 3, 0, 0, 1, 4, 0, 0, 1, 5, 0, 0, 1, 6, 0, 0, 2, 1, 0, 0, 2, 2, 0, 0, 2, 3, 0, 0, 2, 4, 0, 0, 2, 5, 0, 0, 2, 6, 0, 0, 3, 1, 0, 0, 3, 2, 0, 0, 3, 3, 0, 0, 3, 4, 0, 0, 3, 5, 0, 0, 3, 6, 0, 0, 4, 1, 0, 0, 4,... | 1 |
construct-mc-debruijn-l6-s1 | construct | mc_debruijn | de_bruijn_sequence | combinatorics | competition | 6 | MathConstraint/debruijn | CC-BY-4.0 | [
"agentic_trivial"
] | A De Bruijn sequence B(2, 12) is a cyclic sequence x[0..4095] of length 2^12 = 4096 over the alphabet {0, ..., 1} in which every word of length 12 over that alphabet appears exactly once as a window x[i], x[i+1], ..., x[i+11] (indices taken modulo 4096).
Find a De Bruijn sequence B(2, 12).
Answer format: {"seq": [x_0... | {"b": 2, "n": 12, "family": "mc_debruijn", "subset": "construct"} | null | null | null | {"seq": [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0,... | 1 |
construct-mc-debruijn-l6-s2 | construct | mc_debruijn | de_bruijn_sequence | combinatorics | competition | 6 | MathConstraint/debruijn | CC-BY-4.0 | [
"agentic_trivial"
] | A De Bruijn sequence B(3, 7) is a cyclic sequence x[0..2186] of length 3^7 = 2187 over the alphabet {0, ..., 2} in which every word of length 7 over that alphabet appears exactly once as a window x[i], x[i+1], ..., x[i+6] (indices taken modulo 2187).
Find a De Bruijn sequence B(3, 7).
Answer format: {"seq": [x_0, x_1... | {"b": 3, "n": 7, "family": "mc_debruijn", "subset": "construct"} | null | null | null | {"seq": [0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 2, 0, 0, 0, 0, 0, 2, 1, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 1, 2, 0, 0, 0, 0, 1, 2, 1, 0, 0, 0, 0, 1, 2, 2, 0, 0, 0, 0, 2, 0, 1, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 2,... | 1 |
construct-mc-debruijn-l6-s3 | construct | mc_debruijn | de_bruijn_sequence | combinatorics | competition | 6 | MathConstraint/debruijn | CC-BY-4.0 | [
"agentic_trivial"
] | A De Bruijn sequence B(6, 4) is a cyclic sequence x[0..1295] of length 6^4 = 1296 over the alphabet {0, ..., 5} in which every word of length 4 over that alphabet appears exactly once as a window x[i], x[i+1], ..., x[i+3] (indices taken modulo 1296).
Find a De Bruijn sequence B(6, 4).
Answer format: {"seq": [x_0, x_1... | {"b": 6, "n": 4, "family": "mc_debruijn", "subset": "construct"} | null | null | null | {"seq": [0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 0, 3, 0, 0, 0, 4, 0, 0, 0, 5, 0, 0, 1, 1, 0, 0, 1, 2, 0, 0, 1, 3, 0, 0, 1, 4, 0, 0, 1, 5, 0, 0, 2, 1, 0, 0, 2, 2, 0, 0, 2, 3, 0, 0, 2, 4, 0, 0, 2, 5, 0, 0, 3, 1, 0, 0, 3, 2, 0, 0, 3, 3, 0, 0, 3, 4, 0, 0, 3, 5, 0, 0, 4, 1, 0, 0, 4, 2, 0, 0, 4, 3, 0, 0, 4, 4, 0, 0, 4, 5, 0, 0, 5,... | 1 |
construct-mc-golomb-l1-s0 | construct | mc_golomb | golomb_ruler | combinatorics | competition | 1 | MathConstraint/golomb | CC-BY-4.0 | [
"np_search"
] | A Golomb ruler with 5 marks is a list of integers 0 = a_0 < a_1 < ... < a_4 such that all 10 differences a_j - a_i (i < j) are distinct; its length is a_4.
Find a Golomb ruler with 5 marks and length at most 11.
Answer format: {"marks": [a_0, a_1, ..., a_4]}
Write your final answer as JSON to `/workdir/answer.json`.... | {"n": 5, "max_length": 11, "fixed": [], "family": "mc_golomb", "subset": "construct"} | null | null | null | {"marks": [0, 1, 4, 9, 11]} | 1 |
construct-mc-golomb-l1-s1 | construct | mc_golomb | golomb_ruler | combinatorics | competition | 1 | MathConstraint/golomb | CC-BY-4.0 | [
"np_search"
] | A Golomb ruler with 6 marks is a list of integers 0 = a_0 < a_1 < ... < a_5 such that all 15 differences a_j - a_i (i < j) are distinct; its length is a_5.
Find a Golomb ruler with 6 marks and length at most 17.
Answer format: {"marks": [a_0, a_1, ..., a_5]}
Write your final answer as JSON to `/workdir/answer.json`.... | {"n": 6, "max_length": 17, "fixed": [], "family": "mc_golomb", "subset": "construct"} | null | null | null | {"marks": [0, 1, 4, 10, 12, 17]} | 1 |
construct-mc-golomb-l1-s2 | construct | mc_golomb | golomb_ruler | combinatorics | competition | 1 | MathConstraint/golomb | CC-BY-4.0 | [
"np_search"
] | A Golomb ruler with 7 marks is a list of integers 0 = a_0 < a_1 < ... < a_6 such that all 21 differences a_j - a_i (i < j) are distinct; its length is a_6.
Find a Golomb ruler with 7 marks and length at most 25.
Some values are fixed in advance and your answer must agree with them:
marks[1] = 2
(marks[i] is a_i.)
An... | {"n": 7, "max_length": 25, "fixed": [["marks", 1, 2]], "family": "mc_golomb", "subset": "construct"} | null | null | null | {"marks": [0, 2, 6, 9, 14, 24, 25]} | 1 |
construct-mc-golomb-l1-s3 | construct | mc_golomb | golomb_ruler | combinatorics | competition | 1 | MathConstraint/golomb | CC-BY-4.0 | [
"np_search"
] | A Golomb ruler with 7 marks is a list of integers 0 = a_0 < a_1 < ... < a_6 such that all 21 differences a_j - a_i (i < j) are distinct; its length is a_6.
Find a Golomb ruler with 7 marks and length at most 25.
Answer format: {"marks": [a_0, a_1, ..., a_6]}
Write your final answer as JSON to `/workdir/answer.json`.... | {"n": 7, "max_length": 25, "fixed": [], "family": "mc_golomb", "subset": "construct"} | null | null | null | {"marks": [0, 1, 4, 10, 18, 23, 25]} | 1 |
construct-mc-golomb-l2-s0 | construct | mc_golomb | golomb_ruler | combinatorics | competition | 2 | MathConstraint/golomb | CC-BY-4.0 | [
"np_search"
] | A Golomb ruler with 9 marks is a list of integers 0 = a_0 < a_1 < ... < a_8 such that all 36 differences a_j - a_i (i < j) are distinct; its length is a_8.
Find a Golomb ruler with 9 marks and length at most 44.
Answer format: {"marks": [a_0, a_1, ..., a_8]}
Write your final answer as JSON to `/workdir/answer.json`.... | {"n": 9, "max_length": 44, "fixed": [], "family": "mc_golomb", "subset": "construct"} | null | null | null | {"marks": [0, 1, 5, 12, 25, 27, 35, 41, 44]} | 1 |
construct-mc-golomb-l2-s1 | construct | mc_golomb | golomb_ruler | combinatorics | competition | 2 | MathConstraint/golomb | CC-BY-4.0 | [
"np_search"
] | A Golomb ruler with 8 marks is a list of integers 0 = a_0 < a_1 < ... < a_7 such that all 28 differences a_j - a_i (i < j) are distinct; its length is a_7.
Find a Golomb ruler with 8 marks and length at most 34.
Some values are fixed in advance and your answer must agree with them:
marks[1] = 2
(marks[i] is a_i.)
