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-pysms-mtf-l5-s2 | construct | mc_pysms_mtf | maximal_triangle_free_graph | graph_theory | competition | 5 | MathConstraint/pysms_mtf | CC-BY-4.0 | [
"agentic_trivial",
"np_search"
] | Construct a simple undirected graph on the 16 vertices 0..15 such that:
- the graph is maximal triangle-free: it contains no triangle, and adding any missing edge would create one (every two non-adjacent vertices have a common neighbour)
Answer format: {"edges": [[u, v], ...]} where each edge is a pair of distinct v... | {"vertices": 16, "required_edges": [], "mtf": true, "family": "mc_pysms_mtf", "subset": "construct"} | null | null | null | {"edges": [[0, 14], [0, 15], [1, 14], [1, 15], [2, 14], [2, 15], [3, 14], [3, 15], [4, 14], [4, 15], [5, 14], [5, 15], [6, 14], [6, 15], [7, 14], [7, 15], [8, 14], [8, 15], [9, 14], [9, 15], [10, 14], [10, 15], [11, 14], [11, 15], [12, 14], [12, 15], [13, 14], [13, 15]]} | 1 |
construct-mc-pysms-num-edges-bounds-l1-s0 | construct | mc_pysms_num_edges_bounds | graph_existence_num_edges_bounds | graph_theory | competition | 1 | MathConstraint/pysms_num_edges_bounds | CC-BY-4.0 | [
"agentic_trivial",
"np_search"
] | Construct a simple undirected graph on the 10 vertices 0..9 such that:
- the number of edges is between 21 and 30 (inclusive)
Answer format: {"edges": [[u, v], ...]} where each edge is a pair of distinct vertices in 0..9, listed once
Write your final answer as JSON to `/workdir/answer.json`. The instance data is al... | {"vertices": 10, "required_edges": [], "max_edges": 30, "min_edges": 21, "family": "mc_pysms_num_edges_bounds", "subset": "construct"} | null | null | null | {"edges": [[0, 5], [0, 6], [0, 7], [0, 8], [0, 9], [1, 2], [1, 3], [1, 4], [1, 8], [1, 9], [2, 3], [2, 4], [2, 7], [2, 8], [2, 9], [3, 4], [3, 7], [3, 8], [3, 9], [4, 5], [4, 6], [4, 7], [5, 6], [5, 7], [5, 8], [5, 9], [6, 7], [6, 8], [6, 9]]} | 1 |
construct-mc-pysms-num-edges-bounds-l1-s1 | construct | mc_pysms_num_edges_bounds | graph_existence_num_edges_bounds | graph_theory | competition | 1 | MathConstraint/pysms_num_edges_bounds | CC-BY-4.0 | [
"agentic_trivial",
"np_search"
] | Construct a simple undirected graph on the 8 vertices 0..7 such that:
- the number of edges is between 11 and 16 (inclusive)
Answer format: {"edges": [[u, v], ...]} where each edge is a pair of distinct vertices in 0..7, listed once
Write your final answer as JSON to `/workdir/answer.json`. The instance data is als... | {"vertices": 8, "required_edges": [], "max_edges": 16, "min_edges": 11, "family": "mc_pysms_num_edges_bounds", "subset": "construct"} | null | null | null | {"edges": [[0, 4], [0, 5], [0, 6], [0, 7], [1, 4], [1, 5], [1, 6], [1, 7], [2, 4], [2, 5], [2, 6], [2, 7], [3, 4], [3, 5], [3, 6], [3, 7]]} | 1 |
construct-mc-pysms-num-edges-bounds-l2-s0 | construct | mc_pysms_num_edges_bounds | graph_existence_num_edges_bounds | graph_theory | competition | 2 | MathConstraint/pysms_num_edges_bounds | CC-BY-4.0 | [
"agentic_trivial",
"np_search"
] | Construct a simple undirected graph on the 11 vertices 0..10 such that:
- the number of edges is between 32 and 43 (inclusive)
- it contains each of the following edges: (1,9), (2,9), (6,9), (3,10), (5,7), (2,8), (7,9), (4,6)
Answer format: {"edges": [[u, v], ...]} where each edge is a pair of distinct vertices in... | {"vertices": 11, "required_edges": [[1, 9], [2, 9], [6, 9], [3, 10], [5, 7], [2, 8], [7, 9], [4, 6]], "max_edges": 43, "min_edges": 32, "family": "mc_pysms_num_edges_bounds", "subset": "construct"} | null | null | null | {"edges": [[0, 6], [0, 7], [0, 8], [0, 9], [0, 10], [1, 5], [1, 6], [1, 7], [1, 8], [1, 9], [1, 10], [2, 3], [2, 4], [2, 5], [2, 7], [2, 8], [2, 9], [2, 10], [3, 4], [3, 5], [3, 6], [3, 8], [3, 9], [3, 10], [4, 5], [4, 6], [4, 7], [4, 9], [4, 10], [5, 6], [5, 7], [5, 8], [5, 10], [6, 7], [6, 8], [6, 9], [7, 8], [7, 9],... | 1 |
construct-mc-pysms-num-edges-bounds-l2-s1 | construct | mc_pysms_num_edges_bounds | graph_existence_num_edges_bounds | graph_theory | competition | 2 | MathConstraint/pysms_num_edges_bounds | CC-BY-4.0 | [
"agentic_trivial",
"np_search"
] | Construct a simple undirected graph on the 10 vertices 0..9 such that:
- the number of edges is between 27 and 31 (inclusive)
- it contains each of the following edges: (4,8), (3,7), (6,7), (2,8), (0,8), (0,5)
Answer format: {"edges": [[u, v], ...]} where each edge is a pair of distinct vertices in 0..9, listed on... | {"vertices": 10, "required_edges": [[4, 8], [3, 7], [6, 7], [2, 8], [0, 8], [0, 5]], "max_edges": 31, "min_edges": 27, "family": "mc_pysms_num_edges_bounds", "subset": "construct"} | null | null | null | {"edges": [[0, 4], [0, 5], [0, 6], [0, 7], [0, 8], [0, 9], [1, 3], [1, 4], [1, 5], [1, 6], [1, 7], [1, 8], [1, 9], [2, 3], [2, 4], [2, 5], [2, 6], [2, 7], [2, 8], [2, 9], [3, 6], [3, 7], [3, 8], [3, 9], [4, 5], [4, 8], [4, 9], [5, 6], [5, 7], [6, 7], [8, 9]]} | 1 |
construct-mc-pysms-num-edges-bounds-l3-s0 | construct | mc_pysms_num_edges_bounds | graph_existence_num_edges_bounds | graph_theory | competition | 3 | MathConstraint/pysms_num_edges_bounds | CC-BY-4.0 | [
"agentic_trivial",
"np_search"
] | Construct a simple undirected graph on the 11 vertices 0..10 such that:
- the number of edges is between 30 and 36 (inclusive)
Answer format: {"edges": [[u, v], ...]} where each edge is a pair of distinct vertices in 0..10, listed once
Write your final answer as JSON to `/workdir/answer.json`. The instance data is ... | {"vertices": 11, "required_edges": [], "max_edges": 36, "min_edges": 30, "family": "mc_pysms_num_edges_bounds", "subset": "construct"} | null | null | null | {"edges": [[0, 7], [0, 8], [0, 9], [0, 10], [1, 3], [1, 4], [1, 5], [1, 6], [1, 7], [1, 8], [1, 9], [1, 10], [2, 3], [2, 4], [2, 5], [2, 6], [2, 7], [2, 8], [2, 9], [2, 10], [3, 4], [3, 5], [3, 6], [4, 5], [4, 6], [4, 9], [4, 10], [5, 6], [5, 8], [5, 9], [5, 10], [6, 8], [6, 9], [6, 10], [7, 8], [7, 10]]} | 1 |
construct-mc-pysms-num-edges-bounds-l3-s1 | construct | mc_pysms_num_edges_bounds | graph_existence_num_edges_bounds | graph_theory | competition | 3 | MathConstraint/pysms_num_edges_bounds | CC-BY-4.0 | [
"agentic_trivial",
"np_search"
] | Construct a simple undirected graph on the 14 vertices 0..13 such that:
- the number of edges is between 33 and 33 (inclusive)
Answer format: {"edges": [[u, v], ...]} where each edge is a pair of distinct vertices in 0..13, listed once
Write your final answer as JSON to `/workdir/answer.json`. The instance data is ... | {"vertices": 14, "required_edges": [], "max_edges": 33, "min_edges": 33, "family": "mc_pysms_num_edges_bounds", "subset": "construct"} | null | null | null | {"edges": [[0, 4], [0, 5], [0, 6], [0, 7], [0, 8], [0, 9], [0, 10], [0, 11], [0, 12], [0, 13], [1, 2], [1, 3], [1, 4], [1, 5], [1, 6], [1, 7], [1, 8], [1, 9], [1, 10], [1, 11], [1, 12], [1, 13], [2, 3], [2, 4], [2, 5], [2, 6], [2, 7], [2, 8], [2, 9], [2, 10], [2, 11], [2, 12], [2, 13]]} | 1 |
construct-mc-pysms-num-edges-bounds-l3-s2 | construct | mc_pysms_num_edges_bounds | graph_existence_num_edges_bounds | graph_theory | competition | 3 | MathConstraint/pysms_num_edges_bounds | CC-BY-4.0 | [
"agentic_trivial",
"np_search"
] | Construct a simple undirected graph on the 15 vertices 0..14 such that:
- the number of edges is between 28 and 37 (inclusive)
Answer format: {"edges": [[u, v], ...]} where each edge is a pair of distinct vertices in 0..14, listed once
Write your final answer as JSON to `/workdir/answer.json`. The instance data is ... | {"vertices": 15, "required_edges": [], "max_edges": 37, "min_edges": 28, "family": "mc_pysms_num_edges_bounds", "subset": "construct"} | null | null | null | {"edges": [[0, 3], [0, 4], [0, 5], [0, 6], [0, 7], [0, 8], [0, 9], [0, 10], [0, 11], [0, 12], [0, 13], [0, 14], [1, 2], [1, 3], [1, 4], [1, 5], [1, 6], [1, 7], [1, 8], [1, 9], [1, 10], [1, 11], [1, 12], [1, 13], [1, 14], [2, 3], [2, 4], [2, 5], [2, 6], [2, 7], [2, 8], [2, 9], [2, 10], [2, 11], [2, 12], [2, 13], [2, 14]... | 1 |
construct-mc-pysms-num-edges-bounds-l4-s0 | construct | mc_pysms_num_edges_bounds | graph_existence_num_edges_bounds | graph_theory | competition | 4 | MathConstraint/pysms_num_edges_bounds | CC-BY-4.0 | [
"agentic_trivial",
"np_search"
] | Construct a simple undirected graph on the 18 vertices 0..17 such that:
- the number of edges is between 34 and 40 (inclusive)
Answer format: {"edges": [[u, v], ...]} where each edge is a pair of distinct vertices in 0..17, listed once
Write your final answer as JSON to `/workdir/answer.json`. The instance data is ... | {"vertices": 18, "required_edges": [], "max_edges": 40, "min_edges": 34, "family": "mc_pysms_num_edges_bounds", "subset": "construct"} | null | null | null | {"edges": [[0, 6], [0, 7], [0, 8], [0, 9], [0, 10], [0, 11], [0, 12], [0, 13], [0, 14], [0, 15], [0, 16], [0, 17], [1, 2], [1, 3], [1, 4], [1, 5], [1, 7], [1, 8], [1, 9], [1, 10], [1, 11], [1, 12], [1, 13], [1, 14], [1, 15], [1, 16], [1, 17], [2, 5], [2, 6], [2, 17], [3, 4], [3, 8], [3, 9], [3, 10], [3, 11], [3, 12], [... | 1 |
construct-mc-pysms-num-edges-bounds-l4-s1 | construct | mc_pysms_num_edges_bounds | graph_existence_num_edges_bounds | graph_theory | competition | 4 | MathConstraint/pysms_num_edges_bounds | CC-BY-4.0 | [
"agentic_trivial",
"np_search"
] | Construct a simple undirected graph on the 11 vertices 0..10 such that:
- the number of edges is between 23 and 24 (inclusive)
Answer format: {"edges": [[u, v], ...]} where each edge is a pair of distinct vertices in 0..10, listed once
