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-graph-k-coloring-l2-s7 | 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 65 edges:
(0,2), (0,8), (0,22), (0,31), (1,4), (1,8), (1,15), (1,23), (2,4), (2,28), (2,31), (3,7), (3,17), (3,18), (3,21), (3,26), (4,24), (5,6), (5,13), (5,15), (5,18), (6,13), (6,15), (6,21), (6,24), (6,27), (6,29), (7,9), (7,16), (7,19), (7,24), (8,16), (8,20), (8,23), (9... | {"n": 32, "k": 4, "edges": [[0, 2], [0, 8], [0, 22], [0, 31], [1, 4], [1, 8], [1, 15], [1, 23], [2, 4], [2, 28], [2, 31], [3, 7], [3, 17], [3, 18], [3, 21], [3, 26], [4, 24], [5, 6], [5, 13], [5, 15], [5, 18], [6, 13], [6, 15], [6, 21], [6, 24], [6, 27], [6, 29], [7, 9], [7, 16], [7, 19], [7, 24], [8, 16], [8, 20], [8,... | null | null | null | {"coloring": [0, 0, 1, 0, 2, 0, 1, 1, 1, 0, 0, 0, 0, 2, 0, 3, 2, 3, 1, 2, 2, 3, 1, 3, 3, 0, 1, 0, 2, 2, 0, 2]} | 1 |
construct-mc-graph-k-coloring-l3-s0 | construct | mc_graph_k_coloring | graph_k_coloring | graph_theory | competition | 3 | MathConstraint/graph_k_coloring | CC-BY-4.0 | [
"np_search"
] | Graph G with 50 vertices numbered 0..49 and 188 edges:
(0,14), (0,15), (0,25), (0,29), (0,30), (0,43), (0,44), (0,49), (1,2), (1,21), (1,24), (1,28), (1,36), (2,7), (2,16), (2,20), (2,22), (2,29), (2,30), (2,36), (2,41), (2,47), (2,49), (3,10), (3,13), (3,17), (3,18), (3,30), (3,44), (4,6), (4,13), (4,18), (4,28), (4,3... | {"n": 50, "k": 4, "edges": [[0, 14], [0, 15], [0, 25], [0, 29], [0, 30], [0, 43], [0, 44], [0, 49], [1, 2], [1, 21], [1, 24], [1, 28], [1, 36], [2, 7], [2, 16], [2, 20], [2, 22], [2, 29], [2, 30], [2, 36], [2, 41], [2, 47], [2, 49], [3, 10], [3, 13], [3, 17], [3, 18], [3, 30], [3, 44], [4, 6], [4, 13], [4, 18], [4, 28]... | null | null | null | {"coloring": [0, 0, 3, 3, 3, 0, 1, 0, 3, 3, 0, 0, 3, 1, 2, 3, 2, 2, 0, 2, 0, 2, 1, 1, 2, 1, 3, 1, 2, 1, 1, 2, 1, 0, 0, 1, 1, 0, 0, 1, 3, 2, 0, 3, 1, 0, 0, 2, 0, 2]} | 1 |
construct-mc-graph-k-coloring-l3-s1 | construct | mc_graph_k_coloring | graph_k_coloring | graph_theory | competition | 3 | MathConstraint/graph_k_coloring | CC-BY-4.0 | [
"np_search"
] | Graph G with 41 vertices numbered 0..40 and 146 edges:
(0,3), (0,6), (0,7), (0,20), (0,21), (1,2), (1,15), (1,21), (1,25), (1,26), (1,32), (1,38), (2,3), (2,7), (2,13), (2,27), (2,28), (2,36), (2,40), (3,11), (3,17), (3,25), (4,5), (4,13), (4,23), (4,26), (4,29), (4,32), (4,38), (4,40), (5,6), (5,11), (5,15), (5,18), (... | {"n": 41, "k": 4, "edges": [[0, 3], [0, 6], [0, 7], [0, 20], [0, 21], [1, 2], [1, 15], [1, 21], [1, 25], [1, 26], [1, 32], [1, 38], [2, 3], [2, 7], [2, 13], [2, 27], [2, 28], [2, 36], [2, 40], [3, 11], [3, 17], [3, 25], [4, 5], [4, 13], [4, 23], [4, 26], [4, 29], [4, 32], [4, 38], [4, 40], [5, 6], [5, 11], [5, 15], [5,... | null | null | null | {"coloring": [0, 0, 1, 2, 0, 1, 2, 2, 0, 2, 1, 3, 1, 2, 0, 3, 1, 1, 3, 0, 2, 2, 2, 1, 0, 3, 1, 0, 3, 3, 2, 0, 1, 1, 2, 3, 0, 0, 1, 0, 3]} | 1 |
construct-mc-graph-k-coloring-l3-s2 | construct | mc_graph_k_coloring | graph_k_coloring | graph_theory | competition | 3 | MathConstraint/graph_k_coloring | CC-BY-4.0 | [
"np_search"
] | Graph G with 45 vertices numbered 0..44 and 162 edges:
(0,17), (0,20), (0,35), (1,4), (1,6), (1,9), (1,13), (1,17), (1,20), (1,25), (1,35), (1,37), (1,38), (1,40), (2,3), (2,12), (2,14), (2,16), (2,17), (2,18), (2,20), (2,26), (2,27), (3,5), (3,7), (3,8), (3,10), (3,16), (3,37), (3,39), (3,40), (3,43), (4,6), (4,7), (4... | {"n": 45, "k": 4, "edges": [[0, 17], [0, 20], [0, 35], [1, 4], [1, 6], [1, 9], [1, 13], [1, 17], [1, 20], [1, 25], [1, 35], [1, 37], [1, 38], [1, 40], [2, 3], [2, 12], [2, 14], [2, 16], [2, 17], [2, 18], [2, 20], [2, 26], [2, 27], [3, 5], [3, 7], [3, 8], [3, 10], [3, 16], [3, 37], [3, 39], [3, 40], [3, 43], [4, 6], [4,... | null | null | null | {"coloring": [0, 0, 0, 1, 3, 3, 2, 0, 0, 2, 2, 3, 2, 3, 3, 0, 3, 1, 2, 1, 1, 1, 2, 1, 0, 1, 1, 3, 0, 2, 3, 0, 0, 0, 1, 2, 0, 3, 2, 3, 2, 1, 1, 0, 0]} | 1 |
construct-mc-graph-k-coloring-l3-s3 | construct | mc_graph_k_coloring | graph_k_coloring | graph_theory | competition | 3 | MathConstraint/graph_k_coloring | CC-BY-4.0 | [
"np_search"
] | Graph G with 45 vertices numbered 0..44 and 141 edges:
(0,4), (0,5), (0,31), (0,44), (1,3), (1,8), (1,18), (1,21), (1,33), (2,11), (2,13), (2,22), (2,23), (2,27), (2,30), (2,31), (2,41), (3,6), (3,9), (3,17), (3,21), (3,25), (3,28), (3,35), (3,42), (3,43), (4,6), (4,7), (4,8), (4,11), (4,18), (4,22), (4,27), (4,35), (5... | {"n": 45, "k": 4, "edges": [[0, 4], [0, 5], [0, 31], [0, 44], [1, 3], [1, 8], [1, 18], [1, 21], [1, 33], [2, 11], [2, 13], [2, 22], [2, 23], [2, 27], [2, 30], [2, 31], [2, 41], [3, 6], [3, 9], [3, 17], [3, 21], [3, 25], [3, 28], [3, 35], [3, 42], [3, 43], [4, 6], [4, 7], [4, 8], [4, 11], [4, 18], [4, 22], [4, 27], [4, ... | null | null | null | {"coloring": [0, 0, 0, 1, 1, 1, 0, 0, 2, 2, 0, 2, 1, 1, 0, 1, 0, 3, 2, 0, 0, 3, 2, 1, 3, 3, 3, 2, 0, 3, 2, 1, 1, 3, 1, 0, 3, 2, 0, 2, 1, 2, 0, 2, 1]} | 1 |
construct-mc-graph-k-coloring-l3-s4 | construct | mc_graph_k_coloring | graph_k_coloring | graph_theory | competition | 3 | MathConstraint/graph_k_coloring | CC-BY-4.0 | [
"np_search"
] | Graph G with 50 vertices numbered 0..49 and 144 edges:
(0,7), (0,11), (0,12), (0,39), (0,42), (0,46), (1,3), (1,8), (1,9), (1,20), (1,26), (1,30), (1,33), (1,48), (2,8), (2,17), (2,24), (2,27), (2,32), (2,39), (3,10), (3,16), (3,22), (3,25), (3,27), (3,30), (3,33), (3,43), (3,49), (4,21), (4,23), (5,11), (5,17), (5,23)... | {"n": 50, "k": 4, "edges": [[0, 7], [0, 11], [0, 12], [0, 39], [0, 42], [0, 46], [1, 3], [1, 8], [1, 9], [1, 20], [1, 26], [1, 30], [1, 33], [1, 48], [2, 8], [2, 17], [2, 24], [2, 27], [2, 32], [2, 39], [3, 10], [3, 16], [3, 22], [3, 25], [3, 27], [3, 30], [3, 33], [3, 43], [3, 49], [4, 21], [4, 23], [5, 11], [5, 17], ... | null | null | null | {"coloring": [0, 0, 0, 1, 0, 0, 0, 1, 1, 1, 0, 1, 1, 0, 0, 2, 2, 2, 0, 1, 3, 1, 0, 3, 2, 0, 2, 2, 2, 0, 3, 0, 3, 2, 1, 3, 0, 2, 3, 1, 2, 1, 1, 2, 2, 3, 1, 1, 2, 0]} | 1 |
construct-mc-graph-k-coloring-l3-s5 | construct | mc_graph_k_coloring | graph_k_coloring | graph_theory | competition | 3 | MathConstraint/graph_k_coloring | CC-BY-4.0 | [
"np_search"
] | Graph G with 50 vertices numbered 0..49 and 160 edges:
(0,2), (0,34), (1,4), (1,6), (1,15), (1,16), (1,26), (1,29), (1,33), (1,37), (1,38), (1,40), (1,48), (2,8), (2,10), (2,12), (2,15), (2,16), (2,25), (2,32), (2,35), (3,7), (3,9), (3,13), (3,18), (3,33), (3,36), (3,41), (3,45), (4,9), (4,14), (4,23), (4,25), (4,43), ... | {"n": 50, "k": 4, "edges": [[0, 2], [0, 34], [1, 4], [1, 6], [1, 15], [1, 16], [1, 26], [1, 29], [1, 33], [1, 37], [1, 38], [1, 40], [1, 48], [2, 8], [2, 10], [2, 12], [2, 15], [2, 16], [2, 25], [2, 32], [2, 35], [3, 7], [3, 9], [3, 13], [3, 18], [3, 33], [3, 36], [3, 41], [3, 45], [4, 9], [4, 14], [4, 23], [4, 25], [4... | null | null | null | {"coloring": [0, 0, 1, 0, 1, 0, 1, 1, 0, 2, 3, 3, 2, 1, 2, 3, 3, 3, 2, 0, 1, 0, 1, 3, 0, 0, 2, 0, 0, 1, 2, 0, 0, 1, 3, 0, 1, 1, 2, 2, 3, 1, 0, 3, 1, 3, 2, 1, 2, 2]} | 1 |
construct-mc-graph-k-coloring-l3-s6 | construct | mc_graph_k_coloring | graph_k_coloring | graph_theory | competition | 3 | MathConstraint/graph_k_coloring | CC-BY-4.0 | [
"np_search"
] | Graph G with 51 vertices numbered 0..50 and 185 edges:
(0,1), (0,2), (0,7), (0,10), (0,21), (0,23), (0,27), (0,38), (0,43), (0,44), (1,2), (1,7), (1,11), (1,13), (1,14), (1,18), (1,21), (1,22), (1,23), (1,32), (1,36), (2,14), (2,21), (2,30), (3,8), (3,12), (3,15), (3,19), (3,22), (3,23), (3,27), (3,28), (3,30), (3,31),... | {"n": 51, "k": 4, "edges": [[0, 1], [0, 2], [0, 7], [0, 10], [0, 21], [0, 23], [0, 27], [0, 38], [0, 43], [0, 44], [1, 2], [1, 7], [1, 11], [1, 13], [1, 14], [1, 18], [1, 21], [1, 22], [1, 23], [1, 32], [1, 36], [2, 14], [2, 21], [2, 30], [3, 8], [3, 12], [3, 15], [3, 19], [3, 22], [3, 23], [3, 27], [3, 28], [3, 30], [... | null | null | null | {"coloring": [0, 1, 2, 0, 0, 0, 0, 3, 3, 1, 3, 3, 2, 0, 0, 1, 2, 2, 0, 3, 1, 3, 3, 2, 0, 1, 3, 2, 3, 3, 1, 2, 0, 2, 1, 1, 0, 0, 1, 1, 3, 1, 3, 1, 1, 1, 3, 2, 3, 2, 0]} | 1 |
construct-mc-graph-k-coloring-l4-s0 | construct | mc_graph_k_coloring | graph_k_coloring | graph_theory | competition | 4 | MathConstraint/graph_k_coloring | CC-BY-4.0 | [
"np_search"
] | Graph G with 60 vertices numbered 0..59 and 200 edges:
(0,27), (0,36), (0,41), (0,45), (1,3), (1,8), (1,13), (1,15), (1,22), (1,28), (1,29), (1,30), (1,32), (1,43), (1,50), (1,52), (1,55), (2,10), (2,11), (2,15), (2,21), (2,28), (2,30), (2,43), (2,45), (3,21), (3,32), (3,44), (3,51), (4,17), (4,22), (4,24), (4,34), (4,... | {"n": 60, "k": 4, "edges": [[0, 27], [0, 36], [0, 41], [0, 45], [1, 3], [1, 8], [1, 13], [1, 15], [1, 22], [1, 28], [1, 29], [1, 30], [1, 32], [1, 43], [1, 50], [1, 52], [1, 55], [2, 10], [2, 11], [2, 15], [2, 21], [2, 28], [2, 30], [2, 43], [2, 45], [3, 21], [3, 32], [3, 44], [3, 51], [4, 17], [4, 22], [4, 24], [4, 34... | null | null | null | {"coloring": [0, 2, 0, 0, 1, 0, 1, 0, 1, 0, 1, 2, 1, 0, 2, 1, 0, 2, 1, 2, 1, 2, 3, 0, 0, 0, 0, 2, 1, 0, 1, 2, 3, 0, 0, 0, 1, 2, 2, 1, 0, 3, 2, 3, 3, 3, 0, 3, 1, 1, 1, 2, 1, 3, 2, 3, 3, 2, 3, 1]} | 1 |