An... | {"n": 8, "max_length": 34, "fixed": [["marks", 1, 2]], "family": "mc_golomb", "subset": "construct"} | null | null | null | {"marks": [0, 2, 12, 19, 25, 30, 33, 34]} | 1 |
construct-mc-golomb-l2-s2 | construct | mc_golomb | golomb_ruler | combinatorics | competition | 2 | MathConstraint/golomb | CC-BY-4.0 | [
"np_search"
] | A Golomb ruler with 8 marks is a list of integers 0 = a_0 < a_1 < ... < a_7 such that all 28 differences a_j - a_i (i < j) are distinct; its length is a_7.
Find a Golomb ruler with 8 marks and length at most 34.
Answer format: {"marks": [a_0, a_1, ..., a_7]}
Write your final answer as JSON to `/workdir/answer.json`.... | {"n": 8, "max_length": 34, "fixed": [], "family": "mc_golomb", "subset": "construct"} | null | null | null | {"marks": [0, 1, 4, 9, 15, 22, 32, 34]} | 1 |
construct-mc-golomb-l3-s0 | construct | mc_golomb | golomb_ruler | combinatorics | competition | 3 | MathConstraint/golomb | CC-BY-4.0 | [
"np_search"
] | A Golomb ruler with 10 marks is a list of integers 0 = a_0 < a_1 < ... < a_9 such that all 45 differences a_j - a_i (i < j) are distinct; its length is a_9.
Find a Golomb ruler with 10 marks and length at most 55.
Answer format: {"marks": [a_0, a_1, ..., a_9]}
Write your final answer as JSON to `/workdir/answer.json... | {"n": 10, "max_length": 55, "fixed": [], "family": "mc_golomb", "subset": "construct"} | null | null | null | {"marks": [0, 2, 14, 21, 29, 32, 45, 49, 54, 55]} | 1 |
construct-mc-golomb-l3-s1 | construct | mc_golomb | golomb_ruler | combinatorics | competition | 3 | MathConstraint/golomb | CC-BY-4.0 | [
"np_search"
] | A Golomb ruler with 11 marks is a list of integers 0 = a_0 < a_1 < ... < a_10 such that all 55 differences a_j - a_i (i < j) are distinct; its length is a_10.
Find a Golomb ruler with 11 marks and length at most 72.
Answer format: {"marks": [a_0, a_1, ..., a_10]}
Write your final answer as JSON to `/workdir/answer.j... | {"n": 11, "max_length": 72, "fixed": [], "family": "mc_golomb", "subset": "construct"} | null | null | null | {"marks": [0, 3, 14, 16, 20, 41, 48, 53, 63, 71, 72]} | 1 |
construct-mc-golomb-l4-s0 | construct | mc_golomb | golomb_ruler | combinatorics | competition | 4 | MathConstraint/golomb | CC-BY-4.0 | [
"np_search"
] | A Golomb ruler with 13 marks is a list of integers 0 = a_0 < a_1 < ... < a_12 such that all 78 differences a_j - a_i (i < j) are distinct; its length is a_12.
Find a Golomb ruler with 13 marks and length at most 106.
Answer format: {"marks": [a_0, a_1, ..., a_12]}
Write your final answer as JSON to `/workdir/answer.... | {"n": 13, "max_length": 106, "fixed": [], "family": "mc_golomb", "subset": "construct"} | null | null | null | {"marks": [0, 2, 5, 25, 37, 43, 59, 70, 85, 89, 98, 99, 106]} | 1 |
construct-mc-golomb-l4-s1 | construct | mc_golomb | golomb_ruler | combinatorics | competition | 4 | MathConstraint/golomb | CC-BY-4.0 | [
"np_search"
] | A Golomb ruler with 12 marks is a list of integers 0 = a_0 < a_1 < ... < a_11 such that all 66 differences a_j - a_i (i < j) are distinct; its length is a_11.
Find a Golomb ruler with 12 marks and length at most 85.
Answer format: {"marks": [a_0, a_1, ..., a_11]}
Write your final answer as JSON to `/workdir/answer.j... | {"n": 12, "max_length": 85, "fixed": [], "family": "mc_golomb", "subset": "construct"} | null | null | null | {"marks": [0, 2, 6, 24, 29, 40, 43, 55, 68, 75, 76, 85]} | 1 |
construct-mc-golomb-l5-s0 | construct | mc_golomb | golomb_ruler | combinatorics | competition | 5 | MathConstraint/golomb | CC-BY-4.0 | [
"np_search"
] | A Golomb ruler with 15 marks is a list of integers 0 = a_0 < a_1 < ... < a_14 such that all 105 differences a_j - a_i (i < j) are distinct; its length is a_14.
Find a Golomb ruler with 15 marks and length at most 151.
Answer format: {"marks": [a_0, a_1, ..., a_14]}
Write your final answer as JSON to `/workdir/answer... | {"n": 15, "max_length": 151, "fixed": [], "family": "mc_golomb", "subset": "construct"} | null | null | null | {"marks": [0, 4, 20, 30, 57, 59, 62, 76, 100, 111, 123, 136, 144, 145, 151]} | 1 |
construct-mc-golomb-l5-s1 | construct | mc_golomb | golomb_ruler | combinatorics | competition | 5 | MathConstraint/golomb | CC-BY-4.0 | [
"np_search"
] | A Golomb ruler with 14 marks is a list of integers 0 = a_0 < a_1 < ... < a_13 such that all 91 differences a_j - a_i (i < j) are distinct; its length is a_13.
Find a Golomb ruler with 14 marks and length at most 127.
Answer format: {"marks": [a_0, a_1, ..., a_13]}
Write your final answer as JSON to `/workdir/answer.... | {"n": 14, "max_length": 127, "fixed": [], "family": "mc_golomb", "subset": "construct"} | null | null | null | {"marks": [0, 4, 6, 20, 35, 52, 59, 77, 78, 86, 89, 99, 122, 127]} | 1 |
construct-mc-golomb-l5-s2 | construct | mc_golomb | golomb_ruler | combinatorics | competition | 5 | MathConstraint/golomb | CC-BY-4.0 | [
"np_search"
] | A Golomb ruler with 16 marks is a list of integers 0 = a_0 < a_1 < ... < a_15 such that all 120 differences a_j - a_i (i < j) are distinct; its length is a_15.
Find a Golomb ruler with 16 marks and length at most 177.
Answer format: {"marks": [a_0, a_1, ..., a_15]}
Write your final answer as JSON to `/workdir/answer... | {"n": 16, "max_length": 177, "fixed": [], "family": "mc_golomb", "subset": "construct"} | null | null | null | {"marks": [0, 1, 4, 11, 26, 32, 56, 68, 76, 115, 117, 134, 150, 163, 168, 177]} | 1 |
construct-mc-golomb-l6-s0 | construct | mc_golomb | golomb_ruler | combinatorics | competition | 6 | MathConstraint/golomb | CC-BY-4.0 | [
"np_search"
] | A Golomb ruler with 17 marks is a list of integers 0 = a_0 < a_1 < ... < a_16 such that all 136 differences a_j - a_i (i < j) are distinct; its length is a_16.
Find a Golomb ruler with 17 marks and length at most 199.
Answer format: {"marks": [a_0, a_1, ..., a_16]}
Write your final answer as JSON to `/workdir/answer... | {"n": 17, "max_length": 199, "fixed": [], "family": "mc_golomb", "subset": "construct"} | null | null | null | {"marks": [0, 5, 7, 17, 52, 56, 67, 80, 81, 100, 122, 138, 159, 165, 168, 191, 199]} | 1 |
construct-mc-golomb-l6-s1 | construct | mc_golomb | golomb_ruler | combinatorics | competition | 6 | MathConstraint/golomb | CC-BY-4.0 | [
"np_search"
] | A Golomb ruler with 19 marks is a list of integers 0 = a_0 < a_1 < ... < a_18 such that all 171 differences a_j - a_i (i < j) are distinct; its length is a_18.
Find a Golomb ruler with 19 marks and length at most 246.