Write your final answer as JSON to `/workdir/answer.json`. The instance data is ... | {"vertices": 11, "required_edges": [], "max_edges": 24, "min_edges": 23, "family": "mc_pysms_num_edges_bounds", "subset": "construct"} | null | null | null | {"edges": [[0, 3], [0, 4], [0, 5], [0, 6], [0, 7], [0, 8], [0, 9], [0, 10], [1, 3], [1, 4], [1, 5], [1, 6], [1, 7], [1, 8], [1, 9], [1, 10], [2, 3], [2, 4], [2, 5], [2, 6], [2, 7], [2, 8], [2, 9], [2, 10]]} | 1 |
construct-mc-pysms-num-edges-bounds-l5-s0 | construct | mc_pysms_num_edges_bounds | graph_existence_num_edges_bounds | graph_theory | competition | 5 | MathConstraint/pysms_num_edges_bounds | CC-BY-4.0 | [
"agentic_trivial",
"np_search"
] | Construct a simple undirected graph on the 14 vertices 0..13 such that:
- the number of edges is between 16 and 41 (inclusive)
- it contains each of the following edges: (2,11), (1,5), (2,12), (2,4), (0,5), (3,7), (2,13), (3,13)
Answer format: {"edges": [[u, v], ...]} where each edge is a pair of distinct vertices... | {"vertices": 14, "required_edges": [[2, 11], [1, 5], [2, 12], [2, 4], [0, 5], [3, 7], [2, 13], [3, 13]], "max_edges": 41, "min_edges": 16, "family": "mc_pysms_num_edges_bounds", "subset": "construct"} | null | null | null | {"edges": [[0, 3], [0, 4], [0, 5], [0, 6], [0, 7], [0, 8], [0, 9], [0, 10], [0, 11], [0, 12], [0, 13], [1, 3], [1, 4], [1, 5], [1, 6], [1, 7], [1, 8], [1, 9], [1, 10], [1, 11], [1, 12], [1, 13], [2, 4], [2, 5], [2, 6], [2, 7], [2, 8], [2, 9], [2, 10], [2, 11], [2, 12], [2, 13], [3, 5], [3, 6], [3, 7], [3, 8], [3, 9], [... | 1 |
construct-mc-pysms-num-edges-bounds-l5-s1 | construct | mc_pysms_num_edges_bounds | graph_existence_num_edges_bounds | graph_theory | competition | 5 | MathConstraint/pysms_num_edges_bounds | CC-BY-4.0 | [
"agentic_trivial",
"np_search"
] | Construct a simple undirected graph on the 14 vertices 0..13 such that:
- the number of edges is between 14 and 40 (inclusive)
Answer format: {"edges": [[u, v], ...]} where each edge is a pair of distinct vertices in 0..13, listed once
Write your final answer as JSON to `/workdir/answer.json`. The instance data is ... | {"vertices": 14, "required_edges": [], "max_edges": 40, "min_edges": 14, "family": "mc_pysms_num_edges_bounds", "subset": "construct"} | null | null | null | {"edges": [[0, 2], [0, 3], [0, 4], [0, 5], [0, 6], [0, 7], [0, 8], [0, 9], [0, 10], [0, 11], [0, 12], [0, 13], [1, 2], [1, 3], [1, 4], [1, 5], [1, 6], [1, 7], [1, 8], [1, 9], [1, 10], [1, 11], [1, 12], [1, 13], [2, 8], [2, 9], [2, 10], [2, 11], [2, 12], [2, 13], [3, 4], [3, 5], [3, 6], [3, 7], [4, 5], [4, 6], [4, 7], [... | 1 |
construct-mc-pysms-num-edges-bounds-l5-s2 | construct | mc_pysms_num_edges_bounds | graph_existence_num_edges_bounds | graph_theory | competition | 5 | MathConstraint/pysms_num_edges_bounds | CC-BY-4.0 | [
"agentic_trivial",
"np_search"
] | Construct a simple undirected graph on the 13 vertices 0..12 such that:
- the number of edges is between 29 and 39 (inclusive)
Answer format: {"edges": [[u, v], ...]} where each edge is a pair of distinct vertices in 0..12, listed once
Write your final answer as JSON to `/workdir/answer.json`. The instance data is ... | {"vertices": 13, "required_edges": [], "max_edges": 39, "min_edges": 29, "family": "mc_pysms_num_edges_bounds", "subset": "construct"} | null | null | null | {"edges": [[0, 4], [0, 5], [0, 6], [0, 7], [0, 8], [0, 9], [0, 10], [0, 11], [0, 12], [1, 2], [1, 3], [1, 5], [1, 6], [1, 7], [1, 8], [1, 9], [1, 10], [1, 11], [1, 12], [2, 3], [2, 4], [2, 5], [2, 6], [2, 7], [2, 8], [2, 9], [2, 10], [2, 11], [2, 12], [3, 4], [3, 5], [3, 6], [3, 7], [3, 8], [3, 9], [3, 10], [3, 11], [3... | 1 |
construct-mc-quasigroup-idempotent-l1-s0 | construct | mc_quasigroup_idempotent | idempotent_qg3_quasigroup | algebra | competition | 1 | MathConstraint/quasigroup_idempotent | CC-BY-4.0 | [
"np_search"
] | Construct a quasigroup of order 4 on {0, ..., 3}: a 4x4 table T (T[x][y] = x*y) in which every row and every column is a permutation of 0..3, such that
- T[x][x] = x for all x (idempotent), and
- T[T[x][y]][T[y][x]] = x for all x, y (the identity (x*y)*(y*x) = x).
Answer format: {"table": [[row 0], ..., [row 3]]}
... | {"n": 4, "family": "mc_quasigroup_idempotent", "subset": "construct"} | null | null | null | {"table": [[0, 3, 1, 2], [2, 1, 3, 0], [3, 0, 2, 1], [1, 2, 0, 3]]} | 1 |
construct-mc-quasigroup-idempotent-l2-s0 | construct | mc_quasigroup_idempotent | idempotent_qg3_quasigroup | algebra | competition | 2 | MathConstraint/quasigroup_idempotent | CC-BY-4.0 | [
"np_search"
] | Construct a quasigroup of order 8 on {0, ..., 7}: a 8x8 table T (T[x][y] = x*y) in which every row and every column is a permutation of 0..7, such that
- T[x][x] = x for all x (idempotent), and
- T[T[x][y]][T[y][x]] = x for all x, y (the identity (x*y)*(y*x) = x).
Answer format: {"table": [[row 0], ..., [row 7]]}
... | {"n": 8, "family": "mc_quasigroup_idempotent", "subset": "construct"} | null | null | null | {"table": [[0, 3, 6, 5, 7, 4, 1, 2], [2, 1, 4, 7, 5, 6, 3, 0], [4, 7, 2, 1, 3, 0, 5, 6], [6, 5, 0, 3, 1, 2, 7, 4], [3, 0, 5, 6, 4, 7, 2, 1], [1, 2, 7, 4, 6, 5, 0, 3], [7, 4, 1, 2, 0, 3, 6, 5], [5, 6, 3, 0, 2, 1, 4, 7]]} | 1 |
construct-mc-quasigroup-idempotent-l3-s0 | construct | mc_quasigroup_idempotent | idempotent_qg3_quasigroup | algebra | competition | 3 | MathConstraint/quasigroup_idempotent | CC-BY-4.0 | [
"np_search"
] | Construct a quasigroup of order 12 on {0, ..., 11}: a 12x12 table T (T[x][y] = x*y) in which every row and every column is a permutation of 0..11, such that
- T[x][x] = x for all x (idempotent), and
- T[T[x][y]][T[y][x]] = x for all x, y (the identity (x*y)*(y*x) = x).
Answer format: {"table": [[row 0], ..., [row ... | {"n": 12, "family": "mc_quasigroup_idempotent", "subset": "construct"} | null | null | null | {"table": [[0, 6, 8, 1, 7, 3, 2, 11, 10, 4, 5, 9], [7, 1, 11, 4, 6, 9, 5, 8, 2, 3, 0, 10], [1, 10, 2, 5, 3, 11, 8, 6, 9, 0, 7, 4], [10, 2, 0, 3, 1, 8, 9, 4, 11, 7, 6, 5], [3, 5, 1, 9, 4, 7, 11, 2, 6, 10, 8, 0], [2, 11, 3, 6, 10, 5, 4, 1, 0, 8, 9, 7], [9, 7, 4, 10, 8, 1, 6, 0, 5, 11, 2, 3], [5, 9, 10, 0, 11, 6, 1, 7, 3,... | 1 |
construct-mc-quasigroup-idempotent-l3-s1 | construct | mc_quasigroup_idempotent | idempotent_qg3_quasigroup | algebra | competition | 3 | MathConstraint/quasigroup_idempotent | CC-BY-4.0 | [
"np_search"
] | Construct a quasigroup of order 13 on {0, ..., 12}: a 13x13 table T (T[x][y] = x*y) in which every row and every column is a permutation of 0..12, such that
- T[x][x] = x for all x (idempotent), and
- T[T[x][y]][T[y][x]] = x for all x, y (the identity (x*y)*(y*x) = x).
Answer format: {"table": [[row 0], ..., [row ... | {"n": 13, "family": "mc_quasigroup_idempotent", "subset": "construct"} | null | null | null | {"table": [[0, 3, 12, 9, 7, 4, 10, 5, 2, 1, 11, 6, 8], [9, 1, 4, 0, 10, 8, 5, 11, 6, 3, 2, 12, 7], [8, 10, 2, 5, 1, 11, 9, 6, 12, 7, 4, 3, 0], [1, 9, 11, 3, 6, 2, 12, 10, 7, 0, 8, 5, 4], [5, 2, 10, 12, 4, 7, 3, 0, 11, 8, 1, 9, 6], [7, 6, 3, 11, 0, 5, 8, 4, 1, 12, 9, 2, 10], [11, 8, 7, 4, 12, 1, 6, 9, 5, 2, 0, 10, 3], [... | 1 |
construct-mc-quasigroup-idempotent-l4-s0 | construct | mc_quasigroup_idempotent | idempotent_qg3_quasigroup | algebra | competition | 4 | MathConstraint/quasigroup_idempotent | CC-BY-4.0 | [
"np_search"
] | Construct a quasigroup of order 16 on {0, ..., 15}: a 16x16 table T (T[x][y] = x*y) in which every row and every column is a permutation of 0..15, such that
- T[x][x] = x for all x (idempotent), and
- T[T[x][y]][T[y][x]] = x for all x, y (the identity (x*y)*(y*x) = x).
Answer format: {"table": [[row 0], ..., [row ... | {"n": 16, "family": "mc_quasigroup_idempotent", "subset": "construct"} | null | null | null | {"table": [[0, 3, 6, 5, 12, 15, 10, 9, 11, 8, 13, 14, 7, 4, 1, 2], [2, 1, 4, 7, 14, 13, 8, 11, 9, 10, 15, 12, 5, 6, 3, 0], [4, 7, 2, 1, 8, 11, 14, 13, 15, 12, 9, 10, 3, 0, 5, 6], [6, 5, 0, 3, 10, 9, 12, 15, 13, 14, 11, 8, 1, 2, 7, 4], [8, 11, 14, 13, 4, 7, 2, 1, 3, 0, 5, 6, 15, 12, 9, 10], [10, 9, 12, 15, 6, 5, 0, 3, 1... | 1 |
construct-mc-quasigroup-idempotent-l4-s1 | construct | mc_quasigroup_idempotent | idempotent_qg3_quasigroup | algebra | competition | 4 | MathConstraint/quasigroup_idempotent | CC-BY-4.0 | [
"np_search"
] | Construct a quasigroup of order 29 on {0, ..., 28}: a 29x29 table T (T[x][y] = x*y) in which every row and every column is a permutation of 0..28, such that
- T[x][x] = x for all x (idempotent), and
- T[T[x][y]][T[y][x]] = x for all x, y (the identity (x*y)*(y*x) = x).
Answer format: {"table": [[row 0], ..., [row ... | {"n": 29, "family": "mc_quasigroup_idempotent", "subset": "construct"} | null | null | null | {"table": [[0, 2, 6, 9, 23, 7, 20, 14, 26, 1, 18, 4, 10, 24, 13, 27, 3, 22, 15, 28, 11, 5, 25, 17, 19, 21, 12, 8, 16], [17, 1, 3, 7, 10, 24, 8, 21, 15, 27, 2, 19, 5, 11, 25, 14, 28, 4, 23, 16, 0, 12, 6, 26, 18, 20, 22, 13, 9], [10, 18, 2, 4, 8, 11, 25, 9, 22, 16, 28, 3, 20, 6, 12, 26, 15, 0, 5, 24, 17, 1, 13, 7, 27, 19... | 1 |
construct-mc-quasigroup-idempotent-l5-s0 | construct | mc_quasigroup_idempotent | idempotent_qg3_quasigroup | algebra | competition | 5 | MathConstraint/quasigroup_idempotent | CC-BY-4.0 | [
"np_search"
] | Construct a quasigroup of order 32 on {0, ..., 31}: a 32x32 table T (T[x][y] = x*y) in which every row and every column is a permutation of 0..31, such that
- T[x][x] = x for all x (idempotent), and
- T[T[x][y]][T[y][x]] = x for all x, y (the identity (x*y)*(y*x) = x).