construct-mc-graph-k-coloring-l4-s1 | construct | mc_graph_k_coloring | graph_k_coloring | graph_theory | competition | 4 | MathConstraint/graph_k_coloring | CC-BY-4.0 | [
"np_search"
] | Graph G with 59 vertices numbered 0..58 and 235 edges:
(0,11), (0,12), (0,15), (0,18), (0,23), (0,28), (0,36), (0,43), (0,51), (0,58), (1,7), (1,11), (1,13), (1,35), (1,53), (1,55), (2,5), (2,10), (2,22), (2,24), (2,28), (2,32), (2,33), (2,46), (2,50), (2,55), (3,12), (3,21), (3,34), (3,54), (3,55), (3,57), (3,58), (4,... | {"n": 59, "k": 4, "edges": [[0, 11], [0, 12], [0, 15], [0, 18], [0, 23], [0, 28], [0, 36], [0, 43], [0, 51], [0, 58], [1, 7], [1, 11], [1, 13], [1, 35], [1, 53], [1, 55], [2, 5], [2, 10], [2, 22], [2, 24], [2, 28], [2, 32], [2, 33], [2, 46], [2, 50], [2, 55], [3, 12], [3, 21], [3, 34], [3, 54], [3, 55], [3, 57], [3, 58... | null | null | null | {"coloring": [0, 3, 2, 2, 0, 1, 0, 1, 1, 1, 1, 1, 3, 2, 1, 3, 2, 0, 1, 2, 2, 1, 0, 3, 0, 3, 2, 0, 1, 2, 1, 1, 0, 3, 3, 2, 3, 1, 0, 3, 0, 2, 3, 2, 0, 0, 3, 2, 1, 2, 0, 3, 0, 1, 0, 0, 0, 3, 1]} | 1 |
construct-mc-graph-k-coloring-l4-s2 | construct | mc_graph_k_coloring | graph_k_coloring | graph_theory | competition | 4 | MathConstraint/graph_k_coloring | CC-BY-4.0 | [
"np_search"
] | Graph G with 53 vertices numbered 0..52 and 174 edges:
(0,3), (0,22), (0,33), (0,35), (0,38), (0,41), (0,50), (1,7), (1,9), (1,30), (1,33), (1,41), (2,3), (2,6), (2,9), (2,22), (2,27), (2,32), (2,38), (2,39), (2,40), (2,46), (2,51), (2,52), (3,27), (3,29), (3,51), (4,9), (4,16), (4,17), (4,22), (4,37), (4,41), (5,10), ... | {"n": 53, "k": 4, "edges": [[0, 3], [0, 22], [0, 33], [0, 35], [0, 38], [0, 41], [0, 50], [1, 7], [1, 9], [1, 30], [1, 33], [1, 41], [2, 3], [2, 6], [2, 9], [2, 22], [2, 27], [2, 32], [2, 38], [2, 39], [2, 40], [2, 46], [2, 51], [2, 52], [3, 27], [3, 29], [3, 51], [4, 9], [4, 16], [4, 17], [4, 22], [4, 37], [4, 41], [5... | null | null | null | {"coloring": [0, 0, 0, 1, 0, 0, 1, 1, 0, 1, 2, 2, 0, 0, 0, 3, 1, 3, 2, 3, 3, 0, 1, 0, 0, 0, 1, 3, 1, 2, 3, 2, 2, 2, 0, 2, 0, 1, 1, 2, 3, 1, 0, 1, 0, 2, 1, 3, 0, 2, 3, 3, 1]} | 1 |
construct-mc-graph-k-coloring-l5-s0 | construct | mc_graph_k_coloring | graph_k_coloring | graph_theory | competition | 5 | MathConstraint/graph_k_coloring | CC-BY-4.0 | [
"np_search"
] | Graph G with 100 vertices numbered 0..99 and 400 edges:
(0,5), (0,11), (0,16), (0,35), (0,45), (0,64), (0,89), (0,90), (0,91), (1,30), (1,38), (1,40), (1,44), (1,93), (2,7), (2,9), (2,10), (2,12), (2,26), (2,37), (2,42), (2,83), (3,24), (3,30), (3,47), (3,55), (3,58), (3,78), (3,87), (4,16), (4,20), (4,36), (4,51), (4,... | {"n": 100, "k": 4, "edges": [[0, 5], [0, 11], [0, 16], [0, 35], [0, 45], [0, 64], [0, 89], [0, 90], [0, 91], [1, 30], [1, 38], [1, 40], [1, 44], [1, 93], [2, 7], [2, 9], [2, 10], [2, 12], [2, 26], [2, 37], [2, 42], [2, 83], [3, 24], [3, 30], [3, 47], [3, 55], [3, 58], [3, 78], [3, 87], [4, 16], [4, 20], [4, 36], [4, 51... | null | null | null | {"coloring": [3, 2, 2, 3, 0, 2, 0, 0, 1, 1, 0, 1, 3, 0, 2, 3, 2, 2, 0, 0, 2, 3, 2, 1, 1, 0, 3, 1, 1, 1, 1, 2, 2, 3, 1, 0, 3, 1, 3, 0, 3, 1, 0, 2, 0, 1, 2, 0, 3, 2, 2, 2, 3, 1, 1, 2, 1, 3, 1, 3, 3, 0, 0, 1, 1, 3, 3, 2, 2, 3, 2, 3, 1, 1, 0, 1, 0, 3, 2, 2, 1, 1, 3, 3, 0, 0, 2, 2, 2, 0, 0, 0, 0, 3, 3, 2, 0, 3, 1, 0]} | 1 |
construct-mc-graph-k-coloring-l5-s1 | construct | mc_graph_k_coloring | graph_k_coloring | graph_theory | competition | 5 | MathConstraint/graph_k_coloring | CC-BY-4.0 | [
"np_search"
] | Graph G with 100 vertices numbered 0..99 and 400 edges:
(0,1), (0,10), (0,17), (0,23), (0,44), (0,48), (0,51), (0,68), (0,85), (1,17), (1,37), (1,80), (1,83), (1,92), (2,7), (2,10), (2,13), (2,63), (2,64), (2,92), (3,25), (3,27), (3,42), (3,53), (3,92), (3,94), (4,8), (4,19), (4,25), (4,26), (4,48), (4,54), (4,63), (4,... | {"n": 100, "k": 4, "edges": [[0, 1], [0, 10], [0, 17], [0, 23], [0, 44], [0, 48], [0, 51], [0, 68], [0, 85], [1, 17], [1, 37], [1, 80], [1, 83], [1, 92], [2, 7], [2, 10], [2, 13], [2, 63], [2, 64], [2, 92], [3, 25], [3, 27], [3, 42], [3, 53], [3, 92], [3, 94], [4, 8], [4, 19], [4, 25], [4, 26], [4, 48], [4, 54], [4, 63... | null | null | null | {"coloring": [0, 2, 0, 2, 0, 2, 3, 2, 3, 1, 1, 3, 0, 3, 2, 1, 2, 3, 3, 2, 1, 2, 3, 1, 1, 3, 2, 3, 2, 3, 0, 3, 0, 3, 3, 2, 2, 3, 2, 0, 2, 0, 1, 3, 1, 1, 1, 0, 3, 1, 1, 2, 0, 3, 1, 1, 0, 3, 0, 3, 2, 1, 1, 2, 2, 1, 0, 1, 2, 0, 0, 2, 3, 2, 2, 1, 2, 1, 1, 1, 0, 2, 0, 0, 0, 1, 0, 0, 3, 0, 0, 2, 1, 0, 1, 3, 3, 3, 3, 0]} | 1 |
construct-mc-graph-k-coloring-l5-s2 | construct | mc_graph_k_coloring | graph_k_coloring | graph_theory | competition | 5 | MathConstraint/graph_k_coloring | CC-BY-4.0 | [
"np_search"
] | Graph G with 100 vertices numbered 0..99 and 400 edges:
(0,18), (0,19), (0,54), (0,56), (0,67), (0,74), (0,78), (1,54), (1,87), (2,12), (2,14), (2,24), (2,30), (2,77), (3,14), (3,19), (3,25), (3,37), (3,46), (3,55), (3,69), (3,83), (4,33), (4,50), (4,53), (4,58), (4,74), (4,78), (4,83), (4,90), (5,12), (5,24), (5,30), ... | {"n": 100, "k": 4, "edges": [[0, 18], [0, 19], [0, 54], [0, 56], [0, 67], [0, 74], [0, 78], [1, 54], [1, 87], [2, 12], [2, 14], [2, 24], [2, 30], [2, 77], [3, 14], [3, 19], [3, 25], [3, 37], [3, 46], [3, 55], [3, 69], [3, 83], [4, 33], [4, 50], [4, 53], [4, 58], [4, 74], [4, 78], [4, 83], [4, 90], [5, 12], [5, 24], [5,... | null | null | null | {"coloring": [0, 0, 1, 1, 2, 1, 1, 1, 1, 1, 3, 3, 0, 1, 2, 1, 1, 0, 3, 3, 3, 2, 2, 3, 0, 3, 2, 3, 0, 2, 2, 0, 1, 3, 3, 2, 3, 0, 3, 0, 0, 0, 0, 1, 1, 2, 3, 3, 2, 0, 1, 2, 2, 3, 2, 2, 3, 0, 0, 1, 2, 1, 1, 1, 3, 0, 2, 2, 2, 2, 3, 0, 3, 1, 3, 3, 2, 0, 1, 0, 3, 3, 2, 3, 0, 3, 2, 2, 1, 2, 1, 1, 0, 0, 0, 1, 0, 0, 1, 2]} | 1 |
construct-mc-graph-k-coloring-l5-s3 | construct | mc_graph_k_coloring | graph_k_coloring | graph_theory | competition | 5 | MathConstraint/graph_k_coloring | CC-BY-4.0 | [
"np_search"
] | Graph G with 100 vertices numbered 0..99 and 400 edges:
(0,14), (0,23), (0,59), (0,60), (0,72), (0,89), (0,92), (0,95), (0,97), (1,13), (1,16), (1,36), (1,49), (1,93), (1,98), (2,4), (2,30), (2,32), (2,34), (2,45), (2,48), (2,56), (2,66), (3,57), (3,66), (3,73), (3,93), (4,14), (4,18), (4,33), (4,51), (4,84), (5,12), (... | {"n": 100, "k": 4, "edges": [[0, 14], [0, 23], [0, 59], [0, 60], [0, 72], [0, 89], [0, 92], [0, 95], [0, 97], [1, 13], [1, 16], [1, 36], [1, 49], [1, 93], [1, 98], [2, 4], [2, 30], [2, 32], [2, 34], [2, 45], [2, 48], [2, 56], [2, 66], [3, 57], [3, 66], [3, 73], [3, 93], [4, 14], [4, 18], [4, 33], [4, 51], [4, 84], [5, ... | null | null | null | {"coloring": [2, 2, 2, 1, 0, 2, 1, 2, 2, 2, 2, 2, 3, 3, 1, 3, 3, 0, 3, 1, 0, 3, 0, 0, 3, 0, 2, 0, 3, 1, 3, 1, 3, 1, 3, 3, 3, 2, 1, 2, 0, 1, 3, 1, 0, 1, 2, 1, 3, 0, 1, 2, 2, 1, 2, 2, 0, 2, 1, 1, 1, 2, 2, 1, 0, 1, 0, 1, 3, 0, 1, 1, 0, 3, 3, 2, 1, 3, 3, 0, 0, 0, 3, 2, 1, 2, 3, 2, 0, 3, 3, 0, 0, 0, 2, 1, 0, 0, 0, 3]} | 1 |
construct-mc-graph-k-coloring-l5-s4 | construct | mc_graph_k_coloring | graph_k_coloring | graph_theory | competition | 5 | MathConstraint/graph_k_coloring | CC-BY-4.0 | [
"np_search"
] | Graph G with 100 vertices numbered 0..99 and 400 edges:
(0,13), (0,21), (0,25), (0,29), (0,40), (0,53), (0,57), (0,66), (0,77), (1,8), (1,9), (1,14), (1,49), (1,57), (1,67), (1,75), (1,89), (1,97), (2,11), (2,36), (2,52), (2,55), (2,64), (2,79), (3,17), (3,39), (3,43), (3,65), (3,75), (3,76), (3,77), (3,92), (4,28), (4... | {"n": 100, "k": 4, "edges": [[0, 13], [0, 21], [0, 25], [0, 29], [0, 40], [0, 53], [0, 57], [0, 66], [0, 77], [1, 8], [1, 9], [1, 14], [1, 49], [1, 57], [1, 67], [1, 75], [1, 89], [1, 97], [2, 11], [2, 36], [2, 52], [2, 55], [2, 64], [2, 79], [3, 17], [3, 39], [3, 43], [3, 65], [3, 75], [3, 76], [3, 77], [3, 92], [4, 2... | null | null | null | {"coloring": [0, 3, 0, 1, 3, 3, 2, 3, 2, 1, 0, 1, 0, 1, 2, 3, 1, 2, 2, 0, 1, 1, 3, 2, 1, 1, 1, 1, 0, 3, 0, 2, 1, 1, 3, 1, 2, 3, 2, 0, 1, 1, 1, 3, 0, 3, 3, 2, 2, 0, 3, 1, 2, 3, 0, 2, 0, 1, 0, 3, 0, 0, 1, 0, 1, 2, 3, 2, 0, 3, 0, 2, 3, 1, 2, 2, 3, 3, 2, 2, 3, 1, 0, 2, 0, 3, 2, 1, 0, 2, 1, 0, 3, 3, 2, 2, 3, 0, 0, 0]} | 1 |
construct-mc-graph-k-coloring-l5-s5 | construct | mc_graph_k_coloring | graph_k_coloring | graph_theory | competition | 5 | MathConstraint/graph_k_coloring | CC-BY-4.0 | [
"np_search"
] | Graph G with 100 vertices numbered 0..99 and 400 edges:
(0,2), (0,23), (0,33), (0,61), (0,87), (1,26), (1,36), (1,52), (1,63), (1,71), (1,76), (1,79), (1,85), (1,97), (2,28), (2,42), (2,45), (2,95), (3,6), (3,13), (3,15), (3,27), (3,31), (3,33), (3,58), (4,12), (4,17), (4,21), (4,34), (4,42), (4,58), (4,85), (4,88), (4... | {"n": 100, "k": 4, "edges": [[0, 2], [0, 23], [0, 33], [0, 61], [0, 87], [1, 26], [1, 36], [1, 52], [1, 63], [1, 71], [1, 76], [1, 79], [1, 85], [1, 97], [2, 28], [2, 42], [2, 45], [2, 95], [3, 6], [3, 13], [3, 15], [3, 27], [3, 31], [3, 33], [3, 58], [4, 12], [4, 17], [4, 21], [4, 34], [4, 42], [4, 58], [4, 85], [4, 8... | null | null | null | {"coloring": [3, 2, 1, 0, 0, 3, 1, 3, 1, 3, 3, 0, 2, 2, 1, 3, 2, 2, 2, 0, 0, 2, 1, 1, 1, 0, 0, 3, 2, 1, 0, 1, 3, 2, 2, 2, 1, 3, 2, 3, 2, 1, 3, 2, 3, 3, 2, 0, 0, 0, 0, 1, 1, 3, 1, 2, 0, 1, 1, 3, 1, 1, 0, 0, 1, 3, 0, 3, 3, 1, 3, 0, 0, 0, 3, 0, 0, 2, 3, 1, 2, 3, 0, 0, 2, 3, 3, 1, 3, 2, 2, 2, 0, 2, 2, 2, 1, 1, 1, 0]} | 1 |
construct-mc-graph-k-coloring-l5-s6 | construct | mc_graph_k_coloring | graph_k_coloring | graph_theory | competition | 5 | MathConstraint/graph_k_coloring | CC-BY-4.0 | [
"np_search"
] | Graph G with 100 vertices numbered 0..99 and 400 edges:
(0,9), (0,17), (0,36), (0,37), (0,39), (0,47), (0,59), (0,68), (0,69), (0,73), (0,78), (0,80), (0,90), (0,96), (1,6), (1,13), (1,27), (1,38), (1,41), (1,52), (1,79), (1,91), (2,45), (2,63), (2,92), (2,98), (3,11), (3,15), (3,17), (3,18), (3,24), (3,52), (3,62), (3... | {"n": 100, "k": 4, "edges": [[0, 9], [0, 17], [0, 36], [0, 37], [0, 39], [0, 47], [0, 59], [0, 68], [0, 69], [0, 73], [0, 78], [0, 80], [0, 90], [0, 96], [1, 6], [1, 13], [1, 27], [1, 38], [1, 41], [1, 52], [1, 79], [1, 91], [2, 45], [2, 63], [2, 92], [2, 98], [3, 11], [3, 15], [3, 17], [3, 18], [3, 24], [3, 52], [3, 6... | null | null | null | {"coloring": [1, 3, 2, 1, 1, 2, 2, 1, 2, 3, 0, 0, 3, 1, 2, 3, 2, 0, 2, 1, 2, 3, 1, 3, 2, 3, 0, 0, 3, 0, 2, 1, 1, 1, 1, 0, 0, 2, 0, 0, 1, 1, 0, 2, 1, 3, 0, 2, 1, 2, 0, 2, 0, 3, 3, 3, 3, 0, 1, 3, 0, 0, 2, 0, 1, 1, 1, 0, 3, 0, 2, 1, 0, 3, 0, 2, 2, 0, 0, 2, 3, 3, 2, 0, 2, 3, 1, 1, 2, 2, 3, 1, 1, 2, 3, 1, 3, 3, 3, 3]} | 1 |
construct-mc-graph-k-coloring-l5-s7 | construct | mc_graph_k_coloring | graph_k_coloring | graph_theory | competition | 5 | MathConstraint/graph_k_coloring | CC-BY-4.0 | [
"np_search"
] | Graph G with 100 vertices numbered 0..99 and 400 edges:
(0,10), (0,16), (0,41), (0,45), (0,57), (0,65), (0,73), (0,76), (0,79), (1,9), (1,13), (1,18), (1,21), (1,38), (1,58), (2,24), (2,56), (2,60), (2,82), (3,13), (3,19), (3,57), (4,27), (4,43), (4,49), (4,76), (4,87), (4,92), (5,35), (5,36), (5,43), (5,47), (5,60), (... | {"n": 100, "k": 4, "edges": [[0, 10], [0, 16], [0, 41], [0, 45], [0, 57], [0, 65], [0, 73], [0, 76], [0, 79], [1, 9], [1, 13], [1, 18], [1, 21], [1, 38], [1, 58], [2, 24], [2, 56], [2, 60], [2, 82], [3, 13], [3, 19], [3, 57], [4, 27], [4, 43], [4, 49], [4, 76], [4, 87], [4, 92], [5, 35], [5, 36], [5, 43], [5, 47], [5, ... | null | null | null | {"coloring": [2, 0, 0, 2, 3, 1, 1, 1, 0, 1, 1, 0, 2, 3, 0, 2, 3, 0, 1, 3, 3, 2, 1, 0, 3, 1, 1, 1, 2, 1, 2, 3, 3, 1, 3, 2, 0, 0, 2, 1, 3, 1, 2, 0, 0, 0, 0, 2, 0, 2, 3, 1, 0, 3, 3, 1, 3, 3, 1, 2, 3, 0, 2, 1, 2, 1, 1, 2, 3, 3, 1, 3, 1, 0, 0, 1, 0, 0, 2, 3, 0, 0, 1, 2, 2, 2, 2, 0, 2, 3, 2, 0, 1, 3, 0, 3, 3, 2, 3, 2]} | 1 |
construct-mc-graph-k-coloring-l5-s8 | construct | mc_graph_k_coloring | graph_k_coloring | graph_theory | competition | 5 | MathConstraint/graph_k_coloring | CC-BY-4.0 | [
"np_search"
] | Graph G with 100 vertices numbered 0..99 and 400 edges:
(0,1), (0,2), (0,7), (0,26), (0,29), (0,40), (0,49), (0,84), (0,87), (0,91), (1,15), (1,55), (1,69), (1,72), (1,79), (1,81), (1,86), (2,4), (2,31), (2,39), (2,43), (2,86), (3,25), (3,29), (3,45), (3,48), (3,56), (3,57), (3,63), (3,70), (3,71), (3,75), (4,24), (4,2... | {"n": 100, "k": 4, "edges": [[0, 1], [0, 2], [0, 7], [0, 26], [0, 29], [0, 40], [0, 49], [0, 84], [0, 87], [0, 91], [1, 15], [1, 55], [1, 69], [1, 72], [1, 79], [1, 81], [1, 86], [2, 4], [2, 31], [2, 39], [2, 43], [2, 86], [3, 25], [3, 29], [3, 45], [3, 48], [3, 56], [3, 57], [3, 63], [3, 70], [3, 71], [3, 75], [4, 24]... | null | null | null | {"coloring": [2, 1, 1, 3, 0, 0, 0, 3, 0, 0, 0, 3, 1, 1, 0, 0, 1, 0, 3, 2, 0, 0, 2, 3, 1, 2, 1, 0, 3, 1, 3, 0, 3, 2, 2, 2, 2, 3, 2, 3, 1, 1, 1, 3, 3, 1, 2, 3, 1, 0, 0, 3, 1, 2, 2, 3, 1, 0, 3, 1, 3, 2, 0, 0, 3, 1, 1, 2, 3, 2, 1, 2, 3, 2, 2, 0, 1, 1, 1, 2, 0, 2, 1, 2, 0, 1, 0, 3, 1, 2, 0, 0, 2, 3, 3, 2, 0, 3, 3, 2]} | 1 |
construct-mc-graph-k-coloring-l5-s9 | construct | mc_graph_k_coloring | graph_k_coloring | graph_theory | competition | 5 | MathConstraint/graph_k_coloring | CC-BY-4.0 | [
"np_search"
] | Graph G with 100 vertices numbered 0..99 and 400 edges:
(0,11), (0,24), (0,42), (0,53), (0,59), (0,71), (0,76), (0,84), (0,85), (0,96), (1,2), (1,18), (1,24), (1,39), (1,42), (1,53), (1,58), (1,71), (1,90), (1,94), (2,5), (2,32), (2,38), (2,41), (2,73), (2,96), (3,8), (3,9), (3,12), (3,26), (3,31), (3,50), (3,61), (3,6... | {"n": 100, "k": 4, "edges": [[0, 11], [0, 24], [0, 42], [0, 53], [0, 59], [0, 71], [0, 76], [0, 84], [0, 85], [0, 96], [1, 2], [1, 18], [1, 24], [1, 39], [1, 42], [1, 53], [1, 58], [1, 71], [1, 90], [1, 94], [2, 5], [2, 32], [2, 38], [2, 41], [2, 73], [2, 96], [3, 8], [3, 9], [3, 12], [3, 26], [3, 31], [3, 50], [3, 61]... | null | null | null | {"coloring": [0, 0, 3, 1, 2, 0, 3, 1, 3, 2, 1, 3, 0, 0, 1, 0, 2, 3, 2, 1, 1, 1, 2, 3, 1, 2, 0, 0, 1, 1, 2, 0, 1, 0, 2, 3, 2, 0, 2, 2, 1, 1, 2, 0, 3, 3, 3, 2, 0, 1, 3, 0, 0, 2, 3, 0, 3, 0, 3, 3, 0, 0, 0, 3, 3, 1, 0, 3, 2, 0, 1, 3, 3, 1, 2, 2, 1, 1, 2, 1, 1, 2, 3, 2, 2, 2, 2, 2, 0, 3, 3, 0, 3, 1, 1, 3, 2, 1, 0, 1]} | 1 |
construct-mc-graph-k-coloring-l6-s0 | construct | mc_graph_k_coloring | graph_k_coloring | graph_theory | competition | 6 | MathConstraint/graph_k_coloring | CC-BY-4.0 | [
"np_search"
] | Graph G with 250 vertices numbered 0..249 and 1075 edges:
(0,16), (0,25), (0,77), (0,184), (0,193), (0,220), (0,242), (1,32), (1,69), (1,87), (1,93), (1,109), (1,174), (1,204), (1,239), (1,242), (2,13), (2,35), (2,60), (2,62), (2,140), (2,156), (2,169), (2,181), (2,188), (2,239), (2,246), (3,24), (3,26), (3,87), (3,89)... | {"n": 250, "k": 4, "edges": [[0, 16], [0, 25], [0, 77], [0, 184], [0, 193], [0, 220], [0, 242], [1, 32], [1, 69], [1, 87], [1, 93], [1, 109], [1, 174], [1, 204], [1, 239], [1, 242], [2, 13], [2, 35], [2, 60], [2, 62], [2, 140], [2, 156], [2, 169], [2, 181], [2, 188], [2, 239], [2, 246], [3, 24], [3, 26], [3, 87], [3, 8... | null | null | null | {"coloring": [0, 3, 1, 3, 2, 1, 1, 3, 1, 3, 0, 1, 2, 0, 3, 0, 1, 1, 2, 1, 1, 3, 3, 3, 0, 3, 1, 0, 2, 1, 0, 0, 2, 1, 1, 3, 1, 3, 3, 1, 2, 3, 0, 3, 3, 2, 3, 0, 3, 2, 3, 0, 3, 0, 0, 0, 1, 1, 1, 1, 3, 3, 2, 0, 0, 2, 2, 3, 2, 1, 0, 3, 2, 0, 2, 2, 3, 1, 3, 2, 3, 1, 2, 0, 1, 1, 2, 1, 3, 2, 0, 1, 1, 1, 0, 1, 1, 3, 2, 1, 2, 3, ... | 1 |
construct-mc-graph-k-coloring-l6-s1 | construct | mc_graph_k_coloring | graph_k_coloring | graph_theory | competition | 6 | MathConstraint/graph_k_coloring | CC-BY-4.0 | [
"np_search"
] | Graph G with 250 vertices numbered 0..249 and 1075 edges:
(0,44), (0,227), (0,237), (1,20), (1,37), (1,48), (1,65), (1,105), (1,131), (1,141), (1,169), (1,216), (2,32), (2,51), (2,64), (2,65), (2,92), (2,106), (2,122), (2,133), (2,179), (3,18), (3,36), (3,37), (3,44), (3,61), (3,152), (3,180), (3,243), (3,245), (4,19),... | {"n": 250, "k": 4, "edges": [[0, 44], [0, 227], [0, 237], [1, 20], [1, 37], [1, 48], [1, 65], [1, 105], [1, 131], [1, 141], [1, 169], [1, 216], [2, 32], [2, 51], [2, 64], [2, 65], [2, 92], [2, 106], [2, 122], [2, 133], [2, 179], [3, 18], [3, 36], [3, 37], [3, 44], [3, 61], [3, 152], [3, 180], [3, 243], [3, 245], [4, 19... | null | null | null | {"coloring": [1, 2, 2, 2, 3, 1, 2, 3, 2, 1, 2, 3, 2, 3, 1, 1, 2, 3, 0, 1, 1, 3, 1, 2, 2, 0, 3, 2, 1, 3, 3, 0, 0, 2, 1, 2, 0, 1, 0, 0, 1, 3, 0, 3, 3, 2, 2, 2, 1, 2, 0, 1, 2, 3, 3, 0, 2, 0, 1, 1, 3, 0, 1, 0, 3, 1, 1, 0, 0, 2, 0, 1, 1, 2, 3, 2, 1, 3, 3, 2, 0, 3, 0, 3, 3, 3, 2, 1, 0, 3, 3, 3, 3, 0, 2, 1, 2, 3, 0, 3, 0, 2, ... | 1 |
construct-mc-graph-k-coloring-l6-s2 | construct | mc_graph_k_coloring | graph_k_coloring | graph_theory | competition | 6 | MathConstraint/graph_k_coloring | CC-BY-4.0 | [
"np_search"
] | Graph G with 250 vertices numbered 0..249 and 1075 edges:
(0,28), (0,38), (0,57), (0,131), (0,189), (0,241), (1,32), (1,55), (1,97), (1,127), (1,145), (1,147), (1,150), (1,167), (1,189), (1,199), (1,207), (1,225), (2,11), (2,159), (2,181), (2,209), (2,228), (2,233), (3,61), (3,66), (3,74), (3,136), (3,137), (3,141), (3... | {"n": 250, "k": 4, "edges": [[0, 28], [0, 38], [0, 57], [0, 131], [0, 189], [0, 241], [1, 32], [1, 55], [1, 97], [1, 127], [1, 145], [1, 147], [1, 150], [1, 167], [1, 189], [1, 199], [1, 207], [1, 225], [2, 11], [2, 159], [2, 181], [2, 209], [2, 228], [2, 233], [3, 61], [3, 66], [3, 74], [3, 136], [3, 137], [3, 141], [... | null | null | null | {"coloring": [2, 1, 0, 1, 1, 1, 2, 3, 2, 1, 3, 1, 1, 1, 3, 1, 1, 3, 1, 0, 3, 1, 1, 1, 2, 3, 0, 0, 1, 2, 0, 0, 0, 2, 1, 2, 2, 0, 3, 1, 2, 3, 3, 1, 0, 0, 2, 3, 2, 2, 0, 1, 2, 1, 0, 3, 1, 1, 1, 2, 1, 2, 2, 2, 2, 0, 0, 1, 3, 3, 0, 3, 3, 0, 3, 2, 0, 0, 3, 0, 3, 1, 3, 1, 1, 0, 1, 0, 2, 3, 2, 2, 3, 0, 1, 0, 0, 2, 3, 1, 0, 2, ... | 1 |