Answer format: {"marks": [a_0, a_1, ..., a_18]}
Write your final answer as JSON to `/workdir/answer... | {"n": 19, "max_length": 246, "fixed": [], "family": "mc_golomb", "subset": "construct"} | null | null | null | {"marks": [0, 1, 6, 25, 32, 72, 100, 108, 120, 130, 153, 169, 187, 190, 204, 231, 233, 242, 246]} | 1 |
construct-mc-golomb-l6-s2 | construct | mc_golomb | golomb_ruler | combinatorics | competition | 6 | MathConstraint/golomb | CC-BY-4.0 | [
"np_search"
] | A Golomb ruler with 18 marks is a list of integers 0 = a_0 < a_1 < ... < a_17 such that all 153 differences a_j - a_i (i < j) are distinct; its length is a_17.
Find a Golomb ruler with 18 marks and length at most 216.
Answer format: {"marks": [a_0, a_1, ..., a_17]}
Write your final answer as JSON to `/workdir/answer... | {"n": 18, "max_length": 216, "fixed": [], "family": "mc_golomb", "subset": "construct"} | null | null | null | {"marks": [0, 2, 10, 22, 53, 56, 82, 83, 89, 98, 130, 148, 153, 167, 188, 192, 205, 216]} | 1 |
construct-mc-golomb-l6-s3 | construct | mc_golomb | golomb_ruler | combinatorics | competition | 6 | MathConstraint/golomb | CC-BY-4.0 | [
"np_search"
] | A Golomb ruler with 20 marks is a list of integers 0 = a_0 < a_1 < ... < a_19 such that all 190 differences a_j - a_i (i < j) are distinct; its length is a_19.
Find a Golomb ruler with 20 marks and length at most 283.
Answer format: {"marks": [a_0, a_1, ..., a_19]}
Write your final answer as JSON to `/workdir/answer... | {"n": 20, "max_length": 283, "fixed": [], "family": "mc_golomb", "subset": "construct"} | null | null | null | {"marks": [0, 1, 8, 11, 68, 77, 94, 116, 121, 156, 158, 179, 194, 208, 212, 228, 240, 253, 259, 283]} | 1 |
construct-mc-graceful-graph-l1-s0 | construct | mc_graceful_graph | graceful_labeling | graph_theory | competition | 1 | MathConstraint/graceful_graph | CC-BY-4.0 | [
"np_search"
] | Let G be the graph with 10 vertices 0..9 made of 5 disjoint copies of the complete graph K_2 (copy g has vertices g*2, ..., g*2+1), where for each g < 4 and each i < 2 vertex g*2+i is also joined to vertex (g+1)*2+i. G has 13 edges, in this order (index: edge):
0:(0,1), 1:(2,3), 2:(4,5), 3:(6,7), 4:(8,9), 5:(0,2), 6:(1... | {"k": 2, "p": 5, "num_vertices": 10, "edges": [[0, 1], [2, 3], [4, 5], [6, 7], [8, 9], [0, 2], [1, 3], [2, 4], [3, 5], [4, 6], [5, 7], [6, 8], [7, 9]], "fixed": [], "family": "mc_graceful_graph", "subset": "construct"} | null | null | null | {"labels": [11, 6, 4, 10, 1, 2, 12, 0, 3, 13]} | 1 |
construct-mc-graceful-graph-l1-s1 | construct | mc_graceful_graph | graceful_labeling | graph_theory | competition | 1 | MathConstraint/graceful_graph | CC-BY-4.0 | [
"np_search"
] | Let G be the graph with 12 vertices 0..11 made of 6 disjoint copies of the complete graph K_2 (copy g has vertices g*2, ..., g*2+1), where for each g < 5 and each i < 2 vertex g*2+i is also joined to vertex (g+1)*2+i. G has 16 edges, in this order (index: edge):
0:(0,1), 1:(2,3), 2:(4,5), 3:(6,7), 4:(8,9), 5:(10,11), 6... | {"k": 2, "p": 6, "num_vertices": 12, "edges": [[0, 1], [2, 3], [4, 5], [6, 7], [8, 9], [10, 11], [0, 2], [1, 3], [2, 4], [3, 5], [4, 6], [5, 7], [6, 8], [7, 9], [8, 10], [9, 11]], "fixed": [["labels", 0, 6], ["labels", 3, 4], ["d", 10, 11], ["d", 14, 1], ["d", 15, 12]], "family": "mc_graceful_graph", "subset": "constru... | null | null | null | {"labels": [6, 14, 9, 4, 5, 11, 16, 2, 0, 15, 1, 3]} | 1 |
construct-mc-graceful-graph-l1-s2 | construct | mc_graceful_graph | graceful_labeling | graph_theory | competition | 1 | MathConstraint/graceful_graph | CC-BY-4.0 | [
"np_search"
] | Let G be the graph with 6 vertices 0..5 made of 3 disjoint copies of the complete graph K_2 (copy g has vertices g*2, ..., g*2+1), where for each g < 2 and each i < 2 vertex g*2+i is also joined to vertex (g+1)*2+i. G has 7 edges, in this order (index: edge):
0:(0,1), 1:(2,3), 2:(4,5), 3:(0,2), 4:(1,3), 5:(2,4), 6:(3,5... | {"k": 2, "p": 3, "num_vertices": 6, "edges": [[0, 1], [2, 3], [4, 5], [0, 2], [1, 3], [2, 4], [3, 5]], "fixed": [["labels", 2, 7], ["d", 6, 3]], "family": "mc_graceful_graph", "subset": "construct"} | null | null | null | {"labels": [0, 2, 7, 3, 1, 6]} | 1 |
construct-mc-graceful-graph-l2-s0 | construct | mc_graceful_graph | graceful_labeling | graph_theory | competition | 2 | MathConstraint/graceful_graph | CC-BY-4.0 | [
"np_search"
] | Let G be the graph with 9 vertices 0..8 made of 3 disjoint copies of the complete graph K_3 (copy g has vertices g*3, ..., g*3+2), where for each g < 2 and each i < 3 vertex g*3+i is also joined to vertex (g+1)*3+i. G has 15 edges, in this order (index: edge):
0:(0,1), 1:(0,2), 2:(1,2), 3:(3,4), 4:(3,5), 5:(4,5), 6:(6,... | {"k": 3, "p": 3, "num_vertices": 9, "edges": [[0, 1], [0, 2], [1, 2], [3, 4], [3, 5], [4, 5], [6, 7], [6, 8], [7, 8], [0, 3], [1, 4], [2, 5], [3, 6], [4, 7], [5, 8]], "fixed": [], "family": "mc_graceful_graph", "subset": "construct"} | null | null | null | {"labels": [2, 12, 0, 1, 6, 15, 14, 3, 7]} | 1 |
construct-mc-graceful-graph-l2-s1 | construct | mc_graceful_graph | graceful_labeling | graph_theory | competition | 2 | MathConstraint/graceful_graph | CC-BY-4.0 | [
"np_search"
] | Let G be the graph with 12 vertices 0..11 made of 4 disjoint copies of the complete graph K_3 (copy g has vertices g*3, ..., g*3+2), where for each g < 3 and each i < 3 vertex g*3+i is also joined to vertex (g+1)*3+i. G has 21 edges, in this order (index: edge):