Answer format: {"table": [[row 0], ..., [row ... | {"n": 32, "family": "mc_quasigroup_idempotent", "subset": "construct"} | null | null | null | {"table": [[0, 3, 6, 5, 12, 15, 10, 9, 24, 27, 30, 29, 20, 23, 18, 17, 21, 22, 19, 16, 25, 26, 31, 28, 13, 14, 11, 8, 1, 2, 7, 4], [2, 1, 4, 7, 14, 13, 8, 11, 26, 25, 28, 31, 22, 21, 16, 19, 23, 20, 17, 18, 27, 24, 29, 30, 15, 12, 9, 10, 3, 0, 5, 6], [4, 7, 2, 1, 8, 11, 14, 13, 28, 31, 26, 25, 16, 19, 22, 21, 17, 18, 2... | 1 |
construct-mc-quasigroup-idempotent-l5-s1 | construct | mc_quasigroup_idempotent | idempotent_qg3_quasigroup | algebra | competition | 5 | MathConstraint/quasigroup_idempotent | CC-BY-4.0 | [
"np_search"
] | Construct a quasigroup of order 37 on {0, ..., 36}: a 37x37 table T (T[x][y] = x*y) in which every row and every column is a permutation of 0..36, such that
- T[x][x] = x for all x (idempotent), and
- T[T[x][y]][T[y][x]] = x for all x, y (the identity (x*y)*(y*x) = x).
Answer format: {"table": [[row 0], ..., [row ... | {"n": 37, "family": "mc_quasigroup_idempotent", "subset": "construct"} | null | null | null | {"table": [[0, 2, 22, 11, 27, 33, 10, 14, 1, 18, 20, 28, 24, 34, 6, 17, 32, 16, 13, 7, 35, 3, 12, 26, 5, 30, 15, 25, 4, 23, 36, 8, 19, 29, 31, 9, 21], [22, 1, 3, 23, 12, 28, 34, 11, 15, 2, 19, 21, 29, 25, 35, 7, 18, 33, 17, 14, 8, 36, 4, 13, 27, 6, 31, 16, 26, 5, 24, 0, 9, 20, 30, 32, 10], [11, 23, 2, 4, 24, 13, 29, 35... | 1 |
construct-mc-quasigroup-idempotent-l6-s0 | construct | mc_quasigroup_idempotent | idempotent_qg3_quasigroup | algebra | competition | 6 | MathConstraint/quasigroup_idempotent | CC-BY-4.0 | [
"np_search"
] | Construct a quasigroup of order 48 on {0, ..., 47}: a 48x48 table T (T[x][y] = x*y) in which every row and every column is a permutation of 0..47, such that
- T[x][x] = x for all x (idempotent), and
- T[T[x][y]][T[y][x]] = x for all x, y (the identity (x*y)*(y*x) = x).
Answer format: {"table": [[row 0], ..., [row ... | {"n": 48, "family": "mc_quasigroup_idempotent", "subset": "construct"} | null | null | null | {"table": [[0, 6, 8, 1, 7, 3, 2, 11, 10, 4, 5, 9, 36, 42, 44, 37, 43, 39, 38, 47, 46, 40, 41, 45, 12, 18, 20, 13, 19, 15, 14, 23, 22, 16, 17, 21, 24, 30, 32, 25, 31, 27, 26, 35, 34, 28, 29, 33], [7, 1, 11, 4, 6, 9, 5, 8, 2, 3, 0, 10, 43, 37, 47, 40, 42, 45, 41, 44, 38, 39, 36, 46, 19, 13, 23, 16, 18, 21, 17, 20, 14, 15... | 1 |
construct-mc-quasigroup-idempotent-l6-s1 | construct | mc_quasigroup_idempotent | idempotent_qg3_quasigroup | algebra | competition | 6 | MathConstraint/quasigroup_idempotent | CC-BY-4.0 | [
"np_search"
] | Construct a quasigroup of order 53 on {0, ..., 52}: a 53x53 table T (T[x][y] = x*y) in which every row and every column is a permutation of 0..52, such that
- T[x][x] = x for all x (idempotent), and
- T[T[x][y]][T[y][x]] = x for all x, y (the identity (x*y)*(y*x) = x).
Answer format: {"table": [[row 0], ..., [row ... | {"n": 53, "family": "mc_quasigroup_idempotent", "subset": "construct"} | null | null | null | {"table": [[0, 2, 22, 33, 16, 4, 24, 28, 17, 36, 20, 44, 52, 26, 43, 30, 32, 15, 25, 50, 8, 38, 7, 29, 48, 47, 21, 11, 3, 10, 12, 23, 34, 37, 6, 14, 19, 42, 46, 5, 1, 27, 31, 13, 35, 18, 39, 41, 51, 45, 40, 9, 49], [50, 1, 3, 23, 34, 17, 5, 25, 29, 18, 37, 21, 45, 0, 27, 44, 31, 33, 16, 26, 51, 9, 39, 8, 30, 49, 48, 22... | 1 |
construct-mc-quasigroup-idempotent-l6-s2 | construct | mc_quasigroup_idempotent | idempotent_qg3_quasigroup | algebra | competition | 6 | MathConstraint/quasigroup_idempotent | CC-BY-4.0 | [
"np_search"
] | Construct a quasigroup of order 52 on {0, ..., 51}: a 52x52 table T (T[x][y] = x*y) in which every row and every column is a permutation of 0..51, such that
- T[x][x] = x for all x (idempotent), and
- T[T[x][y]][T[y][x]] = x for all x, y (the identity (x*y)*(y*x) = x).
Answer format: {"table": [[row 0], ..., [row ... | {"n": 52, "family": "mc_quasigroup_idempotent", "subset": "construct"} | null | null | null | {"table": [[0, 3, 12, 9, 7, 4, 10, 5, 2, 1, 11, 6, 8, 39, 42, 51, 48, 46, 43, 49, 44, 41, 40, 50, 45, 47, 13, 16, 25, 22, 20, 17, 23, 18, 15, 14, 24, 19, 21, 26, 29, 38, 35, 33, 30, 36, 31, 28, 27, 37, 32, 34], [9, 1, 4, 0, 10, 8, 5, 11, 6, 3, 2, 12, 7, 48, 40, 43, 39, 49, 47, 44, 50, 45, 42, 41, 51, 46, 22, 14, 17, 13... | 1 |
construct-mc-quasigroup-idempotent-l6-s3 | construct | mc_quasigroup_idempotent | idempotent_qg3_quasigroup | algebra | competition | 6 | MathConstraint/quasigroup_idempotent | CC-BY-4.0 | [
"np_search"
] | Construct a quasigroup of order 64 on {0, ..., 63}: a 64x64 table T (T[x][y] = x*y) in which every row and every column is a permutation of 0..63, such that
- T[x][x] = x for all x (idempotent), and
- T[T[x][y]][T[y][x]] = x for all x, y (the identity (x*y)*(y*x) = x).
Answer format: {"table": [[row 0], ..., [row ... | {"n": 64, "family": "mc_quasigroup_idempotent", "subset": "construct"} | null | null | null | {"table": [[0, 3, 6, 5, 12, 15, 10, 9, 24, 27, 30, 29, 20, 23, 18, 17, 48, 51, 54, 53, 60, 63, 58, 57, 40, 43, 46, 45, 36, 39, 34, 33, 35, 32, 37, 38, 47, 44, 41, 42, 59, 56, 61, 62, 55, 52, 49, 50, 19, 16, 21, 22, 31, 28, 25, 26, 11, 8, 13, 14, 7, 4, 1, 2], [2, 1, 4, 7, 14, 13, 8, 11, 26, 25, 28, 31, 22, 21, 16, 19, 5... | 1 |
construct-mc-ramsey-l1-s0 | construct | mc_ramsey | ramsey_two_colouring | combinatorics | competition | 1 | MathConstraint/ramsey | CC-BY-4.0 | [
"np_search"
] | Colour each of the 28 edges of the complete graph K_8 (vertices 0..7) with colour 0 or 1 so that there is no set of 3 vertices whose connecting edges all have colour 0, and no set of 4 vertices whose connecting edges all have colour 1.
Answer format: {"colors": [c_0, ..., c_27]}, one entry (0 or 1) per edge (i, j) wit... | {"n": 8, "r": 3, "s": 4, "fixed": [], "family": "mc_ramsey", "subset": "construct"} | null | null | null | {"colors": [0, 1, 1, 1, 0, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 1, 1]} | 1 |
construct-mc-ramsey-l1-s1 | construct | mc_ramsey | ramsey_two_colouring | combinatorics | competition | 1 | MathConstraint/ramsey | CC-BY-4.0 | [
"np_search"
] | Colour each of the 15 edges of the complete graph K_6 (vertices 0..5) with colour 0 or 1 so that there is no set of 4 vertices whose connecting edges all have colour 0, and no set of 3 vertices whose connecting edges all have colour 1.
Answer format: {"colors": [c_0, ..., c_14]}, one entry (0 or 1) per edge (i, j) wit... | {"n": 6, "r": 4, "s": 3, "fixed": [], "family": "mc_ramsey", "subset": "construct"} | null | null | null | {"colors": [1, 0, 0, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1]} | 1 |
construct-mc-ramsey-l1-s2 | construct | mc_ramsey | ramsey_two_colouring | combinatorics | competition | 1 | MathConstraint/ramsey | CC-BY-4.0 | [
"np_search"
] | Colour each of the 10 edges of the complete graph K_5 (vertices 0..4) with colour 0 or 1 so that there is no set of 3 vertices whose connecting edges all have colour 0, and no set of 3 vertices whose connecting edges all have colour 1.
Answer format: {"colors": [c_0, ..., c_9]}, one entry (0 or 1) per edge (i, j) with... | {"n": 5, "r": 3, "s": 3, "fixed": [], "family": "mc_ramsey", "subset": "construct"} | null | null | null | {"colors": [0, 1, 1, 0, 0, 1, 1, 0, 1, 0]} | 1 |
construct-mc-ramsey-l1-s3 | construct | mc_ramsey | ramsey_two_colouring | combinatorics | competition | 1 | MathConstraint/ramsey | CC-BY-4.0 | [
"np_search"
] | Colour each of the 10 edges of the complete graph K_5 (vertices 0..4) with colour 0 or 1 so that there is no set of 4 vertices whose connecting edges all have colour 0, and no set of 3 vertices whose connecting edges all have colour 1.
Answer format: {"colors": [c_0, ..., c_9]}, one entry (0 or 1) per edge (i, j) with... | {"n": 5, "r": 4, "s": 3, "fixed": [], "family": "mc_ramsey", "subset": "construct"} | null | null | null | {"colors": [1, 0, 0, 1, 1, 0, 0, 1, 0, 1]} | 1 |
construct-mc-ramsey-l1-s4 | construct | mc_ramsey | ramsey_two_colouring | combinatorics | competition | 1 | MathConstraint/ramsey | CC-BY-4.0 | [
"np_search"
] | Colour each of the 10 edges of the complete graph K_5 (vertices 0..4) with colour 0 or 1 so that there is no set of 3 vertices whose connecting edges all have colour 0, and no set of 3 vertices whose connecting edges all have colour 1.
Some values are fixed in advance and your answer must agree with them:
colors[3] = ... | {"n": 5, "r": 3, "s": 3, "fixed": [["colors", 3, 1], ["colors", 9, 0]], "family": "mc_ramsey", "subset": "construct"} | null | null | null | {"colors": [0, 0, 1, 1, 1, 0, 1, 1, 0, 0]} | 1 |
construct-mc-ramsey-l1-s5 | construct | mc_ramsey | ramsey_two_colouring | combinatorics | competition | 1 | MathConstraint/ramsey | CC-BY-4.0 | [
"np_search"
] | Colour each of the 21 edges of the complete graph K_7 (vertices 0..6) with colour 0 or 1 so that there is no set of 4 vertices whose connecting edges all have colour 0, and no set of 3 vertices whose connecting edges all have colour 1.
Answer format: {"colors": [c_0, ..., c_20]}, one entry (0 or 1) per edge (i, j) wit... | {"n": 7, "r": 4, "s": 3, "fixed": [], "family": "mc_ramsey", "subset": "construct"} | null | null | null | {"colors": [1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1]} | 1 |
construct-mc-ramsey-l1-s6 | construct | mc_ramsey | ramsey_two_colouring | combinatorics | competition | 1 | MathConstraint/ramsey | CC-BY-4.0 | [
"np_search"
] | Colour each of the 21 edges of the complete graph K_7 (vertices 0..6) with colour 0 or 1 so that there is no set of 4 vertices whose connecting edges all have colour 0, and no set of 3 vertices whose connecting edges all have colour 1.