construct-mc-graph-k-coloring-l6-s3 | construct | mc_graph_k_coloring | graph_k_coloring | graph_theory | competition | 6 | MathConstraint/graph_k_coloring | CC-BY-4.0 | [
"np_search"
] | Graph G with 250 vertices numbered 0..249 and 1075 edges:
(0,31), (0,37), (0,60), (0,162), (0,181), (0,214), (1,15), (1,30), (1,60), (1,117), (1,126), (1,136), (1,142), (1,159), (1,178), (1,181), (1,199), (1,242), (2,4), (2,17), (2,64), (2,108), (2,210), (2,224), (2,228), (3,12), (3,15), (3,21), (3,35), (3,46), (3,83),... | {"n": 250, "k": 4, "edges": [[0, 31], [0, 37], [0, 60], [0, 162], [0, 181], [0, 214], [1, 15], [1, 30], [1, 60], [1, 117], [1, 126], [1, 136], [1, 142], [1, 159], [1, 178], [1, 181], [1, 199], [1, 242], [2, 4], [2, 17], [2, 64], [2, 108], [2, 210], [2, 224], [2, 228], [3, 12], [3, 15], [3, 21], [3, 35], [3, 46], [3, 83... | null | null | null | {"coloring": [3, 1, 0, 1, 2, 0, 3, 1, 3, 2, 2, 1, 3, 2, 1, 3, 1, 3, 1, 0, 1, 3, 1, 0, 1, 1, 0, 0, 3, 3, 2, 0, 2, 2, 0, 2, 2, 1, 1, 0, 0, 3, 0, 3, 3, 2, 0, 1, 3, 3, 3, 1, 2, 3, 0, 2, 2, 0, 1, 0, 0, 2, 0, 0, 3, 2, 1, 0, 3, 0, 0, 3, 1, 3, 1, 0, 0, 2, 2, 3, 3, 2, 2, 0, 1, 1, 2, 1, 1, 0, 2, 0, 1, 2, 0, 3, 3, 3, 2, 3, 0, 3, ... | 1 |
construct-mc-graph-k-coloring-l6-s4 | construct | mc_graph_k_coloring | graph_k_coloring | graph_theory | competition | 6 | MathConstraint/graph_k_coloring | CC-BY-4.0 | [
"np_search"
] | Graph G with 250 vertices numbered 0..249 and 1075 edges:
(0,6), (0,17), (0,47), (0,54), (0,56), (0,95), (0,137), (0,148), (0,163), (0,184), (0,191), (0,211), (0,216), (1,28), (1,36), (1,79), (1,85), (1,94), (1,149), (1,204), (1,206), (1,207), (1,220), (1,231), (2,6), (2,14), (2,46), (2,57), (2,67), (2,85), (2,177), (3... | {"n": 250, "k": 4, "edges": [[0, 6], [0, 17], [0, 47], [0, 54], [0, 56], [0, 95], [0, 137], [0, 148], [0, 163], [0, 184], [0, 191], [0, 211], [0, 216], [1, 28], [1, 36], [1, 79], [1, 85], [1, 94], [1, 149], [1, 204], [1, 206], [1, 207], [1, 220], [1, 231], [2, 6], [2, 14], [2, 46], [2, 57], [2, 67], [2, 85], [2, 177], ... | null | null | null | {"coloring": [2, 0, 0, 0, 1, 2, 3, 3, 0, 2, 3, 0, 0, 3, 2, 3, 0, 3, 1, 3, 2, 1, 3, 3, 1, 0, 2, 2, 3, 0, 0, 1, 3, 3, 1, 0, 3, 3, 2, 2, 2, 0, 2, 1, 3, 0, 2, 3, 2, 2, 3, 2, 1, 1, 0, 3, 3, 1, 0, 0, 0, 0, 1, 2, 1, 3, 1, 3, 0, 3, 3, 1, 1, 3, 3, 1, 2, 3, 1, 2, 0, 0, 0, 1, 0, 1, 1, 1, 3, 1, 0, 1, 2, 2, 3, 0, 2, 2, 1, 2, 2, 1, ... | 1 |
construct-mc-graph-k-coloring-l6-s5 | construct | mc_graph_k_coloring | graph_k_coloring | graph_theory | competition | 6 | MathConstraint/graph_k_coloring | CC-BY-4.0 | [
"np_search"
] | Graph G with 250 vertices numbered 0..249 and 1075 edges:
(0,15), (0,41), (0,73), (0,86), (0,99), (0,128), (0,164), (0,186), (0,240), (1,15), (1,39), (1,53), (1,74), (1,96), (1,108), (1,116), (1,126), (1,159), (1,175), (1,201), (1,202), (1,213), (1,214), (1,233), (1,240), (2,41), (2,56), (2,120), (2,163), (2,176), (2,1... | {"n": 250, "k": 4, "edges": [[0, 15], [0, 41], [0, 73], [0, 86], [0, 99], [0, 128], [0, 164], [0, 186], [0, 240], [1, 15], [1, 39], [1, 53], [1, 74], [1, 96], [1, 108], [1, 116], [1, 126], [1, 159], [1, 175], [1, 201], [1, 202], [1, 213], [1, 214], [1, 233], [1, 240], [2, 41], [2, 56], [2, 120], [2, 163], [2, 176], [2,... | null | null | null | {"coloring": [3, 3, 1, 1, 2, 1, 1, 1, 0, 1, 0, 3, 2, 3, 2, 1, 1, 2, 0, 3, 2, 1, 1, 2, 0, 2, 1, 2, 2, 1, 3, 2, 0, 1, 3, 1, 0, 0, 3, 1, 3, 0, 1, 0, 0, 3, 2, 2, 1, 3, 1, 2, 1, 2, 3, 1, 0, 1, 3, 0, 2, 0, 1, 2, 3, 0, 0, 2, 3, 3, 2, 3, 0, 0, 2, 0, 3, 2, 1, 0, 2, 0, 3, 0, 1, 1, 1, 0, 0, 0, 2, 3, 1, 2, 1, 0, 2, 2, 2, 0, 3, 3, ... | 1 |
construct-mc-graph-k-coloring-l6-s6 | construct | mc_graph_k_coloring | graph_k_coloring | graph_theory | competition | 6 | MathConstraint/graph_k_coloring | CC-BY-4.0 | [
"np_search"
] | Graph G with 250 vertices numbered 0..249 and 1075 edges:
(0,21), (0,38), (0,48), (0,49), (0,81), (0,83), (0,171), (0,198), (0,237), (0,249), (1,34), (1,39), (1,42), (1,152), (1,203), (1,248), (2,22), (2,50), (2,52), (2,72), (2,116), (2,160), (2,164), (2,169), (2,229), (2,230), (2,235), (2,249), (3,33), (3,58), (3,80),... | {"n": 250, "k": 4, "edges": [[0, 21], [0, 38], [0, 48], [0, 49], [0, 81], [0, 83], [0, 171], [0, 198], [0, 237], [0, 249], [1, 34], [1, 39], [1, 42], [1, 152], [1, 203], [1, 248], [2, 22], [2, 50], [2, 52], [2, 72], [2, 116], [2, 160], [2, 164], [2, 169], [2, 229], [2, 230], [2, 235], [2, 249], [3, 33], [3, 58], [3, 80... | null | null | null | {"coloring": [1, 0, 0, 0, 1, 0, 0, 3, 0, 0, 1, 2, 2, 0, 2, 1, 2, 3, 2, 2, 3, 2, 1, 0, 3, 3, 3, 3, 0, 0, 1, 1, 2, 2, 2, 2, 2, 0, 3, 2, 3, 2, 1, 2, 0, 0, 2, 2, 2, 3, 3, 0, 2, 3, 0, 2, 1, 3, 3, 1, 2, 1, 3, 1, 0, 1, 2, 1, 2, 1, 0, 3, 3, 1, 2, 2, 3, 3, 3, 1, 1, 0, 0, 3, 3, 0, 0, 3, 2, 0, 2, 0, 1, 1, 0, 3, 0, 2, 0, 1, 0, 2, ... | 1 |
construct-mc-graph-k-coloring-l6-s7 | construct | mc_graph_k_coloring | graph_k_coloring | graph_theory | competition | 6 | MathConstraint/graph_k_coloring | CC-BY-4.0 | [
"np_search"
] | Graph G with 250 vertices numbered 0..249 and 1075 edges:
(0,38), (0,68), (0,79), (0,119), (1,40), (1,100), (1,108), (1,121), (1,147), (1,160), (1,172), (1,182), (1,225), (2,9), (2,10), (2,41), (2,74), (2,94), (2,96), (2,191), (2,222), (2,239), (3,21), (3,40), (3,42), (3,52), (3,79), (3,80), (3,82), (3,90), (3,97), (3,... | {"n": 250, "k": 4, "edges": [[0, 38], [0, 68], [0, 79], [0, 119], [1, 40], [1, 100], [1, 108], [1, 121], [1, 147], [1, 160], [1, 172], [1, 182], [1, 225], [2, 9], [2, 10], [2, 41], [2, 74], [2, 94], [2, 96], [2, 191], [2, 222], [2, 239], [3, 21], [3, 40], [3, 42], [3, 52], [3, 79], [3, 80], [3, 82], [3, 90], [3, 97], [... | null | null | null | {"coloring": [1, 3, 2, 1, 2, 2, 1, 1, 1, 3, 3, 0, 3, 3, 1, 2, 0, 2, 2, 1, 1, 0, 2, 3, 0, 3, 1, 2, 1, 0, 0, 2, 1, 0, 2, 2, 1, 2, 0, 1, 0, 3, 3, 3, 3, 2, 3, 0, 2, 2, 1, 0, 3, 3, 1, 1, 1, 3, 1, 1, 3, 3, 3, 1, 3, 3, 0, 2, 2, 1, 3, 3, 0, 2, 0, 3, 1, 0, 3, 3, 2, 3, 0, 0, 3, 2, 0, 1, 3, 2, 0, 1, 0, 3, 0, 1, 3, 0, 3, 3, 1, 1, ... | 1 |
construct-mc-graph-k-coloring-l6-s8 | construct | mc_graph_k_coloring | graph_k_coloring | graph_theory | competition | 6 | MathConstraint/graph_k_coloring | CC-BY-4.0 | [
"np_search"
] | Graph G with 250 vertices numbered 0..249 and 1075 edges:
(0,12), (0,31), (0,41), (0,44), (0,87), (0,121), (0,147), (0,155), (0,174), (0,233), (1,50), (1,54), (1,74), (1,80), (1,93), (1,114), (1,136), (1,142), (1,186), (2,7), (2,38), (2,141), (2,182), (2,213), (2,214), (2,218), (3,5), (3,20), (3,24), (3,38), (3,60), (3... | {"n": 250, "k": 4, "edges": [[0, 12], [0, 31], [0, 41], [0, 44], [0, 87], [0, 121], [0, 147], [0, 155], [0, 174], [0, 233], [1, 50], [1, 54], [1, 74], [1, 80], [1, 93], [1, 114], [1, 136], [1, 142], [1, 186], [2, 7], [2, 38], [2, 141], [2, 182], [2, 213], [2, 214], [2, 218], [3, 5], [3, 20], [3, 24], [3, 38], [3, 60], ... | null | null | null | {"coloring": [1, 2, 1, 2, 2, 3, 1, 0, 2, 3, 2, 0, 3, 2, 1, 3, 1, 1, 0, 3, 0, 1, 0, 2, 0, 3, 2, 3, 0, 2, 0, 2, 1, 3, 3, 0, 1, 1, 0, 2, 0, 0, 3, 0, 3, 2, 1, 3, 3, 2, 0, 0, 3, 0, 0, 1, 0, 2, 1, 0, 3, 0, 3, 3, 1, 2, 2, 2, 0, 3, 2, 3, 0, 0, 1, 0, 1, 3, 2, 0, 1, 2, 0, 2, 3, 0, 0, 2, 1, 3, 2, 3, 2, 1, 3, 0, 2, 2, 3, 1, 1, 0, ... | 1 |
construct-mc-graph-k-coloring-l6-s9 | construct | mc_graph_k_coloring | graph_k_coloring | graph_theory | competition | 6 | MathConstraint/graph_k_coloring | CC-BY-4.0 | [
"np_search"
] | Graph G with 250 vertices numbered 0..249 and 1075 edges:
(0,7), (0,31), (0,75), (0,99), (0,104), (0,126), (0,136), (0,139), (0,204), (0,207), (0,209), (1,2), (1,14), (1,19), (1,110), (1,135), (2,12), (2,23), (2,25), (2,57), (2,61), (2,96), (2,100), (2,131), (2,203), (2,226), (2,227), (3,52), (3,53), (3,74), (3,126), (... | {"n": 250, "k": 4, "edges": [[0, 7], [0, 31], [0, 75], [0, 99], [0, 104], [0, 126], [0, 136], [0, 139], [0, 204], [0, 207], [0, 209], [1, 2], [1, 14], [1, 19], [1, 110], [1, 135], [2, 12], [2, 23], [2, 25], [2, 57], [2, 61], [2, 96], [2, 100], [2, 131], [2, 203], [2, 226], [2, 227], [3, 52], [3, 53], [3, 74], [3, 126],... | null | null | null | {"coloring": [0, 1, 0, 1, 3, 2, 2, 3, 2, 1, 0, 3, 2, 3, 2, 1, 0, 1, 3, 3, 0, 3, 3, 2, 2, 2, 0, 0, 3, 0, 3, 1, 3, 0, 1, 3, 3, 0, 2, 0, 3, 0, 0, 0, 2, 1, 3, 1, 1, 2, 1, 3, 2, 0, 1, 2, 0, 3, 1, 1, 3, 1, 0, 0, 0, 0, 2, 2, 3, 0, 2, 0, 1, 2, 2, 2, 3, 1, 2, 0, 2, 1, 0, 1, 0, 1, 0, 0, 1, 3, 0, 2, 3, 3, 1, 0, 2, 3, 0, 1, 2, 1, ... | 1 |
construct-mc-hadamard-l1-s0 | construct | mc_hadamard | legendre_pair | combinatorics | competition | 1 | MathConstraint/hadamard | CC-BY-4.0 | [
"np_search"
] | Find two sequences x[0..8] and y[0..8] with entries in {-1, +1} (a Legendre pair of length 9) such that
(a) sum(x) = 1 and sum(y) = 1, and
(b) for every k = 1..4: sum_{i=0}^{8} x[i]*x[(i+k) mod 9] + sum_{i=0}^{8} y[i]*y[(i+k) mod 9] = -2.