0:(0,1), 1:(0,2), 2:(1,2), 3:(3,4), 4:(3,5), 5:(4,5), 6:(... | {"k": 3, "p": 4, "num_vertices": 12, "edges": [[0, 1], [0, 2], [1, 2], [3, 4], [3, 5], [4, 5], [6, 7], [6, 8], [7, 8], [9, 10], [9, 11], [10, 11], [0, 3], [1, 4], [2, 5], [3, 6], [4, 7], [5, 8], [6, 9], [7, 10], [8, 11]], "fixed": [["labels", 2, 15], ["labels", 4, 0], ["d", 6, 5], ["d", 9, 11], ["d", 15, 13], ["d", 18,... | null | null | null | {"labels": [3, 21, 15, 20, 0, 1, 7, 2, 17, 16, 5, 9]} | 1 |
construct-mc-graceful-graph-l2-s2 | construct | mc_graceful_graph | graceful_labeling | graph_theory | competition | 2 | MathConstraint/graceful_graph | CC-BY-4.0 | [
"np_search"
] | Let G be the graph with 8 vertices 0..7 made of 4 disjoint copies of the complete graph K_2 (copy g has vertices g*2, ..., g*2+1), where for each g < 3 and each i < 2 vertex g*2+i is also joined to vertex (g+1)*2+i. G has 10 edges, in this order (index: edge):
0:(0,1), 1:(2,3), 2:(4,5), 3:(6,7), 4:(0,2), 5:(1,3), 6:(2,... | {"k": 2, "p": 4, "num_vertices": 8, "edges": [[0, 1], [2, 3], [4, 5], [6, 7], [0, 2], [1, 3], [2, 4], [3, 5], [4, 6], [5, 7]], "fixed": [], "family": "mc_graceful_graph", "subset": "construct"} | null | null | null | {"labels": [0, 2, 10, 3, 1, 7, 9, 4]} | 1 |
construct-mc-graceful-graph-l3-s0 | construct | mc_graceful_graph | graceful_labeling | graph_theory | competition | 3 | MathConstraint/graceful_graph | CC-BY-4.0 | [
"np_search"
] | Let G be the graph with 12 vertices 0..11 made of 3 disjoint copies of the complete graph K_4 (copy g has vertices g*4, ..., g*4+3), where for each g < 2 and each i < 4 vertex g*4+i is also joined to vertex (g+1)*4+i. G has 26 edges, in this order (index: edge):
0:(0,1), 1:(0,2), 2:(0,3), 3:(1,2), 4:(1,3), 5:(2,3), 6:(... | {"k": 4, "p": 3, "num_vertices": 12, "edges": [[0, 1], [0, 2], [0, 3], [1, 2], [1, 3], [2, 3], [4, 5], [4, 6], [4, 7], [5, 6], [5, 7], [6, 7], [8, 9], [8, 10], [8, 11], [9, 10], [9, 11], [10, 11], [0, 4], [1, 5], [2, 6], [3, 7], [4, 8], [5, 9], [6, 10], [7, 11]], "fixed": [], "family": "mc_graceful_graph", "subset": "c... | null | null | null | {"labels": [9, 4, 23, 17, 24, 0, 3, 26, 2, 12, 19, 1]} | 1 |
construct-mc-graceful-graph-l3-s1 | construct | mc_graceful_graph | graceful_labeling | graph_theory | competition | 3 | MathConstraint/graceful_graph | CC-BY-4.0 | [
"np_search"
] | Let G be the graph with 18 vertices 0..17 made of 6 disjoint copies of the complete graph K_3 (copy g has vertices g*3, ..., g*3+2), where for each g < 5 and each i < 3 vertex g*3+i is also joined to vertex (g+1)*3+i. G has 33 edges, in this order (index: edge):
0:(0,1), 1:(0,2), 2:(1,2), 3:(3,4), 4:(3,5), 5:(4,5), 6:(... | {"k": 3, "p": 6, "num_vertices": 18, "edges": [[0, 1], [0, 2], [1, 2], [3, 4], [3, 5], [4, 5], [6, 7], [6, 8], [7, 8], [9, 10], [9, 11], [10, 11], [12, 13], [12, 14], [13, 14], [15, 16], [15, 17], [16, 17], [0, 3], [1, 4], [2, 5], [3, 6], [4, 7], [5, 8], [6, 9], [7, 10], [8, 11], [9, 12], [10, 13], [11, 14], [12, 15], ... | null | null | null | {"labels": [1, 2, 32, 33, 20, 5, 0, 29, 3, 4, 10, 26, 9, 30, 19, 23, 6, 31]} | 1 |
construct-mc-graceful-graph-l3-s2 | construct | mc_graceful_graph | graceful_labeling | graph_theory | competition | 3 | MathConstraint/graceful_graph | CC-BY-4.0 | [
"np_search"
] | Let G be the graph with 12 vertices 0..11 made of 4 disjoint copies of the complete graph K_3 (copy g has vertices g*3, ..., g*3+2), where for each g < 3 and each i < 3 vertex g*3+i is also joined to vertex (g+1)*3+i. G has 21 edges, in this order (index: edge):
0:(0,1), 1:(0,2), 2:(1,2), 3:(3,4), 4:(3,5), 5:(4,5), 6:(... | {"k": 3, "p": 4, "num_vertices": 12, "edges": [[0, 1], [0, 2], [1, 2], [3, 4], [3, 5], [4, 5], [6, 7], [6, 8], [7, 8], [9, 10], [9, 11], [10, 11], [0, 3], [1, 4], [2, 5], [3, 6], [4, 7], [5, 8], [6, 9], [7, 10], [8, 11]], "fixed": [], "family": "mc_graceful_graph", "subset": "construct"} | null | null | null | {"labels": [3, 21, 15, 20, 0, 1, 7, 2, 17, 16, 5, 9]} | 1 |
construct-mc-graceful-graph-l3-s3 | construct | mc_graceful_graph | graceful_labeling | graph_theory | competition | 3 | MathConstraint/graceful_graph | CC-BY-4.0 | [
"np_search"
] | Let G be the graph with 15 vertices 0..14 made of 5 disjoint copies of the complete graph K_3 (copy g has vertices g*3, ..., g*3+2), where for each g < 4 and each i < 3 vertex g*3+i is also joined to vertex (g+1)*3+i. G has 27 edges, in this order (index: edge):
0:(0,1), 1:(0,2), 2:(1,2), 3:(3,4), 4:(3,5), 5:(4,5), 6:(... | {"k": 3, "p": 5, "num_vertices": 15, "edges": [[0, 1], [0, 2], [1, 2], [3, 4], [3, 5], [4, 5], [6, 7], [6, 8], [7, 8], [9, 10], [9, 11], [10, 11], [12, 13], [12, 14], [13, 14], [0, 3], [1, 4], [2, 5], [3, 6], [4, 7], [5, 8], [6, 9], [7, 10], [8, 11], [9, 12], [10, 13], [11, 14]], "fixed": [], "family": "mc_graceful_gra... | null | null | null | {"labels": [5, 24, 14, 23, 3, 7, 1, 6, 18, 25, 12, 26, 2, 27, 0]} | 1 |
construct-mc-graceful-graph-l4-s0 | construct | mc_graceful_graph | graceful_labeling | graph_theory | competition | 4 | MathConstraint/graceful_graph | CC-BY-4.0 | [
"np_search"
] | Let G be the graph with 21 vertices 0..20 made of 7 disjoint copies of the complete graph K_3 (copy g has vertices g*3, ..., g*3+2), where for each g < 6 and each i < 3 vertex g*3+i is also joined to vertex (g+1)*3+i. G has 39 edges, in this order (index: edge):
0:(0,1), 1:(0,2), 2:(1,2), 3:(3,4), 4:(3,5), 5:(4,5), 6:(... | {"k": 3, "p": 7, "num_vertices": 21, "edges": [[0, 1], [0, 2], [1, 2], [3, 4], [3, 5], [4, 5], [6, 7], [6, 8], [7, 8], [9, 10], [9, 11], [10, 11], [12, 13], [12, 14], [13, 14], [15, 16], [15, 17], [16, 17], [18, 19], [18, 20], [19, 20], [0, 3], [1, 4], [2, 5], [3, 6], [4, 7], [5, 8], [6, 9], [7, 10], [8, 11], [9, 12], ... | null | null | null | {"labels": [1, 2, 4, 37, 6, 27, 0, 39, 5, 38, 9, 29, 3, 17, 35, 19, 32, 7, 8, 15, 34]} | 1 |