Some values are fixed in advance and your answer must agree with them:
colors[3] = ... | {"n": 7, "r": 4, "s": 3, "fixed": [["colors", 3, 0], ["colors", 7, 0], ["colors", 12, 0], ["colors", 18, 0]], "family": "mc_ramsey", "subset": "construct"} | null | null | null | {"colors": [0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0]} | 1 |
construct-mc-ramsey-l1-s7 | construct | mc_ramsey | ramsey_two_colouring | combinatorics | competition | 1 | MathConstraint/ramsey | CC-BY-4.0 | [
"np_search"
] | Colour each of the 28 edges of the complete graph K_8 (vertices 0..7) with colour 0 or 1 so that there is no set of 4 vertices whose connecting edges all have colour 0, and no set of 3 vertices whose connecting edges all have colour 1.
Answer format: {"colors": [c_0, ..., c_27]}, one entry (0 or 1) per edge (i, j) wit... | {"n": 8, "r": 4, "s": 3, "fixed": [], "family": "mc_ramsey", "subset": "construct"} | null | null | null | {"colors": [0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 1]} | 1 |
construct-mc-ramsey-l1-s8 | construct | mc_ramsey | ramsey_two_colouring | combinatorics | competition | 1 | MathConstraint/ramsey | CC-BY-4.0 | [
"np_search"
] | Colour each of the 15 edges of the complete graph K_6 (vertices 0..5) with colour 0 or 1 so that there is no set of 3 vertices whose connecting edges all have colour 0, and no set of 4 vertices whose connecting edges all have colour 1.
Answer format: {"colors": [c_0, ..., c_14]}, one entry (0 or 1) per edge (i, j) wit... | {"n": 6, "r": 3, "s": 4, "fixed": [], "family": "mc_ramsey", "subset": "construct"} | null | null | null | {"colors": [0, 1, 1, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0]} | 1 |
construct-mc-ramsey-l1-s9 | construct | mc_ramsey | ramsey_two_colouring | combinatorics | competition | 1 | MathConstraint/ramsey | CC-BY-4.0 | [
"np_search"
] | Colour each of the 10 edges of the complete graph K_5 (vertices 0..4) with colour 0 or 1 so that there is no set of 3 vertices whose connecting edges all have colour 0, and no set of 4 vertices whose connecting edges all have colour 1.
Answer format: {"colors": [c_0, ..., c_9]}, one entry (0 or 1) per edge (i, j) with... | {"n": 5, "r": 3, "s": 4, "fixed": [], "family": "mc_ramsey", "subset": "construct"} | null | null | null | {"colors": [0, 1, 1, 0, 0, 1, 1, 0, 1, 0]} | 1 |
construct-mc-ramsey-l2-s0 | construct | mc_ramsey | ramsey_two_colouring | combinatorics | competition | 2 | MathConstraint/ramsey | CC-BY-4.0 | [
"np_search"
] | Colour each of the 78 edges of the complete graph K_13 (vertices 0..12) with colour 0 or 1 so that there is no set of 6 vertices whose connecting edges all have colour 0, and no set of 3 vertices whose connecting edges all have colour 1.
Answer format: {"colors": [c_0, ..., c_77]}, one entry (0 or 1) per edge (i, j) w... | {"n": 13, "r": 6, "s": 3, "fixed": [], "family": "mc_ramsey", "subset": "construct"} | null | null | null | {"colors": [1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1]} | 1 |
construct-mc-ramsey-l2-s1 | construct | mc_ramsey | ramsey_two_colouring | combinatorics | competition | 2 | MathConstraint/ramsey | CC-BY-4.0 | [
"np_search"
] | Colour each of the 66 edges of the complete graph K_12 (vertices 0..11) with colour 0 or 1 so that there is no set of 3 vertices whose connecting edges all have colour 0, and no set of 5 vertices whose connecting edges all have colour 1.
Answer format: {"colors": [c_0, ..., c_65]}, one entry (0 or 1) per edge (i, j) w... | {"n": 12, "r": 3, "s": 5, "fixed": [], "family": "mc_ramsey", "subset": "construct"} | null | null | null | {"colors": [1, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 1, 0, 0, 1, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1]} | 1 |
construct-mc-ramsey-l2-s2 | construct | mc_ramsey | ramsey_two_colouring | combinatorics | competition | 2 | MathConstraint/ramsey | CC-BY-4.0 | [
"np_search"
] | Colour each of the 78 edges of the complete graph K_13 (vertices 0..12) with colour 0 or 1 so that there is no set of 3 vertices whose connecting edges all have colour 0, and no set of 6 vertices whose connecting edges all have colour 1.
Answer format: {"colors": [c_0, ..., c_77]}, one entry (0 or 1) per edge (i, j) w... | {"n": 13, "r": 3, "s": 6, "fixed": [], "family": "mc_ramsey", "subset": "construct"} | null | null | null | {"colors": [0, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 0, 1, 1, 0, 1, 0, 1, 1, 1, 1, 0, 1, 0, 1, 0, 1, 1, 1, 1, 0, 0, 1, 0, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0]} | 1 |
construct-mc-ramsey-l2-s3 | construct | mc_ramsey | ramsey_two_colouring | combinatorics | competition | 2 | MathConstraint/ramsey | CC-BY-4.0 | [
"np_search"
] | Colour each of the 45 edges of the complete graph K_10 (vertices 0..9) with colour 0 or 1 so that there is no set of 3 vertices whose connecting edges all have colour 0, and no set of 5 vertices whose connecting edges all have colour 1.
Answer format: {"colors": [c_0, ..., c_44]}, one entry (0 or 1) per edge (i, j) wi... | {"n": 10, "r": 3, "s": 5, "fixed": [], "family": "mc_ramsey", "subset": "construct"} | null | null | null | {"colors": [1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1]} | 1 |
construct-mc-ramsey-l2-s4 | construct | mc_ramsey | ramsey_two_colouring | combinatorics | competition | 2 | MathConstraint/ramsey | CC-BY-4.0 | [
"np_search"
] | Colour each of the 78 edges of the complete graph K_13 (vertices 0..12) with colour 0 or 1 so that there is no set of 5 vertices whose connecting edges all have colour 0, and no set of 3 vertices whose connecting edges all have colour 1.
Answer format: {"colors": [c_0, ..., c_77]}, one entry (0 or 1) per edge (i, j) w... | {"n": 13, "r": 5, "s": 3, "fixed": [], "family": "mc_ramsey", "subset": "construct"} | null | null | null | {"colors": [0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0]} | 1 |
construct-mc-ramsey-l2-s5 | construct | mc_ramsey | ramsey_two_colouring | combinatorics | competition | 2 | MathConstraint/ramsey | CC-BY-4.0 | [
"np_search"
] | Colour each of the 66 edges of the complete graph K_12 (vertices 0..11) with colour 0 or 1 so that there is no set of 4 vertices whose connecting edges all have colour 0, and no set of 4 vertices whose connecting edges all have colour 1.
Some values are fixed in advance and your answer must agree with them:
colors[7] ... | {"n": 12, "r": 4, "s": 4, "fixed": [["colors", 7, 0], ["colors", 9, 0], ["colors", 23, 1], ["colors", 27, 0], ["colors", 28, 0], ["colors", 29, 0], ["colors", 33, 1], ["colors", 34, 0], ["colors", 39, 1], ["colors", 40, 0], ["colors", 53, 0], ["colors", 58, 0], ["colors", 63, 0]], "family": "mc_ramsey", "subset": "cons... | null | null | null | {"colors": [1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 1, 1, 0, 1, 0, 1, 1, 1, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0, 0, 1]} | 1 |
construct-mc-ramsey-l2-s6 | construct | mc_ramsey | ramsey_two_colouring | combinatorics | competition | 2 | MathConstraint/ramsey | CC-BY-4.0 | [
"np_search"
] | Colour each of the 55 edges of the complete graph K_11 (vertices 0..10) with colour 0 or 1 so that there is no set of 5 vertices whose connecting edges all have colour 0, and no set of 3 vertices whose connecting edges all have colour 1.
Answer format: {"colors": [c_0, ..., c_54]}, one entry (0 or 1) per edge (i, j) w... | {"n": 11, "r": 5, "s": 3, "fixed": [], "family": "mc_ramsey", "subset": "construct"} | null | null | null | {"colors": [0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0]} | 1 |
construct-mc-ramsey-l2-s7 | construct | mc_ramsey | ramsey_two_colouring | combinatorics | competition | 2 | MathConstraint/ramsey | CC-BY-4.0 | [
"np_search"
] | Colour each of the 45 edges of the complete graph K_10 (vertices 0..9) with colour 0 or 1 so that there is no set of 5 vertices whose connecting edges all have colour 0, and no set of 3 vertices whose connecting edges all have colour 1.
Answer format: {"colors": [c_0, ..., c_44]}, one entry (0 or 1) per edge (i, j) wi... | {"n": 10, "r": 5, "s": 3, "fixed": [], "family": "mc_ramsey", "subset": "construct"} | null | null | null | {"colors": [0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0]} | 1 |
construct-mc-ramsey-l2-s8 | construct | mc_ramsey | ramsey_two_colouring | combinatorics | competition | 2 | MathConstraint/ramsey | CC-BY-4.0 | [
"np_search"
] | Colour each of the 78 edges of the complete graph K_13 (vertices 0..12) with colour 0 or 1 so that there is no set of 4 vertices whose connecting edges all have colour 0, and no set of 4 vertices whose connecting edges all have colour 1.
Some values are fixed in advance and your answer must agree with them:
colors[3] ... | {"n": 13, "r": 4, "s": 4, "fixed": [["colors", 3, 1], ["colors", 6, 0], ["colors", 13, 0], ["colors", 19, 0], ["colors", 27, 0], ["colors", 34, 1], ["colors", 35, 0], ["colors", 43, 1], ["colors", 56, 1], ["colors", 63, 0], ["colors", 65, 1], ["colors", 74, 0], ["colors", 75, 0], ["colors", 76, 0], ["colors", 77, 0]], ... | null | null | null | {"colors": [0, 1, 1, 1, 0, 1, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0, 0, 0, 1, 1, 1, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0]} | 1 |
construct-mc-ramsey-l2-s9 | construct | mc_ramsey | ramsey_two_colouring | combinatorics | competition | 2 | MathConstraint/ramsey | CC-BY-4.0 | [
"np_search"
] | Colour each of the 55 edges of the complete graph K_11 (vertices 0..10) with colour 0 or 1 so that there is no set of 3 vertices whose connecting edges all have colour 0, and no set of 5 vertices whose connecting edges all have colour 1.
Answer format: {"colors": [c_0, ..., c_54]}, one entry (0 or 1) per edge (i, j) w... | {"n": 11, "r": 3, "s": 5, "fixed": [], "family": "mc_ramsey", "subset": "construct"} | null | null | null | {"colors": [1, 0, 0, 1, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1]} | 1 |
construct-mc-ramsey-l3-s0 | construct | mc_ramsey | ramsey_two_colouring | combinatorics | competition | 3 | MathConstraint/ramsey | CC-BY-4.0 | [
"np_search"
] | Colour each of the 91 edges of the complete graph K_14 (vertices 0..13) with colour 0 or 1 so that there is no set of 4 vertices whose connecting edges all have colour 0, and no set of 4 vertices whose connecting edges all have colour 1.
Answer format: {"colors": [c_0, ..., c_90]}, one entry (0 or 1) per edge (i, j) w... | {"n": 14, "r": 4, "s": 4, "fixed": [], "family": "mc_ramsey", "subset": "construct"} | null | null | null | {"colors": [1, 1, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 0, 1, 1, 0, 1, 1, 0, 1, 0, 0, 0, 1, 1, 1, 1, 0, 1, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1]} | 1 |
construct-mc-ramsey-l3-s1 | construct | mc_ramsey | ramsey_two_colouring | combinatorics | competition | 3 | MathConstraint/ramsey | CC-BY-4.0 | [
"np_search"
] | Colour each of the 105 edges of the complete graph K_15 (vertices 0..14) with colour 0 or 1 so that there is no set of 4 vertices whose connecting edges all have colour 0, and no set of 4 vertices whose connecting edges all have colour 1.
Answer format: {"colors": [c_0, ..., c_104]}, one entry (0 or 1) per edge (i, j)... | {"n": 15, "r": 4, "s": 4, "fixed": [], "family": "mc_ramsey", "subset": "construct"} | null | null | null | {"colors": [1, 1, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 0, 1, 1, 0, 1, 1, 0, 1, 0, 0, 0, 1, 1, 1, 1, 0, 1, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1,... | 1 |
construct-mc-ramsey-l3-s2 | construct | mc_ramsey | ramsey_two_colouring | combinatorics | competition | 3 | MathConstraint/ramsey | CC-BY-4.0 | [
"np_search"
] | Colour each of the 105 edges of the complete graph K_15 (vertices 0..14) with colour 0 or 1 so that there is no set of 6 vertices whose connecting edges all have colour 0, and no set of 3 vertices whose connecting edges all have colour 1.