Answer format: {"x": [x_0, ..., x_8], "y": [y_0, ..., y_8]} with entries -1 ... | {"n": 9, "family": "mc_hadamard", "subset": "construct"} | null | null | null | {"x": [1, 1, 1, -1, 1, -1, 1, -1, -1], "y": [1, 1, 1, 1, -1, -1, 1, -1, -1]} | 1 |
construct-mc-hadamard-l1-s1 | construct | mc_hadamard | legendre_pair | combinatorics | competition | 1 | MathConstraint/hadamard | CC-BY-4.0 | [
"np_search"
] | Find two sequences x[0..6] and y[0..6] with entries in {-1, +1} (a Legendre pair of length 7) such that
(a) sum(x) = 1 and sum(y) = 1, and
(b) for every k = 1..3: sum_{i=0}^{6} x[i]*x[(i+k) mod 7] + sum_{i=0}^{6} y[i]*y[(i+k) mod 7] = -2.
Answer format: {"x": [x_0, ..., x_6], "y": [y_0, ..., y_6]} with entries -1 ... | {"n": 7, "family": "mc_hadamard", "subset": "construct"} | null | null | null | {"x": [1, 1, 1, -1, 1, -1, -1], "y": [1, 1, 1, -1, 1, -1, -1]} | 1 |
construct-mc-hadamard-l1-s2 | construct | mc_hadamard | legendre_pair | combinatorics | competition | 1 | MathConstraint/hadamard | CC-BY-4.0 | [
"np_search"
] | Find two sequences x[0..4] and y[0..4] with entries in {-1, +1} (a Legendre pair of length 5) such that
(a) sum(x) = 1 and sum(y) = 1, and
(b) for every k = 1..2: sum_{i=0}^{4} x[i]*x[(i+k) mod 5] + sum_{i=0}^{4} y[i]*y[(i+k) mod 5] = -2.
Answer format: {"x": [x_0, ..., x_4], "y": [y_0, ..., y_4]} with entries -1 ... | {"n": 5, "family": "mc_hadamard", "subset": "construct"} | null | null | null | {"x": [1, 1, -1, -1, 1], "y": [1, -1, 1, 1, -1]} | 1 |
construct-mc-hadamard-l2-s0 | construct | mc_hadamard | legendre_pair | combinatorics | competition | 2 | MathConstraint/hadamard | CC-BY-4.0 | [
"np_search"
] | Find two sequences x[0..12] and y[0..12] with entries in {-1, +1} (a Legendre pair of length 13) such that
(a) sum(x) = 1 and sum(y) = 1, and
(b) for every k = 1..6: sum_{i=0}^{12} x[i]*x[(i+k) mod 13] + sum_{i=0}^{12} y[i]*y[(i+k) mod 13] = -2.
Answer format: {"x": [x_0, ..., x_12], "y": [y_0, ..., y_12]} with en... | {"n": 13, "family": "mc_hadamard", "subset": "construct"} | null | null | null | {"x": [1, -1, -1, 1, -1, 1, 1, -1, -1, 1, 1, 1, -1], "y": [1, 1, -1, -1, -1, -1, 1, -1, 1, 1, 1, -1, 1]} | 1 |
construct-mc-hadamard-l2-s1 | construct | mc_hadamard | legendre_pair | combinatorics | competition | 2 | MathConstraint/hadamard | CC-BY-4.0 | [
"np_search"
] | Find two sequences x[0..14] and y[0..14] with entries in {-1, +1} (a Legendre pair of length 15) such that
(a) sum(x) = 1 and sum(y) = 1, and
(b) for every k = 1..7: sum_{i=0}^{14} x[i]*x[(i+k) mod 15] + sum_{i=0}^{14} y[i]*y[(i+k) mod 15] = -2.
Answer format: {"x": [x_0, ..., x_14], "y": [y_0, ..., y_14]} with en... | {"n": 15, "family": "mc_hadamard", "subset": "construct"} | null | null | null | {"x": [1, 1, 1, 1, -1, 1, -1, 1, 1, -1, -1, 1, -1, -1, -1], "y": [1, 1, 1, 1, -1, 1, -1, 1, 1, -1, -1, 1, -1, -1, -1]} | 1 |
construct-mc-hadamard-l2-s2 | construct | mc_hadamard | legendre_pair | combinatorics | competition | 2 | MathConstraint/hadamard | CC-BY-4.0 | [
"np_search"
] | Find two sequences x[0..10] and y[0..10] with entries in {-1, +1} (a Legendre pair of length 11) such that
(a) sum(x) = 1 and sum(y) = 1, and
(b) for every k = 1..5: sum_{i=0}^{10} x[i]*x[(i+k) mod 11] + sum_{i=0}^{10} y[i]*y[(i+k) mod 11] = -2.
Answer format: {"x": [x_0, ..., x_10], "y": [y_0, ..., y_10]} with en... | {"n": 11, "family": "mc_hadamard", "subset": "construct"} | null | null | null | {"x": [1, 1, -1, 1, 1, 1, -1, -1, -1, 1, -1], "y": [1, 1, -1, 1, 1, 1, -1, -1, -1, 1, -1]} | 1 |
construct-mc-hadamard-l3-s0 | construct | mc_hadamard | legendre_pair | combinatorics | competition | 3 | MathConstraint/hadamard | CC-BY-4.0 | [
"np_search"
] | Find two sequences x[0..16] and y[0..16] with entries in {-1, +1} (a Legendre pair of length 17) such that
(a) sum(x) = 1 and sum(y) = 1, and
(b) for every k = 1..8: sum_{i=0}^{16} x[i]*x[(i+k) mod 17] + sum_{i=0}^{16} y[i]*y[(i+k) mod 17] = -2.
Answer format: {"x": [x_0, ..., x_16], "y": [y_0, ..., y_16]} with en... | {"n": 17, "family": "mc_hadamard", "subset": "construct"} | null | null | null | {"x": [1, 1, 1, -1, 1, -1, -1, -1, 1, 1, -1, -1, -1, 1, -1, 1, 1], "y": [1, -1, -1, 1, -1, 1, 1, 1, -1, -1, 1, 1, 1, -1, 1, -1, -1]} | 1 |
construct-mc-hadamard-l3-s1 | construct | mc_hadamard | legendre_pair | combinatorics | competition | 3 | MathConstraint/hadamard | CC-BY-4.0 | [
"np_search"
] | Find two sequences x[0..18] and y[0..18] with entries in {-1, +1} (a Legendre pair of length 19) such that
(a) sum(x) = 1 and sum(y) = 1, and
(b) for every k = 1..9: sum_{i=0}^{18} x[i]*x[(i+k) mod 19] + sum_{i=0}^{18} y[i]*y[(i+k) mod 19] = -2.
Answer format: {"x": [x_0, ..., x_18], "y": [y_0, ..., y_18]} with en... | {"n": 19, "family": "mc_hadamard", "subset": "construct"} | null | null | null | {"x": [1, 1, -1, -1, 1, 1, 1, 1, -1, 1, -1, 1, -1, -1, -1, -1, 1, 1, -1], "y": [1, 1, -1, -1, 1, 1, 1, 1, -1, 1, -1, 1, -1, -1, -1, -1, 1, 1, -1]} | 1 |
construct-mc-hadamard-l3-s2 | construct | mc_hadamard | legendre_pair | combinatorics | competition | 3 | MathConstraint/hadamard | CC-BY-4.0 | [
"np_search"
] | Find two sequences x[0..22] and y[0..22] with entries in {-1, +1} (a Legendre pair of length 23) such that
(a) sum(x) = 1 and sum(y) = 1, and
(b) for every k = 1..11: sum_{i=0}^{22} x[i]*x[(i+k) mod 23] + sum_{i=0}^{22} y[i]*y[(i+k) mod 23] = -2.
Answer format: {"x": [x_0, ..., x_22], "y": [y_0, ..., y_22]} with e... | {"n": 23, "family": "mc_hadamard", "subset": "construct"} | null | null | null | {"x": [1, 1, 1, 1, -1, 1, -1, -1, -1, -1, 1, -1, -1, -1, 1, 1, 1, -1, 1, -1, -1, 1, 1], "y": [1, 1, 1, -1, -1, 1, 1, -1, 1, 1, -1, -1, 1, -1, 1, 1, -1, 1, -1, 1, -1, -1, -1]} | 1 |
construct-mc-hadamard-l3-s3 | construct | mc_hadamard | legendre_pair | combinatorics | competition | 3 | MathConstraint/hadamard | CC-BY-4.0 | [
"np_search"
] | Find two sequences x[0..20] and y[0..20] with entries in {-1, +1} (a Legendre pair of length 21) such that
(a) sum(x) = 1 and sum(y) = 1, and
(b) for every k = 1..10: sum_{i=0}^{20} x[i]*x[(i+k) mod 21] + sum_{i=0}^{20} y[i]*y[(i+k) mod 21] = -2.
Answer format: {"x": [x_0, ..., x_20], "y": [y_0, ..., y_20]} with e... | {"n": 21, "family": "mc_hadamard", "subset": "construct"} | null | null | null | {"x": [1, 1, 1, 1, 1, -1, 1, -1, 1, -1, -1, 1, -1, -1, 1, 1, -1, 1, -1, -1, -1], "y": [1, 1, 1, 1, 1, -1, 1, -1, 1, 1, -1, -1, -1, 1, 1, -1, -1, -1, 1, -1, -1]} | 1 |
construct-mc-hadamard-l4-s0 | construct | mc_hadamard | legendre_pair | combinatorics | competition | 4 | MathConstraint/hadamard | CC-BY-4.0 | [
"np_search"
] | Find two sequences x[0..28] and y[0..28] with entries in {-1, +1} (a Legendre pair of length 29) such that
(a) sum(x) = 1 and sum(y) = 1, and
(b) for every k = 1..14: sum_{i=0}^{28} x[i]*x[(i+k) mod 29] + sum_{i=0}^{28} y[i]*y[(i+k) mod 29] = -2.