construct-mc-graceful-graph-l4-s1 | construct | mc_graceful_graph | graceful_labeling | graph_theory | competition | 4 | MathConstraint/graceful_graph | CC-BY-4.0 | [
"np_search"
] | Let G be the graph with 27 vertices 0..26 made of 9 disjoint copies of the complete graph K_3 (copy g has vertices g*3, ..., g*3+2), where for each g < 8 and each i < 3 vertex g*3+i is also joined to vertex (g+1)*3+i. G has 51 edges, in this order (index: edge):
0:(0,1), 1:(0,2), 2:(1,2), 3:(3,4), 4:(3,5), 5:(4,5), 6:(... | {"k": 3, "p": 9, "num_vertices": 27, "edges": [[0, 1], [0, 2], [1, 2], [3, 4], [3, 5], [4, 5], [6, 7], [6, 8], [7, 8], [9, 10], [9, 11], [10, 11], [12, 13], [12, 14], [13, 14], [15, 16], [15, 17], [16, 17], [18, 19], [18, 20], [19, 20], [21, 22], [21, 23], [22, 23], [24, 25], [24, 26], [25, 26], [0, 3], [1, 4], [2, 5],... | null | null | null | {"labels": [17, 29, 40, 42, 5, 20, 12, 31, 47, 46, 18, 8, 1, 4, 37, 2, 48, 6, 7, 16, 24, 50, 9, 3, 0, 49, 51]} | 1 |
construct-mc-graceful-graph-l4-s2 | construct | mc_graceful_graph | graceful_labeling | graph_theory | competition | 4 | MathConstraint/graceful_graph | CC-BY-4.0 | [
"np_search"
] | Let G be the graph with 24 vertices 0..23 made of 8 disjoint copies of the complete graph K_3 (copy g has vertices g*3, ..., g*3+2), where for each g < 7 and each i < 3 vertex g*3+i is also joined to vertex (g+1)*3+i. G has 45 edges, in this order (index: edge):
0:(0,1), 1:(0,2), 2:(1,2), 3:(3,4), 4:(3,5), 5:(4,5), 6:(... | {"k": 3, "p": 8, "num_vertices": 24, "edges": [[0, 1], [0, 2], [1, 2], [3, 4], [3, 5], [4, 5], [6, 7], [6, 8], [7, 8], [9, 10], [9, 11], [10, 11], [12, 13], [12, 14], [13, 14], [15, 16], [15, 17], [16, 17], [18, 19], [18, 20], [19, 20], [21, 22], [21, 23], [22, 23], [0, 3], [1, 4], [2, 5], [3, 6], [4, 7], [5, 8], [6, 9... | null | null | null | {"labels": [5, 21, 35, 42, 31, 9, 7, 43, 36, 38, 4, 17, 40, 12, 8, 45, 27, 2, 0, 3, 44, 1, 41, 24]} | 1 |
construct-mc-graceful-graph-l5-s0 | construct | mc_graceful_graph | graceful_labeling | graph_theory | competition | 5 | MathConstraint/graceful_graph | CC-BY-4.0 | [
"np_search"
] | Let G be the graph with 16 vertices 0..15 made of 4 disjoint copies of the complete graph K_4 (copy g has vertices g*4, ..., g*4+3), where for each g < 3 and each i < 4 vertex g*4+i is also joined to vertex (g+1)*4+i. G has 36 edges, in this order (index: edge):
0:(0,1), 1:(0,2), 2:(0,3), 3:(1,2), 4:(1,3), 5:(2,3), 6:(... | {"k": 4, "p": 4, "num_vertices": 16, "edges": [[0, 1], [0, 2], [0, 3], [1, 2], [1, 3], [2, 3], [4, 5], [4, 6], [4, 7], [5, 6], [5, 7], [6, 7], [8, 9], [8, 10], [8, 11], [9, 10], [9, 11], [10, 11], [12, 13], [12, 14], [12, 15], [13, 14], [13, 15], [14, 15], [0, 4], [1, 5], [2, 6], [3, 7], [4, 8], [5, 9], [6, 10], [7, 11... | null | null | null | {"labels": [14, 9, 25, 35, 6, 31, 12, 3, 2, 4, 19, 33, 36, 24, 1, 0]} | 1 |
construct-mc-graceful-graph-l5-s1 | construct | mc_graceful_graph | graceful_labeling | graph_theory | competition | 5 | MathConstraint/graceful_graph | CC-BY-4.0 | [
"np_search"
] | Let G be the graph with 20 vertices 0..19 made of 5 disjoint copies of the complete graph K_4 (copy g has vertices g*4, ..., g*4+3), where for each g < 4 and each i < 4 vertex g*4+i is also joined to vertex (g+1)*4+i. G has 46 edges, in this order (index: edge):
0:(0,1), 1:(0,2), 2:(0,3), 3:(1,2), 4:(1,3), 5:(2,3), 6:(... | {"k": 4, "p": 5, "num_vertices": 20, "edges": [[0, 1], [0, 2], [0, 3], [1, 2], [1, 3], [2, 3], [4, 5], [4, 6], [4, 7], [5, 6], [5, 7], [6, 7], [8, 9], [8, 10], [8, 11], [9, 10], [9, 11], [10, 11], [12, 13], [12, 14], [12, 15], [13, 14], [13, 15], [14, 15], [16, 17], [16, 18], [16, 19], [17, 18], [17, 19], [18, 19], [0,... | null | null | null | {"labels": [8, 1, 26, 45, 40, 6, 2, 0, 4, 3, 31, 46, 27, 44, 5, 13, 39, 9, 18, 29]} | 1 |
construct-mc-graceful-graph-l5-s2 | construct | mc_graceful_graph | graceful_labeling | graph_theory | competition | 5 | MathConstraint/graceful_graph | CC-BY-4.0 | [
"np_search"
] | Let G be the graph with 15 vertices 0..14 made of 3 disjoint copies of the complete graph K_5 (copy g has vertices g*5, ..., g*5+4), where for each g < 2 and each i < 5 vertex g*5+i is also joined to vertex (g+1)*5+i. G has 40 edges, in this order (index: edge):
0:(0,1), 1:(0,2), 2:(0,3), 3:(0,4), 4:(1,2), 5:(1,3), 6:(... | {"k": 5, "p": 3, "num_vertices": 15, "edges": [[0, 1], [0, 2], [0, 3], [0, 4], [1, 2], [1, 3], [1, 4], [2, 3], [2, 4], [3, 4], [5, 6], [5, 7], [5, 8], [5, 9], [6, 7], [6, 8], [6, 9], [7, 8], [7, 9], [8, 9], [10, 11], [10, 12], [10, 13], [10, 14], [11, 12], [11, 13], [11, 14], [12, 13], [12, 14], [13, 14], [0, 5], [1, 6... | null | null | null | {"labels": [1, 3, 6, 26, 37, 0, 22, 32, 39, 4, 40, 10, 16, 2, 31]} | 1 |
construct-mc-graceful-graph-l5-s3 | construct | mc_graceful_graph | graceful_labeling | graph_theory | competition | 5 | MathConstraint/graceful_graph | CC-BY-4.0 | [
"np_search"
] | Let G be the graph with 30 vertices 0..29 made of 10 disjoint copies of the complete graph K_3 (copy g has vertices g*3, ..., g*3+2), where for each g < 9 and each i < 3 vertex g*3+i is also joined to vertex (g+1)*3+i. G has 57 edges, in this order (index: edge):