Answer format: {"colors": [c_0, ..., c_104]}, one entry (0 or 1) per edge (i, j)... | {"n": 15, "r": 6, "s": 3, "fixed": [], "family": "mc_ramsey", "subset": "construct"} | null | null | null | {"colors": [1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 1, 1,... | 1 |
construct-mc-ramsey-l3-s3 | construct | mc_ramsey | ramsey_two_colouring | combinatorics | competition | 3 | MathConstraint/ramsey | CC-BY-4.0 | [
"np_search"
] | Colour each of the 120 edges of the complete graph K_16 (vertices 0..15) with colour 0 or 1 so that there is no set of 3 vertices whose connecting edges all have colour 0, and no set of 6 vertices whose connecting edges all have colour 1.
Answer format: {"colors": [c_0, ..., c_119]}, one entry (0 or 1) per edge (i, j)... | {"n": 16, "r": 3, "s": 6, "fixed": [], "family": "mc_ramsey", "subset": "construct"} | null | null | null | {"colors": [0, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 0, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 0, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 0, 1, 1, 0, 1, 0, 1, 1, 1, 1, 0, 1, 0, 1, 0, 1, 1, 1, 1, 0, 0, 1, 0, 1, 1, 1, 1, 0, 1, 0, 1,... | 1 |
construct-mc-ramsey-l3-s4 | construct | mc_ramsey | ramsey_two_colouring | combinatorics | competition | 3 | MathConstraint/ramsey | CC-BY-4.0 | [
"np_search"
] | Colour each of the 91 edges of the complete graph K_14 (vertices 0..13) with colour 0 or 1 so that there is no set of 6 vertices whose connecting edges all have colour 0, and no set of 3 vertices whose connecting edges all have colour 1.
Answer format: {"colors": [c_0, ..., c_90]}, one entry (0 or 1) per edge (i, j) w... | {"n": 14, "r": 6, "s": 3, "fixed": [], "family": "mc_ramsey", "subset": "construct"} | null | null | null | {"colors": [1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1]} | 1 |
construct-mc-ramsey-l3-s5 | construct | mc_ramsey | ramsey_two_colouring | combinatorics | competition | 3 | MathConstraint/ramsey | CC-BY-4.0 | [
"np_search"
] | Colour each of the 136 edges of the complete graph K_17 (vertices 0..16) with colour 0 or 1 so that there is no set of 4 vertices whose connecting edges all have colour 0, and no set of 4 vertices whose connecting edges all have colour 1.
Answer format: {"colors": [c_0, ..., c_135]}, one entry (0 or 1) per edge (i, j)... | {"n": 17, "r": 4, "s": 4, "fixed": [], "family": "mc_ramsey", "subset": "construct"} | null | null | null | {"colors": [1, 1, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 1, 1, 1, 1, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 1, 1, 1, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 0, 1, 1, 0, 1, 1, 0, 1, 0, 0, 0, 1, 1, 1, 1, 0,... | 1 |
construct-mc-ramsey-l3-s6 | construct | mc_ramsey | ramsey_two_colouring | combinatorics | competition | 3 | MathConstraint/ramsey | CC-BY-4.0 | [
"np_search"
] | Colour each of the 91 edges of the complete graph K_14 (vertices 0..13) with colour 0 or 1 so that there is no set of 3 vertices whose connecting edges all have colour 0, and no set of 6 vertices whose connecting edges all have colour 1.
Answer format: {"colors": [c_0, ..., c_90]}, one entry (0 or 1) per edge (i, j) w... | {"n": 14, "r": 3, "s": 6, "fixed": [], "family": "mc_ramsey", "subset": "construct"} | null | null | null | {"colors": [0, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 0, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 0, 1, 1, 0, 1, 0, 1, 1, 1, 1, 0, 1, 0, 1, 0, 1, 1, 1, 1, 0, 0, 1, 0, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0]} | 1 |
construct-mc-ramsey-l3-s7 | construct | mc_ramsey | ramsey_two_colouring | combinatorics | competition | 3 | MathConstraint/ramsey | CC-BY-4.0 | [
"np_search"
] | Colour each of the 120 edges of the complete graph K_16 (vertices 0..15) with colour 0 or 1 so that there is no set of 6 vertices whose connecting edges all have colour 0, and no set of 3 vertices whose connecting edges all have colour 1.
Answer format: {"colors": [c_0, ..., c_119]}, one entry (0 or 1) per edge (i, j)... | {"n": 16, "r": 6, "s": 3, "fixed": [], "family": "mc_ramsey", "subset": "construct"} | null | null | null | {"colors": [1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0,... | 1 |
construct-mc-ramsey-l3-s8 | construct | mc_ramsey | ramsey_two_colouring | combinatorics | competition | 3 | MathConstraint/ramsey | CC-BY-4.0 | [
"np_search"
] | Colour each of the 120 edges of the complete graph K_16 (vertices 0..15) with colour 0 or 1 so that there is no set of 4 vertices whose connecting edges all have colour 0, and no set of 4 vertices whose connecting edges all have colour 1.
Answer format: {"colors": [c_0, ..., c_119]}, one entry (0 or 1) per edge (i, j)... | {"n": 16, "r": 4, "s": 4, "fixed": [], "family": "mc_ramsey", "subset": "construct"} | null | null | null | {"colors": [1, 1, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 1, 1, 1, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 0, 1, 1, 0, 1, 1, 0, 1, 0, 0, 0, 1, 1, 1, 1, 0, 1, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 0, 1, 1, 0, 1,... | 1 |
construct-mc-ramsey-l3-s9 | construct | mc_ramsey | ramsey_two_colouring | combinatorics | competition | 3 | MathConstraint/ramsey | CC-BY-4.0 | [
"np_search"
] | Colour each of the 105 edges of the complete graph K_15 (vertices 0..14) with colour 0 or 1 so that there is no set of 3 vertices whose connecting edges all have colour 0, and no set of 6 vertices whose connecting edges all have colour 1.
Answer format: {"colors": [c_0, ..., c_104]}, one entry (0 or 1) per edge (i, j)... | {"n": 15, "r": 3, "s": 6, "fixed": [], "family": "mc_ramsey", "subset": "construct"} | null | null | null | {"colors": [0, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 0, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 0, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 0, 1, 1, 0, 1, 0, 1, 1, 1, 1, 0, 1, 0, 1, 0, 1, 1, 1, 1, 0, 0, 1, 0, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 0,... | 1 |
construct-mc-ramsey-l4-s0 | construct | mc_ramsey | ramsey_two_colouring | combinatorics | competition | 4 | MathConstraint/ramsey | CC-BY-4.0 | [
"np_search"
] | Colour each of the 210 edges of the complete graph K_21 (vertices 0..20) with colour 0 or 1 so that there is no set of 3 vertices whose connecting edges all have colour 0, and no set of 7 vertices whose connecting edges all have colour 1.
Answer format: {"colors": [c_0, ..., c_209]}, one entry (0 or 1) per edge (i, j)... | {"n": 21, "r": 3, "s": 7, "fixed": [], "family": "mc_ramsey", "subset": "construct"} | null | null | null | {"colors": [1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1,... | 1 |
construct-mc-ramsey-l4-s1 | construct | mc_ramsey | ramsey_two_colouring | combinatorics | competition | 4 | MathConstraint/ramsey | CC-BY-4.0 | [
"np_search"
] | Colour each of the 190 edges of the complete graph K_20 (vertices 0..19) with colour 0 or 1 so that there is no set of 7 vertices whose connecting edges all have colour 0, and no set of 3 vertices whose connecting edges all have colour 1.
Answer format: {"colors": [c_0, ..., c_189]}, one entry (0 or 1) per edge (i, j)... | {"n": 20, "r": 7, "s": 3, "fixed": [], "family": "mc_ramsey", "subset": "construct"} | null | null | null | {"colors": [0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1,... | 1 |
construct-mc-ramsey-l4-s2 | construct | mc_ramsey | ramsey_two_colouring | combinatorics | competition | 4 | MathConstraint/ramsey | CC-BY-4.0 | [
"np_search"
] | Colour each of the 210 edges of the complete graph K_21 (vertices 0..20) with colour 0 or 1 so that there is no set of 4 vertices whose connecting edges all have colour 0, and no set of 5 vertices whose connecting edges all have colour 1.
Answer format: {"colors": [c_0, ..., c_209]}, one entry (0 or 1) per edge (i, j)... | {"n": 21, "r": 4, "s": 5, "fixed": [], "family": "mc_ramsey", "subset": "construct"} | null | null | null | {"colors": [0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 1, 1, 1, 0, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 1, 0, 1, 1, 0, 1, 1,... | 1 |
construct-mc-ramsey-l4-s3 | construct | mc_ramsey | ramsey_two_colouring | combinatorics | competition | 4 | MathConstraint/ramsey | CC-BY-4.0 | [
"np_search"
] | Colour each of the 231 edges of the complete graph K_22 (vertices 0..21) with colour 0 or 1 so that there is no set of 4 vertices whose connecting edges all have colour 0, and no set of 5 vertices whose connecting edges all have colour 1.
Answer format: {"colors": [c_0, ..., c_230]}, one entry (0 or 1) per edge (i, j)... | {"n": 22, "r": 4, "s": 5, "fixed": [], "family": "mc_ramsey", "subset": "construct"} | null | null | null | {"colors": [1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 0, 1, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 1, 1, 0,... | 1 |
construct-mc-ramsey-l4-s4 | construct | mc_ramsey | ramsey_two_colouring | combinatorics | competition | 4 | MathConstraint/ramsey | CC-BY-4.0 | [
"np_search"
] | Colour each of the 153 edges of the complete graph K_18 (vertices 0..17) with colour 0 or 1 so that there is no set of 7 vertices whose connecting edges all have colour 0, and no set of 3 vertices whose connecting edges all have colour 1.
Answer format: {"colors": [c_0, ..., c_152]}, one entry (0 or 1) per edge (i, j)... | {"n": 18, "r": 7, "s": 3, "fixed": [], "family": "mc_ramsey", "subset": "construct"} | null | null | null | {"colors": [0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1,... | 1 |
construct-mc-ramsey-l4-s5 | construct | mc_ramsey | ramsey_two_colouring | combinatorics | competition | 4 | MathConstraint/ramsey | CC-BY-4.0 | [
"np_search"
] | Colour each of the 171 edges of the complete graph K_19 (vertices 0..18) with colour 0 or 1 so that there is no set of 3 vertices whose connecting edges all have colour 0, and no set of 7 vertices whose connecting edges all have colour 1.
Answer format: {"colors": [c_0, ..., c_170]}, one entry (0 or 1) per edge (i, j)... | {"n": 19, "r": 3, "s": 7, "fixed": [], "family": "mc_ramsey", "subset": "construct"} | null | null | null | {"colors": [1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1,... | 1 |
construct-mc-ramsey-l4-s6 | construct | mc_ramsey | ramsey_two_colouring | combinatorics | competition | 4 | MathConstraint/ramsey | CC-BY-4.0 | [
"np_search"
] | Colour each of the 171 edges of the complete graph K_19 (vertices 0..18) with colour 0 or 1 so that there is no set of 7 vertices whose connecting edges all have colour 0, and no set of 3 vertices whose connecting edges all have colour 1.
Answer format: {"colors": [c_0, ..., c_170]}, one entry (0 or 1) per edge (i, j)... | {"n": 19, "r": 7, "s": 3, "fixed": [], "family": "mc_ramsey", "subset": "construct"} | null | null | null | {"colors": [0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0,... | 1 |
construct-mc-ramsey-l4-s7 | construct | mc_ramsey | ramsey_two_colouring | combinatorics | competition | 4 | MathConstraint/ramsey | CC-BY-4.0 | [
"np_search"
] | Colour each of the 190 edges of the complete graph K_20 (vertices 0..19) with colour 0 or 1 so that there is no set of 5 vertices whose connecting edges all have colour 0, and no set of 4 vertices whose connecting edges all have colour 1.
Answer format: {"colors": [c_0, ..., c_189]}, one entry (0 or 1) per edge (i, j)... | {"n": 20, "r": 5, "s": 4, "fixed": [], "family": "mc_ramsey", "subset": "construct"} | null | null | null | {"colors": [0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 0, 1, 1, 1, 1, 0, 0, 0, 0, 1,... | 1 |
construct-mc-ramsey-l4-s8 | construct | mc_ramsey | ramsey_two_colouring | combinatorics | competition | 4 | MathConstraint/ramsey | CC-BY-4.0 | [
"np_search"
] | Colour each of the 153 edges of the complete graph K_18 (vertices 0..17) with colour 0 or 1 so that there is no set of 3 vertices whose connecting edges all have colour 0, and no set of 7 vertices whose connecting edges all have colour 1.