Answer format: {"x": [x_0, ..., x_28], "y": [y_0, ..., y_28]} with e... | {"n": 29, "family": "mc_hadamard", "subset": "construct"} | null | null | null | {"x": [1, 1, -1, -1, 1, 1, 1, 1, -1, 1, -1, -1, -1, 1, -1, -1, 1, -1, -1, -1, 1, -1, 1, 1, 1, 1, -1, -1, 1], "y": [1, -1, 1, 1, -1, -1, -1, -1, 1, -1, 1, 1, 1, -1, 1, 1, -1, 1, 1, 1, -1, 1, -1, -1, -1, -1, 1, 1, -1]} | 1 |
construct-mc-hadamard-l4-s1 | construct | mc_hadamard | legendre_pair | combinatorics | competition | 4 | MathConstraint/hadamard | CC-BY-4.0 | [
"np_search"
] | Find two sequences x[0..34] and y[0..34] with entries in {-1, +1} (a Legendre pair of length 35) such that
(a) sum(x) = 1 and sum(y) = 1, and
(b) for every k = 1..17: sum_{i=0}^{34} x[i]*x[(i+k) mod 35] + sum_{i=0}^{34} y[i]*y[(i+k) mod 35] = -2.
Answer format: {"x": [x_0, ..., x_34], "y": [y_0, ..., y_34]} with e... | {"n": 35, "family": "mc_hadamard", "subset": "construct"} | null | null | null | {"x": [-1, -1, 1, -1, -1, 1, 1, -1, 1, -1, 1, -1, -1, -1, -1, 1, -1, -1, 1, 1, 1, -1, 1, 1, 1, 1, 1, -1, -1, -1, 1, 1, 1, -1, 1], "y": [-1, -1, 1, -1, -1, 1, 1, -1, 1, -1, 1, -1, -1, -1, -1, 1, -1, -1, 1, 1, 1, -1, 1, 1, 1, 1, 1, -1, -1, -1, 1, 1, 1, -1, 1]} | 1 |
construct-mc-hadamard-l4-s2 | construct | mc_hadamard | legendre_pair | combinatorics | competition | 4 | MathConstraint/hadamard | CC-BY-4.0 | [
"np_search"
] | Find two sequences x[0..30] and y[0..30] with entries in {-1, +1} (a Legendre pair of length 31) such that
(a) sum(x) = 1 and sum(y) = 1, and
(b) for every k = 1..15: sum_{i=0}^{30} x[i]*x[(i+k) mod 31] + sum_{i=0}^{30} y[i]*y[(i+k) mod 31] = -2.
Answer format: {"x": [x_0, ..., x_30], "y": [y_0, ..., y_30]} with e... | {"n": 31, "family": "mc_hadamard", "subset": "construct"} | null | null | null | {"x": [1, 1, 1, -1, 1, 1, -1, 1, 1, 1, 1, -1, -1, -1, 1, -1, 1, -1, 1, 1, 1, -1, -1, -1, -1, 1, -1, -1, 1, -1, -1], "y": [1, 1, 1, -1, 1, 1, -1, 1, 1, 1, 1, -1, -1, -1, 1, -1, 1, -1, 1, 1, 1, -1, -1, -1, -1, 1, -1, -1, 1, -1, -1]} | 1 |
construct-mc-hadamard-l4-s3 | construct | mc_hadamard | legendre_pair | combinatorics | competition | 4 | MathConstraint/hadamard | CC-BY-4.0 | [
"np_search"
] | Find two sequences x[0..26] and y[0..26] with entries in {-1, +1} (a Legendre pair of length 27) such that
(a) sum(x) = 1 and sum(y) = 1, and
(b) for every k = 1..13: sum_{i=0}^{26} x[i]*x[(i+k) mod 27] + sum_{i=0}^{26} y[i]*y[(i+k) mod 27] = -2.
Answer format: {"x": [x_0, ..., x_26], "y": [y_0, ..., y_26]} with e... | {"n": 27, "family": "mc_hadamard", "subset": "construct"} | null | null | null | {"x": [-1, 1, 1, 1, -1, -1, 1, 1, -1, -1, 1, -1, 1, 1, -1, -1, 1, -1, 1, 1, 1, 1, -1, 1, -1, -1, -1], "y": [1, -1, -1, -1, -1, -1, 1, 1, -1, -1, 1, -1, 1, -1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, -1, 1, -1]} | 1 |
construct-mc-hadamard-l4-s4 | construct | mc_hadamard | legendre_pair | combinatorics | competition | 4 | MathConstraint/hadamard | CC-BY-4.0 | [
"np_search"
] | Find two sequences x[0..24] and y[0..24] with entries in {-1, +1} (a Legendre pair of length 25) such that
(a) sum(x) = 1 and sum(y) = 1, and
(b) for every k = 1..12: sum_{i=0}^{24} x[i]*x[(i+k) mod 25] + sum_{i=0}^{24} y[i]*y[(i+k) mod 25] = -2.
Answer format: {"x": [x_0, ..., x_24], "y": [y_0, ..., y_24]} with e... | {"n": 25, "family": "mc_hadamard", "subset": "construct"} | null | null | null | {"x": [1, 1, 1, 1, 1, 1, -1, -1, 1, -1, 1, -1, 1, -1, -1, 1, 1, -1, -1, -1, 1, 1, -1, -1, -1], "y": [1, 1, 1, 1, 1, 1, -1, 1, -1, 1, -1, -1, 1, -1, -1, 1, -1, -1, 1, 1, -1, 1, -1, -1, -1]} | 1 |
construct-mc-hadamard-l5-s0 | construct | mc_hadamard | legendre_pair | combinatorics | competition | 5 | MathConstraint/hadamard | CC-BY-4.0 | [
"np_search"
] | Find two sequences x[0..36] and y[0..36] with entries in {-1, +1} (a Legendre pair of length 37) such that
(a) sum(x) = 1 and sum(y) = 1, and
(b) for every k = 1..18: sum_{i=0}^{36} x[i]*x[(i+k) mod 37] + sum_{i=0}^{36} y[i]*y[(i+k) mod 37] = -2.
Answer format: {"x": [x_0, ..., x_36], "y": [y_0, ..., y_36]} with e... | {"n": 37, "family": "mc_hadamard", "subset": "construct"} | null | null | null | {"x": [1, 1, -1, 1, 1, -1, -1, 1, -1, 1, 1, 1, 1, -1, -1, -1, 1, -1, -1, -1, -1, 1, -1, -1, -1, 1, 1, 1, 1, -1, 1, -1, -1, 1, 1, -1, 1], "y": [1, -1, 1, -1, -1, 1, 1, -1, 1, -1, -1, -1, -1, 1, 1, 1, -1, 1, 1, 1, 1, -1, 1, 1, 1, -1, -1, -1, -1, 1, -1, 1, 1, -1, -1, 1, -1]} | 1 |
construct-mc-hadamard-l5-s1 | construct | mc_hadamard | legendre_pair | combinatorics | competition | 5 | MathConstraint/hadamard | CC-BY-4.0 | [
"np_search"
] | Find two sequences x[0..52] and y[0..52] with entries in {-1, +1} (a Legendre pair of length 53) such that
(a) sum(x) = 1 and sum(y) = 1, and
(b) for every k = 1..26: sum_{i=0}^{52} x[i]*x[(i+k) mod 53] + sum_{i=0}^{52} y[i]*y[(i+k) mod 53] = -2.
Answer format: {"x": [x_0, ..., x_52], "y": [y_0, ..., y_52]} with e... | {"n": 53, "family": "mc_hadamard", "subset": "construct"} | null | null | null | {"x": [1, 1, -1, -1, 1, -1, 1, 1, -1, 1, 1, 1, -1, 1, -1, 1, 1, 1, -1, -1, -1, -1, -1, -1, 1, 1, -1, -1, 1, 1, -1, -1, -1, -1, -1, -1, 1, 1, 1, -1, 1, -1, 1, 1, 1, -1, 1, 1, -1, 1, -1, -1, 1], "y": [1, -1, 1, 1, -1, 1, -1, -1, 1, -1, -1, -1, 1, -1, 1, -1, -1, -1, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1... | 1 |
construct-mc-hadamard-l5-s2 | construct | mc_hadamard | legendre_pair | combinatorics | competition | 5 | MathConstraint/hadamard | CC-BY-4.0 | [
"np_search"
] | Find two sequences x[0..40] and y[0..40] with entries in {-1, +1} (a Legendre pair of length 41) such that
(a) sum(x) = 1 and sum(y) = 1, and
(b) for every k = 1..20: sum_{i=0}^{40} x[i]*x[(i+k) mod 41] + sum_{i=0}^{40} y[i]*y[(i+k) mod 41] = -2.
Answer format: {"x": [x_0, ..., x_40], "y": [y_0, ..., y_40]} with e... | {"n": 41, "family": "mc_hadamard", "subset": "construct"} | null | null | null | {"x": [1, 1, 1, -1, 1, 1, -1, -1, 1, 1, 1, -1, -1, -1, -1, -1, 1, -1, 1, -1, 1, 1, -1, 1, -1, 1, -1, -1, -1, -1, -1, 1, 1, 1, -1, -1, 1, 1, -1, 1, 1], "y": [1, -1, -1, 1, -1, -1, 1, 1, -1, -1, -1, 1, 1, 1, 1, 1, -1, 1, -1, 1, -1, -1, 1, -1, 1, -1, 1, 1, 1, 1, 1, -1, -1, -1, 1, 1, -1, -1, 1, -1, -1]} | 1 |
construct-mc-hadamard-l5-s3 | construct | mc_hadamard | legendre_pair | combinatorics | competition | 5 | MathConstraint/hadamard | CC-BY-4.0 | [
"np_search"
] | Find two sequences x[0..42] and y[0..42] with entries in {-1, +1} (a Legendre pair of length 43) such that
(a) sum(x) = 1 and sum(y) = 1, and
(b) for every k = 1..21: sum_{i=0}^{42} x[i]*x[(i+k) mod 43] + sum_{i=0}^{42} y[i]*y[(i+k) mod 43] = -2.
Answer format: {"x": [x_0, ..., x_42], "y": [y_0, ..., y_42]} with e... | {"n": 43, "family": "mc_hadamard", "subset": "construct"} | null | null | null | {"x": [1, 1, -1, -1, 1, -1, 1, -1, -1, 1, 1, 1, -1, 1, 1, 1, 1, 1, -1, -1, -1, 1, -1, 1, 1, 1, -1, -1, -1, -1, -1, 1, -1, -1, -1, 1, 1, -1, 1, -1, 1, 1, -1], "y": [1, 1, -1, -1, 1, -1, 1, -1, -1, 1, 1, 1, -1, 1, 1, 1, 1, 1, -1, -1, -1, 1, -1, 1, 1, 1, -1, -1, -1, -1, -1, 1, -1, -1, -1, 1, 1, -1, 1, -1, 1, 1, -1]} | 1 |
construct-mc-hadamard-l5-s4 | construct | mc_hadamard | legendre_pair | combinatorics | competition | 5 | MathConstraint/hadamard | CC-BY-4.0 | [
"np_search"
] | Find two sequences x[0..46] and y[0..46] with entries in {-1, +1} (a Legendre pair of length 47) such that
(a) sum(x) = 1 and sum(y) = 1, and
(b) for every k = 1..23: sum_{i=0}^{46} x[i]*x[(i+k) mod 47] + sum_{i=0}^{46} y[i]*y[(i+k) mod 47] = -2.
Answer format: {"x": [x_0, ..., x_46], "y": [y_0, ..., y_46]} with e... | {"n": 47, "family": "mc_hadamard", "subset": "construct"} | null | null | null | {"x": [1, 1, 1, 1, 1, -1, 1, 1, 1, 1, -1, -1, 1, -1, 1, -1, 1, 1, 1, -1, -1, 1, -1, -1, 1, 1, -1, 1, 1, -1, -1, -1, 1, -1, 1, -1, 1, 1, -1, -1, -1, -1, 1, -1, -1, -1, -1], "y": [1, 1, 1, 1, 1, -1, 1, 1, 1, 1, -1, -1, 1, -1, 1, -1, 1, 1, 1, -1, -1, 1, -1, -1, 1, 1, -1, 1, 1, -1, -1, -1, 1, -1, 1, -1, 1, 1, -1, -1, -1, -... | 1 |
construct-mc-hadamard-l6-s0 | construct | mc_hadamard | legendre_pair | combinatorics | competition | 6 | MathConstraint/hadamard | CC-BY-4.0 | [
"np_search"
] | Find two sequences x[0..96] and y[0..96] with entries in {-1, +1} (a Legendre pair of length 97) such that
(a) sum(x) = 1 and sum(y) = 1, and
(b) for every k = 1..48: sum_{i=0}^{96} x[i]*x[(i+k) mod 97] + sum_{i=0}^{96} y[i]*y[(i+k) mod 97] = -2.
Answer format: {"x": [x_0, ..., x_96], "y": [y_0, ..., y_96]} with e... | {"n": 97, "family": "mc_hadamard", "subset": "construct"} | null | null | null | {"x": [1, 1, 1, 1, 1, -1, 1, -1, 1, 1, -1, 1, 1, -1, -1, -1, 1, -1, 1, -1, -1, -1, 1, -1, 1, 1, -1, 1, -1, -1, -1, 1, 1, 1, -1, 1, 1, -1, -1, -1, -1, -1, -1, 1, 1, -1, -1, 1, 1, 1, 1, -1, -1, 1, 1, -1, -1, -1, -1, -1, -1, 1, 1, -1, 1, 1, 1, -1, -1, -1, 1, -1, 1, 1, -1, 1, -1, -1, -1, 1, -1, 1, -1, -1, -1, 1, 1, -1, 1, ... | 1 |
construct-mc-hadamard-l6-s1 | construct | mc_hadamard | legendre_pair | combinatorics | competition | 6 | MathConstraint/hadamard | CC-BY-4.0 | [
"np_search"
] | Find two sequences x[0..78] and y[0..78] with entries in {-1, +1} (a Legendre pair of length 79) such that
(a) sum(x) = 1 and sum(y) = 1, and
(b) for every k = 1..39: sum_{i=0}^{78} x[i]*x[(i+k) mod 79] + sum_{i=0}^{78} y[i]*y[(i+k) mod 79] = -2.