0:(0,1), 1:(0,2), 2:(1,2), 3:(3,4), 4:(3,5), 5:(4,5), 6:... | {"k": 3, "p": 10, "num_vertices": 30, "edges": [[0, 1], [0, 2], [1, 2], [3, 4], [3, 5], [4, 5], [6, 7], [6, 8], [7, 8], [9, 10], [9, 11], [10, 11], [12, 13], [12, 14], [13, 14], [15, 16], [15, 17], [16, 17], [18, 19], [18, 20], [19, 20], [21, 22], [21, 23], [22, 23], [24, 25], [24, 26], [25, 26], [27, 28], [27, 29], [2... | null | null | null | {"labels": [39, 51, 20, 10, 35, 53, 45, 9, 30, 23, 50, 6, 37, 3, 57, 5, 55, 0, 16, 7, 56, 24, 52, 14, 54, 15, 8, 1, 2, 4]} | 1 |
construct-mc-graph-k-coloring-l1-s0 | construct | mc_graph_k_coloring | graph_k_coloring | graph_theory | competition | 1 | MathConstraint/graph_k_coloring | CC-BY-4.0 | [
"np_search"
] | Graph G with 20 vertices numbered 0..19 and 30 edges:
(0,2), (0,8), (0,12), (0,13), (0,16), (0,17), (1,11), (2,4), (2,13), (3,5), (3,9), (3,15), (3,16), (4,13), (4,16), (4,17), (5,14), (5,15), (7,16), (9,14), (9,19), (10,13), (10,17), (11,16), (13,17), (13,19), (14,18), (14,19), (15,17), (15,19)
Give a proper colourin... | {"n": 20, "k": 3, "edges": [[0, 2], [0, 8], [0, 12], [0, 13], [0, 16], [0, 17], [1, 11], [2, 4], [2, 13], [3, 5], [3, 9], [3, 15], [3, 16], [4, 13], [4, 16], [4, 17], [5, 14], [5, 15], [7, 16], [9, 14], [9, 19], [10, 13], [10, 17], [11, 16], [13, 17], [13, 19], [14, 18], [14, 19], [15, 17], [15, 19]], "family": "mc_gra... | null | null | null | {"coloring": [1, 0, 0, 1, 1, 0, 2, 1, 2, 2, 1, 1, 2, 2, 1, 2, 0, 0, 0, 0]} | 1 |
construct-mc-graph-k-coloring-l1-s1 | construct | mc_graph_k_coloring | graph_k_coloring | graph_theory | competition | 1 | MathConstraint/graph_k_coloring | CC-BY-4.0 | [
"np_search"
] | Graph G with 20 vertices numbered 0..19 and 30 edges:
(0,9), (1,10), (1,11), (1,19), (2,3), (2,6), (3,4), (3,9), (3,19), (4,10), (4,12), (4,13), (4,14), (4,15), (5,10), (5,13), (6,8), (7,8), (8,12), (8,19), (9,11), (10,13), (10,14), (10,19), (11,14), (12,13), (12,18), (12,19), (13,18), (15,17)
Give a proper colouring ... | {"n": 20, "k": 3, "edges": [[0, 9], [1, 10], [1, 11], [1, 19], [2, 3], [2, 6], [3, 4], [3, 9], [3, 19], [4, 10], [4, 12], [4, 13], [4, 14], [4, 15], [5, 10], [5, 13], [6, 8], [7, 8], [8, 12], [8, 19], [9, 11], [10, 13], [10, 14], [10, 19], [11, 14], [12, 13], [12, 18], [12, 19], [13, 18], [15, 17]], "family": "mc_graph... | null | null | null | {"coloring": [2, 1, 0, 2, 1, 1, 2, 0, 1, 0, 2, 2, 2, 0, 0, 0, 1, 1, 1, 0]} | 1 |
construct-mc-graph-k-coloring-l1-s2 | construct | mc_graph_k_coloring | graph_k_coloring | graph_theory | competition | 1 | MathConstraint/graph_k_coloring | CC-BY-4.0 | [
"np_search"
] | Graph G with 20 vertices numbered 0..19 and 30 edges:
(0,4), (0,15), (0,16), (1,8), (1,14), (1,15), (2,5), (2,10), (2,16), (2,18), (2,19), (3,9), (4,7), (4,13), (4,15), (4,18), (4,19), (5,6), (5,13), (5,18), (6,19), (7,9), (7,18), (9,15), (11,13), (11,17), (12,19), (13,15), (14,19), (15,17)
Give a proper colouring of ... | {"n": 20, "k": 3, "edges": [[0, 4], [0, 15], [0, 16], [1, 8], [1, 14], [1, 15], [2, 5], [2, 10], [2, 16], [2, 18], [2, 19], [3, 9], [4, 7], [4, 13], [4, 15], [4, 18], [4, 19], [5, 6], [5, 13], [5, 18], [6, 19], [7, 9], [7, 18], [9, 15], [11, 13], [11, 17], [12, 19], [13, 15], [14, 19], [15, 17]], "family": "mc_graph_k_... | null | null | null | {"coloring": [1, 1, 2, 0, 2, 0, 2, 0, 0, 2, 1, 2, 2, 1, 0, 0, 0, 1, 1, 1]} | 1 |
construct-mc-graph-k-coloring-l1-s3 | construct | mc_graph_k_coloring | graph_k_coloring | graph_theory | competition | 1 | MathConstraint/graph_k_coloring | CC-BY-4.0 | [
"np_search"
] | Graph G with 20 vertices numbered 0..19 and 30 edges:
(0,4), (0,7), (0,13), (0,14), (1,6), (1,10), (1,14), (1,18), (2,4), (2,9), (2,16), (4,11), (4,12), (4,14), (5,8), (5,16), (6,7), (6,13), (6,14), (6,15), (7,12), (7,19), (8,14), (10,12), (10,19), (11,16), (11,17), (12,13), (13,18), (18,19)
Give a proper colouring of... | {"n": 20, "k": 3, "edges": [[0, 4], [0, 7], [0, 13], [0, 14], [1, 6], [1, 10], [1, 14], [1, 18], [2, 4], [2, 9], [2, 16], [4, 11], [4, 12], [4, 14], [5, 8], [5, 16], [6, 7], [6, 13], [6, 14], [6, 15], [7, 12], [7, 19], [8, 14], [10, 12], [10, 19], [11, 16], [11, 17], [12, 13], [13, 18], [18, 19]], "family": "mc_graph_k... | null | null | null | {"coloring": [0, 0, 0, 2, 2, 1, 2, 1, 0, 1, 2, 1, 0, 1, 1, 1, 2, 0, 2, 0]} | 1 |
construct-mc-graph-k-coloring-l1-s4 | construct | mc_graph_k_coloring | graph_k_coloring | graph_theory | competition | 1 | MathConstraint/graph_k_coloring | CC-BY-4.0 | [
"np_search"
] | Graph G with 20 vertices numbered 0..19 and 30 edges:
(0,5), (0,7), (0,9), (0,12), (0,15), (1,9), (2,4), (2,12), (2,15), (2,17), (2,19), (3,6), (3,9), (3,15), (3,16), (4,10), (4,13), (5,9), (5,10), (6,8), (6,16), (6,17), (7,11), (8,9), (8,14), (8,18), (9,17), (10,19), (12,15), (12,17)
Give a proper colouring of G with... | {"n": 20, "k": 3, "edges": [[0, 5], [0, 7], [0, 9], [0, 12], [0, 15], [1, 9], [2, 4], [2, 12], [2, 15], [2, 17], [2, 19], [3, 6], [3, 9], [3, 15], [3, 16], [4, 10], [4, 13], [5, 9], [5, 10], [6, 8], [6, 16], [6, 17], [7, 11], [8, 9], [8, 14], [8, 18], [9, 17], [10, 19], [12, 15], [12, 17]], "family": "mc_graph_k_colori... | null | null | null | {"coloring": [1, 1, 1, 1, 0, 0, 2, 0, 0, 2, 1, 1, 2, 2, 2, 0, 0, 0, 1, 2]} | 1 |
construct-mc-graph-k-coloring-l1-s5 | construct | mc_graph_k_coloring | graph_k_coloring | graph_theory | competition | 1 | MathConstraint/graph_k_coloring | CC-BY-4.0 | [
"np_search"
] | Graph G with 20 vertices numbered 0..19 and 30 edges:
(0,1), (0,14), (1,11), (1,13), (1,19), (2,11), (2,16), (3,5), (3,18), (4,7), (4,14), (4,18), (5,6), (5,8), (5,15), (5,17), (6,7), (7,9), (7,16), (7,17), (8,17), (9,10), (9,11), (10,17), (12,13), (12,14), (12,16), (13,17), (15,18), (16,17)