Answer format: {"colors": [c_0, ..., c_152]}, one entry (0 or 1) per edge (i, j)... | {"n": 18, "r": 3, "s": 7, "fixed": [], "family": "mc_ramsey", "subset": "construct"} | null | null | null | {"colors": [1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0,... | 1 |
construct-mc-ramsey-l4-s9 | construct | mc_ramsey | ramsey_two_colouring | combinatorics | competition | 4 | MathConstraint/ramsey | CC-BY-4.0 | [
"np_search"
] | Colour each of the 190 edges of the complete graph K_20 (vertices 0..19) with colour 0 or 1 so that there is no set of 3 vertices whose connecting edges all have colour 0, and no set of 7 vertices whose connecting edges all have colour 1.
Answer format: {"colors": [c_0, ..., c_189]}, one entry (0 or 1) per edge (i, j)... | {"n": 20, "r": 3, "s": 7, "fixed": [], "family": "mc_ramsey", "subset": "construct"} | null | null | null | {"colors": [1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0,... | 1 |
construct-mc-ramsey-l5-s0 | construct | mc_ramsey | ramsey_two_colouring | combinatorics | competition | 5 | MathConstraint/ramsey | CC-BY-4.0 | [
"np_search"
] | Colour each of the 300 edges of the complete graph K_25 (vertices 0..24) with colour 0 or 1 so that there is no set of 8 vertices whose connecting edges all have colour 0, and no set of 3 vertices whose connecting edges all have colour 1.
Answer format: {"colors": [c_0, ..., c_299]}, one entry (0 or 1) per edge (i, j)... | {"n": 25, "r": 8, "s": 3, "fixed": [], "family": "mc_ramsey", "subset": "construct"} | null | null | null | {"colors": [0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 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, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 1,... | 1 |
construct-mc-ramsey-l5-s1 | construct | mc_ramsey | ramsey_two_colouring | combinatorics | competition | 5 | MathConstraint/ramsey | CC-BY-4.0 | [
"np_search"
] | Colour each of the 276 edges of the complete graph K_24 (vertices 0..23) with colour 0 or 1 so that there is no set of 4 vertices whose connecting edges all have colour 0, and no set of 5 vertices whose connecting edges all have colour 1.
Answer format: {"colors": [c_0, ..., c_275]}, one entry (0 or 1) per edge (i, j)... | {"n": 24, "r": 4, "s": 5, "fixed": [], "family": "mc_ramsey", "subset": "construct"} | null | null | null | {"colors": [0, 0, 1, 0, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 0, 1, 0, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 0, 1, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 0, 0, 1,... | 1 |
construct-mc-ramsey-l5-s2 | construct | mc_ramsey | ramsey_two_colouring | combinatorics | competition | 5 | MathConstraint/ramsey | CC-BY-4.0 | [
"np_search"
] | Colour each of the 210 edges of the complete graph K_21 (vertices 0..20) with colour 0 or 1 so that there is no set of 5 vertices whose connecting edges all have colour 0, and no set of 5 vertices whose connecting edges all have colour 1.
Answer format: {"colors": [c_0, ..., c_209]}, one entry (0 or 1) per edge (i, j)... | {"n": 21, "r": 5, "s": 5, "fixed": [], "family": "mc_ramsey", "subset": "construct"} | null | null | null | {"colors": [0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 1, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0,... | 1 |
construct-mc-ramsey-l5-s3 | construct | mc_ramsey | ramsey_two_colouring | combinatorics | competition | 5 | MathConstraint/ramsey | CC-BY-4.0 | [
"np_search"
] | Colour each of the 276 edges of the complete graph K_24 (vertices 0..23) with colour 0 or 1 so that there is no set of 5 vertices whose connecting edges all have colour 0, and no set of 4 vertices whose connecting edges all have colour 1.
Answer format: {"colors": [c_0, ..., c_275]}, one entry (0 or 1) per edge (i, j)... | {"n": 24, "r": 5, "s": 4, "fixed": [], "family": "mc_ramsey", "subset": "construct"} | null | null | null | {"colors": [1, 1, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 1, 1, 1, 1, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 1, 1, 1, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 1, 0,... | 1 |
construct-mc-ramsey-l5-s4 | construct | mc_ramsey | ramsey_two_colouring | combinatorics | competition | 5 | MathConstraint/ramsey | CC-BY-4.0 | [
"np_search"
] | Colour each of the 276 edges of the complete graph K_24 (vertices 0..23) with colour 0 or 1 so that there is no set of 3 vertices whose connecting edges all have colour 0, and no set of 8 vertices whose connecting edges all have colour 1.
Answer format: {"colors": [c_0, ..., c_275]}, one entry (0 or 1) per edge (i, j)... | {"n": 24, "r": 3, "s": 8, "fixed": [], "family": "mc_ramsey", "subset": "construct"} | null | null | null | {"colors": [1, 1, 1, 0, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 1, 0, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 0, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1,... | 1 |
construct-mc-ramsey-l5-s5 | construct | mc_ramsey | ramsey_two_colouring | combinatorics | competition | 5 | MathConstraint/ramsey | CC-BY-4.0 | [
"np_search"
] | Colour each of the 253 edges of the complete graph K_23 (vertices 0..22) with colour 0 or 1 so that there is no set of 8 vertices whose connecting edges all have colour 0, and no set of 3 vertices whose connecting edges all have colour 1.
Answer format: {"colors": [c_0, ..., c_252]}, one entry (0 or 1) per edge (i, j)... | {"n": 23, "r": 8, "s": 3, "fixed": [], "family": "mc_ramsey", "subset": "construct"} | null | null | null | {"colors": [0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0,... | 1 |
construct-mc-ramsey-l5-s6 | construct | mc_ramsey | ramsey_two_colouring | combinatorics | competition | 5 | MathConstraint/ramsey | CC-BY-4.0 | [
"np_search"
] | Colour each of the 253 edges of the complete graph K_23 (vertices 0..22) with colour 0 or 1 so that there is no set of 5 vertices whose connecting edges all have colour 0, and no set of 4 vertices whose connecting edges all have colour 1.
Answer format: {"colors": [c_0, ..., c_252]}, one entry (0 or 1) per edge (i, j)... | {"n": 23, "r": 5, "s": 4, "fixed": [], "family": "mc_ramsey", "subset": "construct"} | null | null | null | {"colors": [1, 1, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 1, 1, 1, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1, 0,... | 1 |
construct-mc-ramsey-l5-s7 | construct | mc_ramsey | ramsey_two_colouring | combinatorics | competition | 5 | MathConstraint/ramsey | CC-BY-4.0 | [
"np_search"
] | Colour each of the 253 edges of the complete graph K_23 (vertices 0..22) with colour 0 or 1 so that there is no set of 3 vertices whose connecting edges all have colour 0, and no set of 8 vertices whose connecting edges all have colour 1.
Answer format: {"colors": [c_0, ..., c_252]}, one entry (0 or 1) per edge (i, j)... | {"n": 23, "r": 3, "s": 8, "fixed": [], "family": "mc_ramsey", "subset": "construct"} | null | null | null | {"colors": [1, 1, 1, 0, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 0, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1,... | 1 |
construct-mc-ramsey-l5-s8 | construct | mc_ramsey | ramsey_two_colouring | combinatorics | competition | 5 | MathConstraint/ramsey | CC-BY-4.0 | [
"np_search"
] | Colour each of the 325 edges of the complete graph K_26 (vertices 0..25) with colour 0 or 1 so that there is no set of 8 vertices whose connecting edges all have colour 0, and no set of 3 vertices whose connecting edges all have colour 1.
Answer format: {"colors": [c_0, ..., c_324]}, one entry (0 or 1) per edge (i, j)... | {"n": 26, "r": 8, "s": 3, "fixed": [], "family": "mc_ramsey", "subset": "construct"} | null | null | null | {"colors": [0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 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, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0, 1, 1, 0, 1, 0, 0,... | 1 |
construct-mc-ramsey-l5-s9 | construct | mc_ramsey | ramsey_two_colouring | combinatorics | competition | 5 | MathConstraint/ramsey | CC-BY-4.0 | [
"np_search"
] | Colour each of the 276 edges of the complete graph K_24 (vertices 0..23) with colour 0 or 1 so that there is no set of 8 vertices whose connecting edges all have colour 0, and no set of 3 vertices whose connecting edges all have colour 1.
Answer format: {"colors": [c_0, ..., c_275]}, one entry (0 or 1) per edge (i, j)... | {"n": 24, "r": 8, "s": 3, "fixed": [], "family": "mc_ramsey", "subset": "construct"} | null | null | null | {"colors": [0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0,... | 1 |
construct-mc-ramsey-l6-s0 | construct | mc_ramsey | ramsey_two_colouring | combinatorics | competition | 6 | MathConstraint/ramsey | CC-BY-4.0 | [
"np_search"
] | Colour each of the 630 edges of the complete graph K_36 (vertices 0..35) with colour 0 or 1 so that there is no set of 5 vertices whose connecting edges all have colour 0, and no set of 5 vertices whose connecting edges all have colour 1.
Answer format: {"colors": [c_0, ..., c_629]}, one entry (0 or 1) per edge (i, j)... | {"n": 36, "r": 5, "s": 5, "fixed": [], "family": "mc_ramsey", "subset": "construct"} | null | null | null | {"colors": [0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 1, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0,... | 1 |
construct-mc-ramsey-l6-s1 | construct | mc_ramsey | ramsey_two_colouring | combinatorics | competition | 6 | MathConstraint/ramsey | CC-BY-4.0 | [
"np_search"
] | Colour each of the 666 edges of the complete graph K_37 (vertices 0..36) with colour 0 or 1 so that there is no set of 5 vertices whose connecting edges all have colour 0, and no set of 5 vertices whose connecting edges all have colour 1.
Answer format: {"colors": [c_0, ..., c_665]}, one entry (0 or 1) per edge (i, j)... | {"n": 37, "r": 5, "s": 5, "fixed": [], "family": "mc_ramsey", "subset": "construct"} | null | null | null | {"colors": [0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 1, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 0, 0, 0, 1, 0, 1, 1,... | 1 |
construct-mc-ramsey-l6-s2 | construct | mc_ramsey | ramsey_two_colouring | combinatorics | competition | 6 | MathConstraint/ramsey | CC-BY-4.0 | [
"np_search"
] | Colour each of the 595 edges of the complete graph K_35 (vertices 0..34) with colour 0 or 1 so that there is no set of 5 vertices whose connecting edges all have colour 0, and no set of 5 vertices whose connecting edges all have colour 1.
Answer format: {"colors": [c_0, ..., c_594]}, one entry (0 or 1) per edge (i, j)... | {"n": 35, "r": 5, "s": 5, "fixed": [], "family": "mc_ramsey", "subset": "construct"} | null | null | null | {"colors": [0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 0, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0,... | 1 |
construct-mc-ramsey-l6-s3 | construct | mc_ramsey | ramsey_two_colouring | combinatorics | competition | 6 | MathConstraint/ramsey | CC-BY-4.0 | [
"np_search"
] | Colour each of the 561 edges of the complete graph K_34 (vertices 0..33) with colour 0 or 1 so that there is no set of 5 vertices whose connecting edges all have colour 0, and no set of 5 vertices whose connecting edges all have colour 1.
Answer format: {"colors": [c_0, ..., c_560]}, one entry (0 or 1) per edge (i, j)... | {"n": 34, "r": 5, "s": 5, "fixed": [], "family": "mc_ramsey", "subset": "construct"} | null | null | null | {"colors": [0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 0, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 1, 1, 0,... | 1 |
construct-mc-social-golfers-l1-s0 | construct | mc_social_golfers | social_golfer | combinatorics | competition | 1 | MathConstraint/social_golfers | CC-BY-4.0 | [
"np_search"
] | Schedule 9 golfers (numbered 0..8) for 4 weeks. Every week the golfers are split into 3 groups (numbered 0..2) of exactly 3 golfers each. No two golfers may play in the same group in more than one week.
Find such a schedule.
Answer format: {"schedule": [week_0, ..., week_3]} where week_t is a list of 9 integers and w... | {"n_groups": 3, "group_size": 3, "n_weeks": 4, "family": "mc_social_golfers", "subset": "construct"} | null | null | null | {"schedule": [[0, 1, 2, 0, 1, 2, 0, 1, 2], [0, 1, 2, 2, 0, 1, 1, 2, 0], [0, 1, 2, 1, 2, 0, 2, 0, 1], [0, 0, 0, 1, 1, 1, 2, 2, 2]]} | 1 |
construct-mc-social-golfers-l1-s1 | construct | mc_social_golfers | social_golfer | combinatorics | competition | 1 | MathConstraint/social_golfers | CC-BY-4.0 | [
"np_search"
] | Schedule 25 golfers (numbered 0..24) for 3 weeks. Every week the golfers are split into 5 groups (numbered 0..4) of exactly 5 golfers each. No two golfers may play in the same group in more than one week.