Answer format: {"x": [x_0, ..., x_78], "y": [y_0, ..., y_78]} with e... | {"n": 79, "family": "mc_hadamard", "subset": "construct"} | null | null | null | {"x": [1, 1, 1, -1, 1, 1, -1, -1, 1, 1, 1, 1, -1, 1, -1, -1, 1, -1, 1, 1, 1, 1, 1, 1, -1, 1, 1, -1, -1, -1, -1, 1, 1, -1, -1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, 1, 1, -1, -1, 1, 1, 1, 1, -1, -1, 1, -1, -1, -1, -1, -1, -1, 1, -1, 1, 1, -1, 1, -1, -1, -1, -1, 1, 1, -1, -1, 1, -1, -1], "y": [1, 1, 1, -1, 1, 1, -1, -1, 1, ... | 1 |
construct-mc-hadamard-l6-s2 | construct | mc_hadamard | legendre_pair | combinatorics | competition | 6 | MathConstraint/hadamard | CC-BY-4.0 | [
"np_search"
] | Find two sequences x[0..142] and y[0..142] with entries in {-1, +1} (a Legendre pair of length 143) such that
(a) sum(x) = 1 and sum(y) = 1, and
(b) for every k = 1..71: sum_{i=0}^{142} x[i]*x[(i+k) mod 143] + sum_{i=0}^{142} y[i]*y[(i+k) mod 143] = -2.
Answer format: {"x": [x_0, ..., x_142], "y": [y_0, ..., y_142... | {"n": 143, "family": "mc_hadamard", "subset": "construct"} | null | null | null | {"x": [-1, -1, -1, -1, -1, 1, -1, -1, -1, -1, 1, 1, -1, -1, -1, 1, -1, 1, -1, -1, 1, -1, 1, -1, -1, -1, -1, -1, -1, 1, 1, 1, -1, 1, 1, 1, -1, 1, -1, -1, 1, -1, -1, 1, 1, 1, -1, 1, -1, -1, -1, 1, -1, -1, -1, 1, -1, -1, 1, 1, 1, 1, 1, -1, -1, -1, 1, 1, 1, -1, 1, 1, -1, -1, 1, -1, -1, 1, -1, 1, 1, -1, -1, -1, -1, -1, 1, 1... | 1 |
construct-mc-hadamard-l6-s3 | construct | mc_hadamard | legendre_pair | combinatorics | competition | 6 | MathConstraint/hadamard | CC-BY-4.0 | [
"np_search"
] | Find two sequences x[0..100] and y[0..100] with entries in {-1, +1} (a Legendre pair of length 101) such that
(a) sum(x) = 1 and sum(y) = 1, and
(b) for every k = 1..50: sum_{i=0}^{100} x[i]*x[(i+k) mod 101] + sum_{i=0}^{100} y[i]*y[(i+k) mod 101] = -2.
Answer format: {"x": [x_0, ..., x_100], "y": [y_0, ..., y_100... | {"n": 101, "family": "mc_hadamard", "subset": "construct"} | null | null | null | {"x": [1, 1, -1, -1, 1, 1, 1, -1, -1, 1, -1, -1, -1, 1, 1, -1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, -1, 1, -1, -1, 1, 1, -1, -1, -1, -1, -1, 1, -1, 1, -1, 1, -1, 1, -1, -1, 1, -1, 1, -1, 1, -1, 1, -1, -1, -1, -1, -1, 1, 1, -1, -1, 1, -1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, -1, 1, 1, -1, 1, 1, -1,... | 1 |
construct-mc-hadamard-l6-s4 | construct | mc_hadamard | legendre_pair | combinatorics | competition | 6 | MathConstraint/hadamard | CC-BY-4.0 | [
"np_search"
] | Find two sequences x[0..70] and y[0..70] with entries in {-1, +1} (a Legendre pair of length 71) such that
(a) sum(x) = 1 and sum(y) = 1, and
(b) for every k = 1..35: sum_{i=0}^{70} x[i]*x[(i+k) mod 71] + sum_{i=0}^{70} y[i]*y[(i+k) mod 71] = -2.
Answer format: {"x": [x_0, ..., x_70], "y": [y_0, ..., y_70]} with e... | {"n": 71, "family": "mc_hadamard", "subset": "construct"} | null | null | null | {"x": [1, 1, 1, 1, 1, 1, 1, -1, 1, 1, 1, -1, 1, -1, -1, 1, 1, -1, 1, 1, 1, -1, -1, -1, 1, 1, -1, 1, -1, 1, 1, -1, 1, -1, -1, -1, 1, 1, 1, -1, 1, -1, -1, 1, -1, 1, -1, -1, 1, 1, 1, -1, -1, -1, 1, -1, -1, 1, 1, -1, 1, -1, -1, -1, 1, -1, -1, -1, -1, -1, -1], "y": [1, 1, 1, 1, 1, 1, 1, -1, 1, 1, 1, -1, 1, -1, -1, 1, 1, -1,... | 1 |
construct-mc-hadamard-l6-s5 | construct | mc_hadamard | legendre_pair | combinatorics | competition | 6 | MathConstraint/hadamard | CC-BY-4.0 | [
"np_search"
] | Find two sequences x[0..82] and y[0..82] with entries in {-1, +1} (a Legendre pair of length 83) such that
(a) sum(x) = 1 and sum(y) = 1, and
(b) for every k = 1..41: sum_{i=0}^{82} x[i]*x[(i+k) mod 83] + sum_{i=0}^{82} y[i]*y[(i+k) mod 83] = -2.
Answer format: {"x": [x_0, ..., x_82], "y": [y_0, ..., y_82]} with e... | {"n": 83, "family": "mc_hadamard", "subset": "construct"} | null | null | null | {"x": [1, 1, -1, 1, 1, -1, -1, 1, -1, 1, 1, 1, 1, -1, -1, -1, 1, 1, -1, -1, -1, 1, -1, 1, -1, 1, 1, 1, 1, 1, 1, 1, -1, 1, -1, -1, 1, 1, 1, -1, 1, 1, -1, -1, 1, -1, -1, -1, 1, 1, -1, 1, -1, -1, -1, -1, -1, -1, -1, 1, -1, 1, -1, 1, 1, 1, -1, -1, 1, 1, 1, -1, -1, -1, -1, 1, -1, 1, 1, -1, -1, 1, -1], "y": [1, 1, -1, 1, 1, ... | 1 |
construct-mc-hadamard-l6-s6 | construct | mc_hadamard | legendre_pair | combinatorics | competition | 6 | MathConstraint/hadamard | CC-BY-4.0 | [
"np_search"
] | Find two sequences x[0..60] and y[0..60] with entries in {-1, +1} (a Legendre pair of length 61) such that
(a) sum(x) = 1 and sum(y) = 1, and
(b) for every k = 1..30: sum_{i=0}^{60} x[i]*x[(i+k) mod 61] + sum_{i=0}^{60} y[i]*y[(i+k) mod 61] = -2.
Answer format: {"x": [x_0, ..., x_60], "y": [y_0, ..., y_60]} with e... | {"n": 61, "family": "mc_hadamard", "subset": "construct"} | null | null | null | {"x": [1, 1, -1, 1, 1, 1, -1, -1, -1, 1, -1, -1, 1, 1, 1, 1, 1, -1, -1, 1, 1, -1, 1, -1, -1, 1, -1, 1, -1, -1, -1, -1, -1, -1, 1, -1, 1, -1, -1, 1, -1, 1, 1, -1, -1, 1, 1, 1, 1, 1, -1, -1, 1, -1, -1, -1, 1, 1, 1, -1, 1], "y": [1, -1, 1, -1, -1, -1, 1, 1, 1, -1, 1, 1, -1, -1, -1, -1, -1, 1, 1, -1, -1, 1, -1, 1, 1, -1, 1... | 1 |
construct-mc-hadamard-l6-s7 | construct | mc_hadamard | legendre_pair | combinatorics | competition | 6 | MathConstraint/hadamard | CC-BY-4.0 | [
"np_search"
] | Find two sequences x[0..62] and y[0..62] with entries in {-1, +1} (a Legendre pair of length 63) such that
(a) sum(x) = 1 and sum(y) = 1, and
(b) for every k = 1..31: sum_{i=0}^{62} x[i]*x[(i+k) mod 63] + sum_{i=0}^{62} y[i]*y[(i+k) mod 63] = -2.
Answer format: {"x": [x_0, ..., x_62], "y": [y_0, ..., y_62]} with e... | {"n": 63, "family": "mc_hadamard", "subset": "construct"} | null | null | null | {"x": [1, -1, -1, -1, -1, -1, 1, -1, -1, -1, -1, 1, 1, -1, -1, -1, 1, -1, 1, -1, -1, 1, 1, 1, 1, -1, 1, -1, -1, -1, 1, 1, 1, -1, -1, 1, -1, -1, 1, -1, 1, 1, -1, 1, 1, 1, -1, 1, 1, -1, -1, 1, 1, -1, 1, -1, 1, -1, 1, 1, 1, 1, 1], "y": [1, -1, -1, -1, -1, -1, 1, -1, -1, -1, -1, 1, 1, -1, -1, -1, 1, -1, 1, -1, -1, 1, 1, 1,... | 1 |
construct-mc-hadamard-l6-s8 | construct | mc_hadamard | legendre_pair | combinatorics | competition | 6 | MathConstraint/hadamard | CC-BY-4.0 | [
"np_search"
] | Find two sequences x[0..58] and y[0..58] with entries in {-1, +1} (a Legendre pair of length 59) such that
(a) sum(x) = 1 and sum(y) = 1, and
(b) for every k = 1..29: sum_{i=0}^{58} x[i]*x[(i+k) mod 59] + sum_{i=0}^{58} y[i]*y[(i+k) mod 59] = -2.
Answer format: {"x": [x_0, ..., x_58], "y": [y_0, ..., y_58]} with e... | {"n": 59, "family": "mc_hadamard", "subset": "construct"} | null | null | null | {"x": [1, 1, -1, 1, 1, 1, -1, 1, -1, 1, -1, -1, 1, -1, -1, 1, 1, 1, -1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, 1, 1, -1, -1, -1, -1, 1, -1, -1, -1, 1, 1, -1, 1, 1, -1, 1, -1, 1, -1, -1, -1, 1, -1], "y": [1, 1, -1, 1, 1, 1, -1, 1, -1, 1, -1, -1, 1, -1, -1, 1, 1, 1, -1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, ... | 1 |
construct-mc-hadamard-l6-s9 | construct | mc_hadamard | legendre_pair | combinatorics | competition | 6 | MathConstraint/hadamard | CC-BY-4.0 | [
"np_search"
] | Find two sequences x[0..66] and y[0..66] with entries in {-1, +1} (a Legendre pair of length 67) such that
(a) sum(x) = 1 and sum(y) = 1, and
(b) for every k = 1..33: sum_{i=0}^{66} x[i]*x[(i+k) mod 67] + sum_{i=0}^{66} y[i]*y[(i+k) mod 67] = -2.
Answer format: {"x": [x_0, ..., x_66], "y": [y_0, ..., y_66]} with e... | {"n": 67, "family": "mc_hadamard", "subset": "construct"} | null | null | null | {"x": [1, 1, -1, -1, 1, -1, 1, -1, -1, 1, 1, -1, -1, -1, 1, 1, 1, 1, -1, 1, -1, 1, 1, 1, 1, 1, 1, -1, -1, 1, -1, -1, -1, 1, -1, 1, 1, 1, -1, 1, 1, -1, -1, -1, -1, -1, -1, 1, -1, 1, -1, -1, -1, -1, 1, 1, 1, -1, -1, 1, 1, -1, 1, -1, 1, 1, -1], "y": [1, 1, -1, -1, 1, -1, 1, -1, -1, 1, 1, -1, -1, -1, 1, 1, 1, 1, -1, 1, -1,... | 1 |
construct-mc-langford-l1-s0 | construct | mc_langford | langford_pairing | combinatorics | competition | 1 | MathConstraint/langford | CC-BY-4.0 | [
"agentic_trivial",
"np_search"
] | A Langford sequence L(2,7) is a sequence seq[0..13] of length 14 that contains exactly two copies of each integer 1..7, such that the two copies of every value v are exactly v+1 positions apart (their indices differ by v+1). Example: L(2,3) = [2, 3, 1, 2, 1, 3].
Find a Langford sequence L(2,7).
Answer format: {"seq":... | {"n": 7, "fixed": [], "family": "mc_langford", "subset": "construct"} | null | null | null | {"seq": [1, 7, 1, 2, 5, 6, 2, 3, 4, 7, 5, 3, 6, 4]} | 1 |
construct-mc-langford-l1-s1 | construct | mc_langford | langford_pairing | combinatorics | competition | 1 | MathConstraint/langford | CC-BY-4.0 | [
"agentic_trivial",
"np_search"
] | A Langford sequence L(2,4) is a sequence seq[0..7] of length 8 that contains exactly two copies of each integer 1..4, such that the two copies of every value v are exactly v+1 positions apart (their indices differ by v+1). Example: L(2,3) = [2, 3, 1, 2, 1, 3].
Find a Langford sequence L(2,4).
Answer format: {"seq": [... | {"n": 4, "fixed": [], "family": "mc_langford", "subset": "construct"} | null | null | null | {"seq": [2, 3, 4, 2, 1, 3, 1, 4]} | 1 |
construct-mc-langford-l1-s2 | construct | mc_langford | langford_pairing | combinatorics | competition | 1 | MathConstraint/langford | CC-BY-4.0 | [
"agentic_trivial",
"np_search"
] | A Langford sequence L(2,3) is a sequence seq[0..5] of length 6 that contains exactly two copies of each integer 1..3, such that the two copies of every value v are exactly v+1 positions apart (their indices differ by v+1). Example: L(2,3) = [2, 3, 1, 2, 1, 3].