Give a proper colouring of... | {"n": 20, "k": 3, "edges": [[0, 1], [0, 14], [1, 11], [1, 13], [1, 19], [2, 11], [2, 16], [3, 5], [3, 18], [4, 7], [4, 14], [4, 18], [5, 6], [5, 8], [5, 15], [5, 17], [6, 7], [7, 9], [7, 16], [7, 17], [8, 17], [9, 10], [9, 11], [10, 17], [12, 13], [12, 14], [12, 16], [13, 17], [15, 18], [16, 17]], "family": "mc_graph_k... | null | null | null | {"coloring": [0, 1, 2, 1, 0, 0, 1, 2, 2, 1, 0, 0, 1, 2, 2, 1, 0, 1, 2, 0]} | 1 |
construct-mc-graph-k-coloring-l1-s6 | construct | mc_graph_k_coloring | graph_k_coloring | graph_theory | competition | 1 | MathConstraint/graph_k_coloring | CC-BY-4.0 | [
"np_search"
] | Graph G with 20 vertices numbered 0..19 and 30 edges:
(0,2), (0,4), (0,9), (0,15), (0,19), (1,17), (1,19), (2,16), (3,9), (3,11), (3,19), (4,8), (4,14), (4,17), (5,7), (5,15), (6,11), (6,16), (7,10), (7,12), (7,15), (7,16), (7,19), (10,14), (10,16), (10,18), (11,19), (12,16), (13,14), (15,18)
Give a proper colouring o... | {"n": 20, "k": 3, "edges": [[0, 2], [0, 4], [0, 9], [0, 15], [0, 19], [1, 17], [1, 19], [2, 16], [3, 9], [3, 11], [3, 19], [4, 8], [4, 14], [4, 17], [5, 7], [5, 15], [6, 11], [6, 16], [7, 10], [7, 12], [7, 15], [7, 16], [7, 19], [10, 14], [10, 16], [10, 18], [11, 19], [12, 16], [13, 14], [15, 18]], "family": "mc_graph_... | null | null | null | {"coloring": [1, 0, 2, 1, 0, 0, 2, 1, 1, 0, 2, 0, 2, 0, 1, 2, 0, 1, 1, 2]} | 1 |
construct-mc-graph-k-coloring-l1-s7 | construct | mc_graph_k_coloring | graph_k_coloring | graph_theory | competition | 1 | MathConstraint/graph_k_coloring | CC-BY-4.0 | [
"np_search"
] | Graph G with 20 vertices numbered 0..19 and 30 edges:
(0,5), (0,12), (0,14), (0,15), (1,5), (1,7), (1,14), (1,16), (1,17), (1,19), (2,10), (2,18), (3,8), (3,13), (4,16), (6,11), (6,17), (7,11), (7,18), (9,11), (9,19), (11,13), (11,14), (11,17), (11,19), (12,13), (12,16), (13,15), (14,15), (15,19)
Give a proper colouri... | {"n": 20, "k": 3, "edges": [[0, 5], [0, 12], [0, 14], [0, 15], [1, 5], [1, 7], [1, 14], [1, 16], [1, 17], [1, 19], [2, 10], [2, 18], [3, 8], [3, 13], [4, 16], [6, 11], [6, 17], [7, 11], [7, 18], [9, 11], [9, 19], [11, 13], [11, 14], [11, 17], [11, 19], [12, 13], [12, 16], [13, 15], [14, 15], [15, 19]], "family": "mc_gr... | null | null | null | {"coloring": [1, 2, 0, 0, 2, 0, 1, 0, 1, 1, 1, 2, 2, 1, 0, 2, 1, 0, 2, 0]} | 1 |
construct-mc-graph-k-coloring-l1-s8 | construct | mc_graph_k_coloring | graph_k_coloring | graph_theory | competition | 1 | MathConstraint/graph_k_coloring | CC-BY-4.0 | [
"np_search"
] | Graph G with 20 vertices numbered 0..19 and 30 edges:
(0,7), (0,8), (0,9), (0,11), (0,13), (1,7), (1,9), (1,17), (2,16), (3,6), (3,8), (3,9), (3,14), (4,13), (5,6), (5,16), (5,19), (7,13), (7,18), (8,19), (9,10), (9,12), (9,16), (9,19), (11,12), (11,17), (12,13), (12,15), (12,17), (14,19)
Give a proper colouring of G ... | {"n": 20, "k": 3, "edges": [[0, 7], [0, 8], [0, 9], [0, 11], [0, 13], [1, 7], [1, 9], [1, 17], [2, 16], [3, 6], [3, 8], [3, 9], [3, 14], [4, 13], [5, 6], [5, 16], [5, 19], [7, 13], [7, 18], [8, 19], [9, 10], [9, 12], [9, 16], [9, 19], [11, 12], [11, 17], [12, 13], [12, 15], [12, 17], [14, 19]], "family": "mc_graph_k_co... | null | null | null | {"coloring": [1, 1, 1, 1, 0, 0, 2, 0, 0, 0, 1, 0, 1, 2, 0, 2, 2, 2, 2, 1]} | 1 |
construct-mc-graph-k-coloring-l1-s9 | construct | mc_graph_k_coloring | graph_k_coloring | graph_theory | competition | 1 | MathConstraint/graph_k_coloring | CC-BY-4.0 | [
"np_search"
] | Graph G with 20 vertices numbered 0..19 and 30 edges:
(1,7), (1,8), (2,5), (2,7), (2,8), (3,6), (3,15), (3,16), (4,5), (4,7), (4,11), (5,7), (6,9), (6,14), (6,19), (7,9), (7,10), (9,11), (10,14), (11,15), (12,14), (12,15), (13,14), (13,17), (13,18), (15,17), (15,18), (16,18), (16,19), (17,19)
Give a proper colouring o... | {"n": 20, "k": 3, "edges": [[1, 7], [1, 8], [2, 5], [2, 7], [2, 8], [3, 6], [3, 15], [3, 16], [4, 5], [4, 7], [4, 11], [5, 7], [6, 9], [6, 14], [6, 19], [7, 9], [7, 10], [9, 11], [10, 14], [11, 15], [12, 14], [12, 15], [13, 14], [13, 17], [13, 18], [15, 17], [15, 18], [16, 18], [16, 19], [17, 19]], "family": "mc_graph_... | null | null | null | {"coloring": [0, 1, 1, 0, 1, 0, 1, 2, 2, 0, 1, 2, 2, 1, 0, 1, 2, 2, 0, 0]} | 1 |
construct-mc-graph-k-coloring-l2-s0 | construct | mc_graph_k_coloring | graph_k_coloring | graph_theory | competition | 2 | MathConstraint/graph_k_coloring | CC-BY-4.0 | [
"np_search"
] | Graph G with 32 vertices numbered 0..31 and 85 edges:
(0,5), (0,10), (0,24), (0,28), (1,5), (1,15), (1,16), (1,18), (1,19), (1,20), (1,25), (2,13), (2,15), (2,20), (2,22), (3,23), (3,30), (3,31), (4,12), (4,23), (4,29), (5,8), (5,12), (5,17), (5,19), (5,23), (5,30), (6,8), (6,13), (6,28), (6,29), (6,30), (6,31), (7,18)... | {"n": 32, "k": 4, "edges": [[0, 5], [0, 10], [0, 24], [0, 28], [1, 5], [1, 15], [1, 16], [1, 18], [1, 19], [1, 20], [1, 25], [2, 13], [2, 15], [2, 20], [2, 22], [3, 23], [3, 30], [3, 31], [4, 12], [4, 23], [4, 29], [5, 8], [5, 12], [5, 17], [5, 19], [5, 23], [5, 30], [6, 8], [6, 13], [6, 28], [6, 29], [6, 30], [6, 31],... | null | null | null | {"coloring": [0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 1, 1, 2, 1, 0, 1, 2, 3, 1, 2, 1, 3, 1, 2, 2, 1, 0, 3, 2, 2, 3, 1]} | 1 |
construct-mc-graph-k-coloring-l2-s1 | construct | mc_graph_k_coloring | graph_k_coloring | graph_theory | competition | 2 | MathConstraint/graph_k_coloring | CC-BY-4.0 | [
"np_search"
] | Graph G with 34 vertices numbered 0..33 and 111 edges:
(0,8), (0,12), (0,21), (0,28), (0,29), (0,30), (0,33), (1,17), (1,28), (1,31), (2,6), (2,18), (2,21), (2,26), (3,12), (3,18), (3,23), (3,33), (4,17), (4,19), (4,20), (4,21), (4,22), (4,24), (4,28), (4,32), (5,6), (5,10), (5,17), (5,19), (5,28), (6,16), (6,20), (6,2... | {"n": 34, "k": 4, "edges": [[0, 8], [0, 12], [0, 21], [0, 28], [0, 29], [0, 30], [0, 33], [1, 17], [1, 28], [1, 31], [2, 6], [2, 18], [2, 21], [2, 26], [3, 12], [3, 18], [3, 23], [3, 33], [4, 17], [4, 19], [4, 20], [4, 21], [4, 22], [4, 24], [4, 28], [4, 32], [5, 6], [5, 10], [5, 17], [5, 19], [5, 28], [6, 16], [6, 20]... | null | null | null | {"coloring": [0, 1, 2, 3, 1, 1, 0, 1, 3, 0, 2, 2, 2, 1, 1, 3, 1, 0, 0, 3, 3, 3, 0, 1, 0, 3, 1, 2, 2, 2, 1, 2, 0, 1]} | 1 |
construct-mc-graph-k-coloring-l2-s2 | construct | mc_graph_k_coloring | graph_k_coloring | graph_theory | competition | 2 | MathConstraint/graph_k_coloring | CC-BY-4.0 | [
"np_search"
] | Graph G with 32 vertices numbered 0..31 and 50 edges:
(0,5), (0,12), (0,14), (1,3), (1,6), (1,12), (1,14), (1,23), (2,19), (2,25), (3,14), (3,18), (4,21), (4,22), (6,11), (6,26), (7,9), (7,24), (8,12), (8,25), (9,11), (9,13), (9,19), (9,20), (9,31), (10,18), (10,19), (11,21), (12,16), (12,18), (12,28), (13,14), (13,24)... | {"n": 32, "k": 3, "edges": [[0, 5], [0, 12], [0, 14], [1, 3], [1, 6], [1, 12], [1, 14], [1, 23], [2, 19], [2, 25], [3, 14], [3, 18], [4, 21], [4, 22], [6, 11], [6, 26], [7, 9], [7, 24], [8, 12], [8, 25], [9, 11], [9, 13], [9, 19], [9, 20], [9, 31], [10, 18], [10, 19], [11, 21], [12, 16], [12, 18], [12, 28], [13, 14], [... | null | null | null | {"coloring": [0, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 2, 0, 2, 0, 0, 2, 0, 1, 1, 1, 1, 2, 0, 0, 0, 1, 1, 0]} | 1 |
construct-mc-graph-k-coloring-l2-s3 | construct | mc_graph_k_coloring | graph_k_coloring | graph_theory | competition | 2 | MathConstraint/graph_k_coloring | CC-BY-4.0 | [
"np_search"
] | Graph G with 37 vertices numbered 0..36 and 133 edges:
(0,1), (0,3), (0,6), (0,7), (0,9), (0,18), (0,21), (0,24), (1,7), (1,8), (1,12), (1,13), (1,24), (1,26), (1,28), (2,3), (2,11), (2,15), (2,20), (2,21), (2,22), (2,24), (2,36), (3,11), (3,12), (3,28), (3,29), (3,36), (4,5), (4,14), (4,20), (4,30), (4,35), (5,17), (5... | {"n": 37, "k": 4, "edges": [[0, 1], [0, 3], [0, 6], [0, 7], [0, 9], [0, 18], [0, 21], [0, 24], [1, 7], [1, 8], [1, 12], [1, 13], [1, 24], [1, 26], [1, 28], [2, 3], [2, 11], [2, 15], [2, 20], [2, 21], [2, 22], [2, 24], [2, 36], [3, 11], [3, 12], [3, 28], [3, 29], [3, 36], [4, 5], [4, 14], [4, 20], [4, 30], [4, 35], [5, ... | null | null | null | {"coloring": [0, 1, 0, 1, 0, 1, 1, 2, 2, 3, 0, 3, 0, 0, 1, 1, 2, 0, 1, 1, 2, 1, 3, 1, 3, 3, 3, 1, 0, 2, 2, 2, 1, 0, 0, 2, 3]} | 1 |
construct-mc-graph-k-coloring-l2-s4 | construct | mc_graph_k_coloring | graph_k_coloring | graph_theory | competition | 2 | MathConstraint/graph_k_coloring | CC-BY-4.0 | [
"np_search"
] | Graph G with 37 vertices numbered 0..36 and 105 edges:
(0,4), (0,27), (0,30), (0,34), (1,19), (1,26), (2,16), (2,17), (2,35), (3,9), (3,12), (3,25), (3,29), (3,30), (3,36), (4,15), (4,21), (4,24), (4,36), (5,10), (5,11), (5,13), (5,15), (5,17), (5,20), (5,29), (6,10), (6,17), (6,21), (7,14), (7,24), (7,25), (7,28), (7,... | {"n": 37, "k": 4, "edges": [[0, 4], [0, 27], [0, 30], [0, 34], [1, 19], [1, 26], [2, 16], [2, 17], [2, 35], [3, 9], [3, 12], [3, 25], [3, 29], [3, 30], [3, 36], [4, 15], [4, 21], [4, 24], [4, 36], [5, 10], [5, 11], [5, 13], [5, 15], [5, 17], [5, 20], [5, 29], [6, 10], [6, 17], [6, 21], [7, 14], [7, 24], [7, 25], [7, 28... | null | null | null | {"coloring": [0, 0, 0, 0, 1, 0, 0, 2, 0, 3, 1, 2, 2, 1, 0, 2, 1, 1, 0, 2, 1, 3, 3, 0, 0, 1, 1, 2, 3, 1, 1, 0, 2, 1, 2, 3, 2]} | 1 |
construct-mc-graph-k-coloring-l2-s5 | construct | mc_graph_k_coloring | graph_k_coloring | graph_theory | competition | 2 | MathConstraint/graph_k_coloring | CC-BY-4.0 | [
"np_search"
] | Graph G with 27 vertices numbered 0..26 and 51 edges:
(0,3), (0,9), (0,12), (0,21), (1,6), (1,11), (1,14), (1,16), (1,17), (1,20), (2,16), (2,17), (3,14), (3,22), (4,5), (4,8), (5,6), (5,11), (5,14), (5,20), (6,18), (6,24), (7,8), (7,11), (7,16), (7,22), (8,12), (8,14), (9,10), (9,11), (9,18), (9,25), (9,26), (10,13), ... | {"n": 27, "k": 3, "edges": [[0, 3], [0, 9], [0, 12], [0, 21], [1, 6], [1, 11], [1, 14], [1, 16], [1, 17], [1, 20], [2, 16], [2, 17], [3, 14], [3, 22], [4, 5], [4, 8], [5, 6], [5, 11], [5, 14], [5, 20], [6, 18], [6, 24], [7, 8], [7, 11], [7, 16], [7, 22], [8, 12], [8, 14], [9, 10], [9, 11], [9, 18], [9, 25], [9, 26], [1... | null | null | null | {"coloring": [0, 0, 0, 1, 1, 0, 1, 2, 0, 2, 0, 1, 1, 1, 2, 2, 1, 1, 0, 0, 2, 1, 0, 1, 2, 0, 0]} | 1 |
construct-mc-graph-k-coloring-l2-s6 | construct | mc_graph_k_coloring | graph_k_coloring | graph_theory | competition | 2 | MathConstraint/graph_k_coloring | CC-BY-4.0 | [
"np_search"
] | Graph G with 33 vertices numbered 0..32 and 76 edges:
(0,4), (0,5), (0,13), (0,18), (0,27), (0,31), (1,15), (1,17), (2,4), (2,12), (2,14), (2,15), (2,16), (2,29), (3,5), (3,7), (3,8), (3,17), (3,19), (3,22), (4,5), (4,6), (4,13), (4,24), (4,25), (4,28), (4,31), (6,12), (6,13), (6,14), (6,15), (6,18), (6,19), (6,22), (6... | {"n": 33, "k": 4, "edges": [[0, 4], [0, 5], [0, 13], [0, 18], [0, 27], [0, 31], [1, 15], [1, 17], [2, 4], [2, 12], [2, 14], [2, 15], [2, 16], [2, 29], [3, 5], [3, 7], [3, 8], [3, 17], [3, 19], [3, 22], [4, 5], [4, 6], [4, 13], [4, 24], [4, 25], [4, 28], [4, 31], [6, 12], [6, 13], [6, 14], [6, 15], [6, 18], [6, 19], [6,... | null | null | null | {"coloring": [0, 0, 0, 0, 1, 2, 0, 1, 1, 0, 0, 1, 1, 2, 1, 2, 1, 3, 2, 2, 0, 2, 3, 0, 2, 0, 0, 1, 2, 1, 0, 2, 1]} | 1 |
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