Find such a schedule.
Answer format: {"schedule": [week_0, ..., week_2]} where week_t is a list of 25 integers an... | {"n_groups": 5, "group_size": 5, "n_weeks": 3, "family": "mc_social_golfers", "subset": "construct"} | null | null | null | {"schedule": [[0, 1, 2, 3, 4, 0, 1, 2, 3, 4, 0, 1, 2, 3, 4, 0, 1, 2, 3, 4, 0, 1, 2, 3, 4], [0, 1, 2, 3, 4, 4, 0, 1, 2, 3, 3, 4, 0, 1, 2, 2, 3, 4, 0, 1, 1, 2, 3, 4, 0], [0, 1, 2, 3, 4, 3, 4, 0, 1, 2, 1, 2, 3, 4, 0, 4, 0, 1, 2, 3, 2, 3, 4, 0, 1]]} | 1 |
construct-mc-social-golfers-l1-s2 | construct | mc_social_golfers | social_golfer | combinatorics | competition | 1 | MathConstraint/social_golfers | CC-BY-4.0 | [
"np_search"
] | Schedule 16 golfers (numbered 0..15) for 3 weeks. Every week the golfers are split into 4 groups (numbered 0..3) of exactly 4 golfers each. No two golfers may play in the same group in more than one week.
Find such a schedule.
Answer format: {"schedule": [week_0, ..., week_2]} where week_t is a list of 16 integers an... | {"n_groups": 4, "group_size": 4, "n_weeks": 3, "family": "mc_social_golfers", "subset": "construct"} | null | null | null | {"schedule": [[0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3], [0, 1, 2, 3, 1, 0, 3, 2, 2, 3, 0, 1, 3, 2, 1, 0], [0, 1, 2, 3, 2, 3, 0, 1, 3, 2, 1, 0, 1, 0, 3, 2]]} | 1 |
construct-mc-social-golfers-l2-s0 | construct | mc_social_golfers | social_golfer | combinatorics | competition | 2 | MathConstraint/social_golfers | CC-BY-4.0 | [
"np_search"
] | Schedule 24 golfers (numbered 0..23) for 4 weeks. Every week the golfers are split into 6 groups (numbered 0..5) of exactly 4 golfers each. No two golfers may play in the same group in more than one week.
Find such a schedule.
Answer format: {"schedule": [week_0, ..., week_3]} where week_t is a list of 24 integers an... | {"n_groups": 6, "group_size": 4, "n_weeks": 4, "family": "mc_social_golfers", "subset": "construct"} | null | null | null | {"schedule": [[0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5], [4, 3, 0, 1, 2, 3, 1, 5, 2, 4, 0, 1, 3, 5, 2, 0, 5, 4, 1, 0, 2, 4, 3, 5], [5, 0, 3, 2, 5, 4, 0, 2, 1, 4, 5, 3, 1, 3, 2, 0, 0, 2, 1, 4, 3, 1, 5, 4], [0, 1, 2, 3, 1, 0, 2, 4, 0, 1, 3, 5, 4, 3, 5, 0, 5, 2, 1, 4, 4, 3, 5, 2]]} | 1 |
construct-mc-social-golfers-l2-s1 | construct | mc_social_golfers | social_golfer | combinatorics | competition | 2 | MathConstraint/social_golfers | CC-BY-4.0 | [
"np_search"
] | Schedule 27 golfers (numbered 0..26) for 7 weeks. Every week the golfers are split into 9 groups (numbered 0..8) of exactly 3 golfers each. No two golfers may play in the same group in more than one week.
Find such a schedule.
Answer format: {"schedule": [week_0, ..., week_6]} where week_t is a list of 27 integers an... | {"n_groups": 9, "group_size": 3, "n_weeks": 7, "family": "mc_social_golfers", "subset": "construct"} | null | null | null | {"schedule": [[0, 0, 0, 1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4, 5, 5, 5, 6, 6, 6, 7, 7, 7, 8, 8, 8], [8, 1, 0, 5, 0, 3, 6, 2, 5, 6, 8, 7, 6, 7, 4, 2, 5, 1, 2, 4, 7, 3, 1, 4, 8, 3, 0], [6, 7, 8, 8, 5, 4, 7, 4, 5, 1, 3, 0, 0, 1, 2, 2, 6, 3, 3, 4, 5, 6, 8, 7, 1, 2, 0], [8, 7, 4, 3, 6, 7, 8, 3, 4, 4, 5, 7, 2, 0, 8, 0, 1, 2, 1,... | 1 |
construct-mc-social-golfers-l2-s2 | construct | mc_social_golfers | social_golfer | combinatorics | competition | 2 | MathConstraint/social_golfers | CC-BY-4.0 | [
"np_search"
] | Schedule 27 golfers (numbered 0..26) for 6 weeks. Every week the golfers are split into 9 groups (numbered 0..8) of exactly 3 golfers each. No two golfers may play in the same group in more than one week.
Find such a schedule.
Answer format: {"schedule": [week_0, ..., week_5]} where week_t is a list of 27 integers an... | {"n_groups": 9, "group_size": 3, "n_weeks": 6, "family": "mc_social_golfers", "subset": "construct"} | null | null | null | {"schedule": [[0, 0, 0, 1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4, 5, 5, 5, 6, 6, 6, 7, 7, 7, 8, 8, 8], [0, 1, 2, 2, 3, 4, 3, 4, 5, 3, 4, 5, 5, 6, 7, 6, 7, 8, 6, 8, 7, 1, 0, 2, 8, 1, 0], [1, 0, 2, 3, 2, 4, 3, 5, 4, 4, 3, 5, 6, 5, 7, 7, 8, 6, 8, 7, 6, 1, 8, 0, 1, 2, 0], [2, 3, 4, 3, 2, 4, 4, 5, 6, 5, 7, 8, 7, 6, 8, 7, 5, 6, 8,... | 1 |
construct-mc-social-golfers-l2-s3 | construct | mc_social_golfers | social_golfer | combinatorics | competition | 2 | MathConstraint/social_golfers | CC-BY-4.0 | [
"np_search"
] | Schedule 32 golfers (numbered 0..31) for 6 weeks. Every week the golfers are split into 8 groups (numbered 0..7) of exactly 4 golfers each. No two golfers may play in the same group in more than one week.
Find such a schedule.
Answer format: {"schedule": [week_0, ..., week_5]} where week_t is a list of 32 integers an... | {"n_groups": 8, "group_size": 4, "n_weeks": 6, "family": "mc_social_golfers", "subset": "construct"} | null | null | null | {"schedule": [[0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 6, 6, 6, 6, 7, 7, 7, 7], [3, 0, 1, 2, 7, 1, 2, 0, 1, 6, 0, 2, 6, 7, 5, 4, 7, 6, 4, 2, 5, 7, 0, 3, 4, 5, 3, 1, 5, 6, 4, 3], [5, 7, 3, 4, 0, 2, 5, 6, 6, 4, 3, 7, 5, 6, 1, 0, 5, 7, 4, 3, 7, 4, 2, 1, 6, 0, 2, 1, 3, 2, 1, 0], [1, 3, 0, 2,... | 1 |
construct-mc-social-golfers-l3-s0 | construct | mc_social_golfers | social_golfer | combinatorics | competition | 3 | MathConstraint/social_golfers | CC-BY-4.0 | [
"np_search"
] | Schedule 30 golfers (numbered 0..29) for 7 weeks. Every week the golfers are split into 10 groups (numbered 0..9) of exactly 3 golfers each. No two golfers may play in the same group in more than one week.
Find such a schedule.
Answer format: {"schedule": [week_0, ..., week_6]} where week_t is a list of 30 integers a... | {"n_groups": 10, "group_size": 3, "n_weeks": 7, "family": "mc_social_golfers", "subset": "construct"} | null | null | null | {"schedule": [[0, 0, 0, 1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4, 5, 5, 5, 6, 6, 6, 7, 7, 7, 8, 8, 8, 9, 9, 9], [0, 1, 2, 3, 0, 8, 4, 0, 5, 7, 8, 3, 3, 1, 9, 4, 1, 6, 6, 9, 5, 4, 2, 7, 6, 9, 5, 7, 8, 2], [9, 7, 8, 8, 6, 9, 9, 7, 6, 1, 5, 0, 3, 0, 1, 8, 5, 4, 5, 3, 2, 1, 7, 4, 3, 2, 0, 6, 4, 2], [7, 8, 6, 8, 9, 3, 2, 3, 4, 4,... | 1 |
construct-mc-social-golfers-l3-s1 | construct | mc_social_golfers | social_golfer | combinatorics | competition | 3 | MathConstraint/social_golfers | CC-BY-4.0 | [
"np_search"
] | Schedule 24 golfers (numbered 0..23) for 5 weeks. Every week the golfers are split into 8 groups (numbered 0..7) of exactly 3 golfers each. No two golfers may play in the same group in more than one week.
Find such a schedule.
Answer format: {"schedule": [week_0, ..., week_4]} where week_t is a list of 24 integers an... | {"n_groups": 8, "group_size": 3, "n_weeks": 5, "family": "mc_social_golfers", "subset": "construct"} | null | null | null | {"schedule": [[0, 0, 0, 1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4, 5, 5, 5, 6, 6, 6, 7, 7, 7], [3, 4, 5, 3, 4, 5, 4, 6, 7, 5, 6, 7, 2, 1, 0, 6, 2, 3, 7, 1, 0, 2, 1, 0], [0, 1, 2, 1, 0, 3, 2, 0, 1, 4, 2, 3, 3, 4, 5, 5, 6, 7, 6, 7, 4, 7, 5, 6], [0, 1, 2, 2, 3, 4, 4, 5, 3, 3, 6, 5, 6, 7, 4, 7, 5, 6, 7, 0, 1, 2, 1, 0], [1, 0, 2, ... | 1 |
construct-mc-social-golfers-l3-s2 | construct | mc_social_golfers | social_golfer | combinatorics | competition | 3 | MathConstraint/social_golfers | CC-BY-4.0 | [
"np_search"
] | Schedule 30 golfers (numbered 0..29) for 8 weeks. Every week the golfers are split into 10 groups (numbered 0..9) of exactly 3 golfers each. No two golfers may play in the same group in more than one week.
Find such a schedule.
Answer format: {"schedule": [week_0, ..., week_7]} where week_t is a list of 30 integers a... | {"n_groups": 10, "group_size": 3, "n_weeks": 8, "family": "mc_social_golfers", "subset": "construct"} | null | null | null | {"schedule": [[0, 0, 0, 1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4, 5, 5, 5, 6, 6, 6, 7, 7, 7, 8, 8, 8, 9, 9, 9], [0, 1, 2, 3, 0, 8, 4, 0, 5, 7, 8, 3, 3, 1, 9, 4, 1, 6, 6, 9, 5, 4, 2, 7, 6, 9, 5, 7, 8, 2], [9, 7, 8, 8, 7, 9, 7, 6, 5, 1, 5, 0, 3, 0, 1, 8, 5, 4, 6, 3, 2, 1, 9, 4, 3, 2, 0, 6, 4, 2], [7, 8, 6, 8, 9, 3, 2, 3, 4, 3,... | 1 |
construct-mc-social-golfers-l3-s3 | construct | mc_social_golfers | social_golfer | combinatorics | competition | 3 | MathConstraint/social_golfers | CC-BY-4.0 | [
"np_search"
] | Schedule 36 golfers (numbered 0..35) for 6 weeks. Every week the golfers are split into 9 groups (numbered 0..8) of exactly 4 golfers each. No two golfers may play in the same group in more than one week.
Find such a schedule.
Answer format: {"schedule": [week_0, ..., week_5]} where week_t is a list of 36 integers an... | {"n_groups": 9, "group_size": 4, "n_weeks": 6, "family": "mc_social_golfers", "subset": "construct"} | null | null | null | {"schedule": [[0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 6, 6, 6, 6, 7, 7, 7, 7, 8, 8, 8, 8], [8, 5, 3, 4, 7, 6, 0, 1, 8, 7, 1, 0, 8, 2, 0, 3, 6, 5, 2, 1, 7, 2, 0, 4, 7, 6, 2, 1, 8, 4, 5, 3, 6, 3, 4, 5], [1, 2, 0, 4, 7, 0, 5, 2, 2, 1, 0, 8, 4, 1, 3, 2, 8, 7, 5, 6, 5, 6, 7, 3, 3, 6, 4, 8, 0... | 1 |
construct-mc-social-golfers-l4-s0 | construct | mc_social_golfers | social_golfer | combinatorics | competition | 4 | MathConstraint/social_golfers | CC-BY-4.0 | [
"np_search"
] | Schedule 24 golfers (numbered 0..23) for 8 weeks. Every week the golfers are split into 8 groups (numbered 0..7) of exactly 3 golfers each. No two golfers may play in the same group in more than one week.
Find such a schedule.
Answer format: {"schedule": [week_0, ..., week_7]} where week_t is a list of 24 integers an... | {"n_groups": 8, "group_size": 3, "n_weeks": 8, "family": "mc_social_golfers", "subset": "construct"} | null | null | null | {"schedule": [[0, 0, 0, 1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4, 5, 5, 5, 6, 6, 6, 7, 7, 7], [2, 7, 5, 2, 4, 3, 1, 6, 0, 0, 4, 1, 1, 5, 3, 0, 6, 7, 4, 6, 7, 5, 3, 2], [3, 4, 5, 1, 3, 2, 4, 1, 6, 1, 0, 2, 7, 4, 5, 2, 5, 6, 6, 0, 7, 0, 3, 7], [4, 0, 3, 1, 7, 5, 6, 3, 5, 4, 2, 1, 3, 7, 4, 2, 0, 6, 0, 1, 7, 6, 2, 5], [0, 1, 7, ... | 1 |
construct-mc-social-golfers-l4-s1 | construct | mc_social_golfers | social_golfer | combinatorics | competition | 4 | MathConstraint/social_golfers | CC-BY-4.0 | [
"np_search"
] | Schedule 21 golfers (numbered 0..20) for 5 weeks. Every week the golfers are split into 7 groups (numbered 0..6) of exactly 3 golfers each. No two golfers may play in the same group in more than one week.
Find such a schedule.
Answer format: {"schedule": [week_0, ..., week_4]} where week_t is a list of 21 integers an... | {"n_groups": 7, "group_size": 3, "n_weeks": 5, "family": "mc_social_golfers", "subset": "construct"} | null | null | null | {"schedule": [[0, 0, 0, 1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4, 5, 5, 5, 6, 6, 6], [3, 5, 6, 5, 4, 6, 5, 4, 6, 1, 3, 0, 1, 0, 2, 2, 4, 1, 3, 2, 0], [1, 2, 3, 1, 2, 4, 4, 5, 6, 5, 6, 0, 3, 5, 2, 1, 3, 0, 0, 6, 4], [1, 3, 4, 4, 5, 6, 5, 6, 3, 4, 6, 5, 1, 2, 0, 2, 3, 0, 2, 1, 0], [3, 4, 5, 6, 3, 4, 5, 6, 3, 4, 5, 6, 1, 2, 0, ... | 1 |
construct-mc-social-golfers-l4-s2 | construct | mc_social_golfers | social_golfer | combinatorics | competition | 4 | MathConstraint/social_golfers | CC-BY-4.0 | [
"np_search"
] | Schedule 18 golfers (numbered 0..17) for 7 weeks. Every week the golfers are split into 6 groups (numbered 0..5) of exactly 3 golfers each. No two golfers may play in the same group in more than one week.
Find such a schedule.
Answer format: {"schedule": [week_0, ..., week_6]} where week_t is a list of 18 integers an... | {"n_groups": 6, "group_size": 3, "n_weeks": 7, "family": "mc_social_golfers", "subset": "construct"} | null | null | null | {"schedule": [[0, 0, 0, 1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4, 5, 5, 5], [2, 1, 0, 1, 5, 3, 0, 4, 2, 2, 4, 1, 5, 0, 3, 3, 4, 5], [5, 2, 4, 5, 3, 2, 2, 0, 4, 3, 5, 1, 4, 0, 1, 3, 1, 0], [0, 5, 1, 1, 0, 2, 4, 3, 2, 4, 5, 3, 5, 0, 4, 3, 2, 1], [1, 0, 5, 3, 5, 2, 1, 3, 4, 2, 4, 5, 2, 0, 3, 1, 0, 4], [5, 0, 4, 1, 2, 3, 2, 5, 1... | 1 |
construct-mc-social-golfers-l4-s3 | construct | mc_social_golfers | social_golfer | combinatorics | competition | 4 | MathConstraint/social_golfers | CC-BY-4.0 | [
"np_search"
] | Schedule 40 golfers (numbered 0..39) for 5 weeks. Every week the golfers are split into 10 groups (numbered 0..9) of exactly 4 golfers each. No two golfers may play in the same group in more than one week.
Find such a schedule.
Answer format: {"schedule": [week_0, ..., week_4]} where week_t is a list of 40 integers a... | {"n_groups": 10, "group_size": 4, "n_weeks": 5, "family": "mc_social_golfers", "subset": "construct"} | null | null | null | {"schedule": [[0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 6, 6, 6, 6, 7, 7, 7, 7, 8, 8, 8, 8, 9, 9, 9, 9], [5, 8, 2, 3, 9, 7, 0, 1, 7, 6, 1, 0, 9, 4, 3, 5, 3, 2, 1, 4, 3, 4, 8, 7, 4, 6, 0, 1, 8, 9, 5, 2, 8, 6, 2, 0, 9, 5, 6, 7], [5, 2, 0, 7, 7, 4, 6, 3, 2, 5, 1, 3, 5, 6, 9, 7, 6, 8, 7, 4, 2... | 1 |
construct-mc-social-golfers-l5-s0 | construct | mc_social_golfers | social_golfer | combinatorics | competition | 5 | MathConstraint/social_golfers | CC-BY-4.0 | [
"np_search"
] | Schedule 50 golfers (numbered 0..49) for 7 weeks. Every week the golfers are split into 10 groups (numbered 0..9) of exactly 5 golfers each. No two golfers may play in the same group in more than one week.
Find such a schedule.
Answer format: {"schedule": [week_0, ..., week_6]} where week_t is a list of 50 integers a... | {"n_groups": 10, "group_size": 5, "n_weeks": 7, "family": "mc_social_golfers", "subset": "construct"} | null | null | null | {"schedule": [[0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9], [4, 2, 8, 9, 1, 7, 1, 4, 3, 6, 3, 6, 8, 9, 7, 0, 7, 8, 3, 5, 9, 0, 8, 5, 6, 9, 5, 2, 6, 7, 5, 1, 4, 0, 2, 6, 5, 4, 7, 9, 1, 4, 3, 0, 2, 3, 2, 8, 1, 0], [9... | 1 |
construct-mc-social-golfers-l5-s1 | construct | mc_social_golfers | social_golfer | combinatorics | competition | 5 | MathConstraint/social_golfers | CC-BY-4.0 | [
"np_search"
] | Schedule 32 golfers (numbered 0..31) for 7 weeks. Every week the golfers are split into 8 groups (numbered 0..7) of exactly 4 golfers each. No two golfers may play in the same group in more than one week.
Find such a schedule.
Answer format: {"schedule": [week_0, ..., week_6]} where week_t is a list of 32 integers an... | {"n_groups": 8, "group_size": 4, "n_weeks": 7, "family": "mc_social_golfers", "subset": "construct"} | null | null | null | {"schedule": [[0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 6, 6, 6, 6, 7, 7, 7, 7], [6, 4, 7, 2, 5, 1, 2, 4, 7, 5, 3, 0, 0, 6, 1, 2, 7, 3, 1, 0, 6, 4, 7, 5, 0, 1, 2, 3, 6, 5, 4, 3], [7, 5, 6, 4, 5, 3, 6, 0, 3, 7, 4, 6, 1, 0, 2, 7, 2, 0, 1, 3, 5, 4, 1, 2, 7, 4, 2, 1, 6, 0, 3, 5], [1, 0, 2, 6,... | 1 |
construct-mc-social-golfers-l5-s2 | construct | mc_social_golfers | social_golfer | combinatorics | competition | 5 | MathConstraint/social_golfers | CC-BY-4.0 | [
"np_search"
] | Schedule 50 golfers (numbered 0..49) for 6 weeks. Every week the golfers are split into 10 groups (numbered 0..9) of exactly 5 golfers each. No two golfers may play in the same group in more than one week.
Find such a schedule.
Answer format: {"schedule": [week_0, ..., week_5]} where week_t is a list of 50 integers a... | {"n_groups": 10, "group_size": 5, "n_weeks": 6, "family": "mc_social_golfers", "subset": "construct"} | null | null | null | {"schedule": [[0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9], [5, 6, 0, 1, 9, 3, 9, 4, 1, 2, 5, 6, 2, 1, 4, 8, 7, 4, 2, 1, 7, 0, 9, 3, 8, 8, 3, 7, 6, 0, 2, 0, 5, 7, 9, 5, 8, 1, 9, 6, 4, 3, 2, 6, 5, 4, 7, 8, 3, 0], [3... | 1 |
construct-mc-social-golfers-l5-s3 | construct | mc_social_golfers | social_golfer | combinatorics | competition | 5 | MathConstraint/social_golfers | CC-BY-4.0 | [
"np_search"
] | Schedule 35 golfers (numbered 0..34) for 5 weeks. Every week the golfers are split into 7 groups (numbered 0..6) of exactly 5 golfers each. No two golfers may play in the same group in more than one week.
Find such a schedule.
Answer format: {"schedule": [week_0, ..., week_4]} where week_t is a list of 35 integers an... | {"n_groups": 7, "group_size": 5, "n_weeks": 5, "family": "mc_social_golfers", "subset": "construct"} | null | null | null | {"schedule": [[0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6], [5, 6, 4, 0, 1, 0, 6, 5, 4, 1, 2, 5, 6, 4, 3, 1, 2, 0, 6, 3, 3, 0, 5, 2, 1, 3, 6, 2, 5, 4, 4, 1, 0, 2, 3], [4, 0, 3, 1, 2, 2, 1, 3, 4, 0, 1, 6, 2, 5, 0, 3, 2, 0, 6, 5, 1, 4, 2, 6, 5, 6, 3, 4, 5, 0, 6... | 1 |
construct-mc-social-golfers-l6-s0 | construct | mc_social_golfers | social_golfer | combinatorics | competition | 6 | MathConstraint/social_golfers | CC-BY-4.0 | [
"np_search"
] | Schedule 25 golfers (numbered 0..24) for 6 weeks. Every week the golfers are split into 5 groups (numbered 0..4) of exactly 5 golfers each. No two golfers may play in the same group in more than one week.
Find such a schedule.
Answer format: {"schedule": [week_0, ..., week_5]} where week_t is a list of 25 integers an... | {"n_groups": 5, "group_size": 5, "n_weeks": 6, "family": "mc_social_golfers", "subset": "construct"} | null | null | null | {"schedule": [[0, 1, 2, 3, 4, 0, 1, 2, 3, 4, 0, 1, 2, 3, 4, 0, 1, 2, 3, 4, 0, 1, 2, 3, 4], [0, 1, 2, 3, 4, 4, 0, 1, 2, 3, 3, 4, 0, 1, 2, 2, 3, 4, 0, 1, 1, 2, 3, 4, 0], [0, 1, 2, 3, 4, 3, 4, 0, 1, 2, 1, 2, 3, 4, 0, 4, 0, 1, 2, 3, 2, 3, 4, 0, 1], [0, 1, 2, 3, 4, 2, 3, 4, 0, 1, 4, 0, 1, 2, 3, 1, 2, 3, 4, 0, 3, 4, 0, 1, 2]... | 1 |
construct-mc-social-golfers-l6-s1 | construct | mc_social_golfers | social_golfer | combinatorics | competition | 6 | MathConstraint/social_golfers | CC-BY-4.0 | [
"np_search"
] | Schedule 64 golfers (numbered 0..63) for 9 weeks. Every week the golfers are split into 8 groups (numbered 0..7) of exactly 8 golfers each. No two golfers may play in the same group in more than one week.
Find such a schedule.
Answer format: {"schedule": [week_0, ..., week_8]} where week_t is a list of 64 integers an... | {"n_groups": 8, "group_size": 8, "n_weeks": 9, "family": "mc_social_golfers", "subset": "construct"} | null | null | null | {"schedule": [[0, 1, 2, 3, 4, 5, 6, 7, 0, 1, 2, 3, 4, 5, 6, 7, 0, 1, 2, 3, 4, 5, 6, 7, 0, 1, 2, 3, 4, 5, 6, 7, 0, 1, 2, 3, 4, 5, 6, 7, 0, 1, 2, 3, 4, 5, 6, 7, 0, 1, 2, 3, 4, 5, 6, 7, 0, 1, 2, 3, 4, 5, 6, 7], [0, 1, 2, 3, 4, 5, 6, 7, 1, 0, 3, 2, 5, 4, 7, 6, 2, 3, 0, 1, 6, 7, 4, 5, 3, 2, 1, 0, 7, 6, 5, 4, 4, 5, 6, 7, 0, ... | 1 |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.