Find a Langford sequence L(2,3).
Answer format: {"seq": [... | {"n": 3, "fixed": [], "family": "mc_langford", "subset": "construct"} | null | null | null | {"seq": [2, 3, 1, 2, 1, 3]} | 1 |
construct-mc-langford-l2-s0 | construct | mc_langford | langford_pairing | combinatorics | competition | 2 | MathConstraint/langford | CC-BY-4.0 | [
"agentic_trivial",
"np_search"
] | A Langford sequence L(2,8) is a sequence seq[0..15] of length 16 that contains exactly two copies of each integer 1..8, such that the two copies of every value v are exactly v+1 positions apart (their indices differ by v+1). Example: L(2,3) = [2, 3, 1, 2, 1, 3].
Find a Langford sequence L(2,8).
Answer format: {"seq":... | {"n": 8, "fixed": [], "family": "mc_langford", "subset": "construct"} | null | null | null | {"seq": [7, 4, 6, 8, 2, 5, 4, 2, 7, 6, 3, 5, 8, 1, 3, 1]} | 1 |
construct-mc-langford-l2-s1 | construct | mc_langford | langford_pairing | combinatorics | competition | 2 | MathConstraint/langford | CC-BY-4.0 | [
"agentic_trivial",
"np_search"
] | A Langford sequence L(2,12) is a sequence seq[0..23] of length 24 that contains exactly two copies of each integer 1..12, such that the two copies of every value v are exactly v+1 positions apart (their indices differ by v+1). Example: L(2,3) = [2, 3, 1, 2, 1, 3].
Find a Langford sequence L(2,12).
Answer format: {"se... | {"n": 12, "fixed": [], "family": "mc_langford", "subset": "construct"} | null | null | null | {"seq": [4, 2, 7, 11, 2, 4, 5, 10, 8, 12, 7, 9, 5, 6, 1, 11, 1, 8, 10, 3, 6, 9, 12, 3]} | 1 |
construct-mc-langford-l2-s2 | construct | mc_langford | langford_pairing | combinatorics | competition | 2 | MathConstraint/langford | CC-BY-4.0 | [
"agentic_trivial",
"np_search"
] | A Langford sequence L(2,11) is a sequence seq[0..21] of length 22 that contains exactly two copies of each integer 1..11, such that the two copies of every value v are exactly v+1 positions apart (their indices differ by v+1). Example: L(2,3) = [2, 3, 1, 2, 1, 3].
Find a Langford sequence L(2,11).
Answer format: {"se... | {"n": 11, "fixed": [], "family": "mc_langford", "subset": "construct"} | null | null | null | {"seq": [6, 2, 3, 11, 2, 10, 3, 6, 9, 1, 8, 1, 4, 7, 5, 11, 10, 4, 9, 8, 5, 7]} | 1 |
construct-mc-langford-l2-s3 | construct | mc_langford | langford_pairing | combinatorics | competition | 2 | MathConstraint/langford | CC-BY-4.0 | [
"agentic_trivial",
"np_search"
] | A Langford sequence L(2,8) is a sequence seq[0..15] of length 16 that contains exactly two copies of each integer 1..8, such that the two copies of every value v are exactly v+1 positions apart (their indices differ by v+1). Example: L(2,3) = [2, 3, 1, 2, 1, 3].
Find a Langford sequence L(2,8).
Some values are fixed ... | {"n": 8, "fixed": [["seq", 4, 7], ["seq", 8, 5], ["seq", 10, 4]], "family": "mc_langford", "subset": "construct"} | null | null | null | {"seq": [2, 3, 8, 2, 7, 3, 6, 1, 5, 1, 4, 8, 7, 6, 5, 4]} | 1 |
construct-mc-langford-l3-s0 | construct | mc_langford | langford_pairing | combinatorics | competition | 3 | MathConstraint/langford | CC-BY-4.0 | [
"agentic_trivial",
"np_search"
] | A Langford sequence L(2,16) is a sequence seq[0..31] of length 32 that contains exactly two copies of each integer 1..16, such that the two copies of every value v are exactly v+1 positions apart (their indices differ by v+1). Example: L(2,3) = [2, 3, 1, 2, 1, 3].
Find a Langford sequence L(2,16).
Answer format: {"se... | {"n": 16, "fixed": [], "family": "mc_langford", "subset": "construct"} | null | null | null | {"seq": [14, 15, 8, 6, 16, 7, 11, 12, 13, 4, 6, 8, 10, 7, 4, 14, 9, 15, 11, 5, 12, 16, 13, 10, 3, 5, 9, 2, 3, 1, 2, 1]} | 1 |
construct-mc-langford-l3-s1 | construct | mc_langford | langford_pairing | combinatorics | competition | 3 | MathConstraint/langford | CC-BY-4.0 | [
"agentic_trivial",
"np_search"
] | A Langford sequence L(2,15) is a sequence seq[0..29] of length 30 that contains exactly two copies of each integer 1..15, such that the two copies of every value v are exactly v+1 positions apart (their indices differ by v+1). Example: L(2,3) = [2, 3, 1, 2, 1, 3].
Find a Langford sequence L(2,15).
Some values are fix... | {"n": 15, "fixed": [["seq", 3, 2], ["seq", 11, 14], ["seq", 13, 11], ["seq", 26, 14], ["seq", 27, 7], ["seq", 28, 10]], "family": "mc_langford", "subset": "construct"} | null | null | null | {"seq": [2, 6, 3, 2, 4, 12, 3, 15, 6, 4, 13, 14, 9, 11, 1, 5, 1, 10, 12, 7, 8, 5, 9, 15, 13, 11, 14, 7, 10, 8]} | 1 |
construct-mc-langford-l3-s2 | construct | mc_langford | langford_pairing | combinatorics | competition | 3 | MathConstraint/langford | CC-BY-4.0 | [
"agentic_trivial",
"np_search"
] | A Langford sequence L(2,15) is a sequence seq[0..29] of length 30 that contains exactly two copies of each integer 1..15, such that the two copies of every value v are exactly v+1 positions apart (their indices differ by v+1). Example: L(2,3) = [2, 3, 1, 2, 1, 3].
Find a Langford sequence L(2,15).
Answer format: {"se... | {"n": 15, "fixed": [], "family": "mc_langford", "subset": "construct"} | null | null | null | {"seq": [10, 14, 15, 11, 7, 1, 13, 1, 8, 12, 2, 10, 7, 2, 9, 11, 14, 8, 15, 6, 13, 5, 12, 4, 9, 3, 6, 5, 4, 3]} | 1 |
construct-mc-langford-l3-s3 | construct | mc_langford | langford_pairing | combinatorics | competition | 3 | MathConstraint/langford | CC-BY-4.0 | [
"agentic_trivial",
"np_search"
] | A Langford sequence L(2,20) is a sequence seq[0..39] of length 40 that contains exactly two copies of each integer 1..20, such that the two copies of every value v are exactly v+1 positions apart (their indices differ by v+1). Example: L(2,3) = [2, 3, 1, 2, 1, 3].
Find a Langford sequence L(2,20).
Answer format: {"se... | {"n": 20, "fixed": [], "family": "mc_langford", "subset": "construct"} | null | null | null | {"seq": [13, 7, 9, 1, 10, 1, 19, 14, 16, 7, 2, 11, 9, 2, 13, 10, 18, 12, 20, 8, 17, 15, 14, 11, 6, 16, 19, 5, 8, 4, 12, 6, 3, 5, 4, 18, 3, 15, 17, 20]} | 1 |
construct-mc-langford-l3-s4 | construct | mc_langford | langford_pairing | combinatorics | competition | 3 | MathConstraint/langford | CC-BY-4.0 | [
"agentic_trivial",
"np_search"
] | A Langford sequence L(2,19) is a sequence seq[0..37] of length 38 that contains exactly two copies of each integer 1..19, such that the two copies of every value v are exactly v+1 positions apart (their indices differ by v+1). Example: L(2,3) = [2, 3, 1, 2, 1, 3].
Find a Langford sequence L(2,19).
Answer format: {"se... | {"n": 19, "fixed": [], "family": "mc_langford", "subset": "construct"} | null | null | null | {"seq": [10, 13, 11, 9, 19, 12, 14, 15, 8, 16, 1, 10, 1, 9, 11, 13, 18, 8, 12, 17, 7, 14, 6, 15, 19, 5, 16, 4, 7, 6, 3, 5, 4, 2, 3, 18, 2, 17]} | 1 |
construct-mc-langford-l3-s5 | construct | mc_langford | langford_pairing | combinatorics | competition | 3 | MathConstraint/langford | CC-BY-4.0 | [
"agentic_trivial",
"np_search"
] | A Langford sequence L(2,16) is a sequence seq[0..31] of length 32 that contains exactly two copies of each integer 1..16, such that the two copies of every value v are exactly v+1 positions apart (their indices differ by v+1). Example: L(2,3) = [2, 3, 1, 2, 1, 3].
Find a Langford sequence L(2,16).
Some values are fix... | {"n": 16, "fixed": [["seq", 5, 14], ["seq", 9, 4], ["seq", 11, 15], ["seq", 21, 9], ["seq", 26, 13], ["seq", 29, 10]], "family": "mc_langford", "subset": "construct"} | null | null | null | {"seq": [2, 6, 3, 2, 4, 14, 3, 11, 6, 4, 5, 15, 13, 16, 8, 12, 5, 7, 10, 11, 14, 9, 1, 8, 1, 7, 13, 15, 12, 10, 16, 9]} | 1 |
construct-mc-langford-l4-s0 | construct | mc_langford | langford_pairing | combinatorics | competition | 4 | MathConstraint/langford | CC-BY-4.0 | [
"agentic_trivial",
"np_search"
] | A Langford sequence L(2,24) is a sequence seq[0..47] of length 48 that contains exactly two copies of each integer 1..24, such that the two copies of every value v are exactly v+1 positions apart (their indices differ by v+1). Example: L(2,3) = [2, 3, 1, 2, 1, 3].
Find a Langford sequence L(2,24).
Answer format: {"se... | {"n": 24, "fixed": [], "family": "mc_langford", "subset": "construct"} | null | null | null | {"seq": [20, 21, 13, 24, 12, 14, 8, 10, 17, 19, 22, 2, 18, 11, 2, 8, 13, 12, 10, 16, 14, 20, 23, 21, 9, 11, 17, 15, 24, 19, 7, 18, 6, 22, 9, 5, 16, 4, 7, 6, 3, 5, 4, 15, 3, 1, 23, 1]} | 1 |
construct-mc-langford-l4-s1 | construct | mc_langford | langford_pairing | combinatorics | competition | 4 | MathConstraint/langford | CC-BY-4.0 | [
"agentic_trivial",
"np_search"
] | A Langford sequence L(2,28) is a sequence seq[0..55] of length 56 that contains exactly two copies of each integer 1..28, such that the two copies of every value v are exactly v+1 positions apart (their indices differ by v+1). Example: L(2,3) = [2, 3, 1, 2, 1, 3].
Find a Langford sequence L(2,28).
Answer format: {"se... | {"n": 28, "fixed": [], "family": "mc_langford", "subset": "construct"} | null | null | null | {"seq": [25, 12, 20, 27, 28, 7, 10, 13, 2, 24, 14, 2, 23, 7, 12, 8, 26, 10, 22, 17, 19, 13, 6, 20, 8, 14, 25, 11, 18, 6, 21, 27, 9, 28, 24, 15, 23, 17, 16, 11, 19, 22, 9, 26, 1, 4, 1, 18, 5, 3, 4, 15, 21, 3, 5, 16]} | 1 |
construct-mc-langford-l4-s2 | construct | mc_langford | langford_pairing | combinatorics | competition | 4 | MathConstraint/langford | CC-BY-4.0 | [
"agentic_trivial",
"np_search"
] | A Langford sequence L(2,27) is a sequence seq[0..53] of length 54 that contains exactly two copies of each integer 1..27, such that the two copies of every value v are exactly v+1 positions apart (their indices differ by v+1). Example: L(2,3) = [2, 3, 1, 2, 1, 3].
Find a Langford sequence L(2,27).
Answer format: {"se... | {"n": 27, "fixed": [], "family": "mc_langford", "subset": "construct"} | null | null | null | {"seq": [8, 21, 27, 25, 10, 26, 7, 2, 3, 8, 2, 12, 3, 11, 7, 10, 14, 9, 22, 19, 24, 16, 20, 21, 12, 11, 23, 9, 17, 25, 27, 14, 26, 1, 18, 1, 15, 13, 16, 19, 6, 22, 5, 20, 4, 24, 17, 6, 5, 4, 23, 13, 15, 18]} | 1 |
construct-mc-langford-l4-s3 | construct | mc_langford | langford_pairing | combinatorics | competition | 4 | MathConstraint/langford | CC-BY-4.0 | [
"agentic_trivial",
"np_search"
] | A Langford sequence L(2,23) is a sequence seq[0..45] of length 46 that contains exactly two copies of each integer 1..23, such that the two copies of every value v are exactly v+1 positions apart (their indices differ by v+1). Example: L(2,3) = [2, 3, 1, 2, 1, 3].
Find a Langford sequence L(2,23).
Answer format: {"se... | {"n": 23, "fixed": [], "family": "mc_langford", "subset": "construct"} | null | null | null | {"seq": [10, 1, 20, 1, 15, 2, 11, 6, 2, 3, 18, 10, 13, 3, 6, 21, 14, 23, 11, 22, 15, 16, 9, 20, 19, 8, 13, 17, 7, 18, 12, 14, 9, 5, 8, 4, 7, 21, 16, 5, 4, 23, 22, 12, 19, 17]} | 1 |
construct-mc-langford-l5-s0 | construct | mc_langford | langford_pairing | combinatorics | competition | 5 | MathConstraint/langford | CC-BY-4.0 | [
"agentic_trivial",
"np_search"
] | A Langford sequence L(2,32) is a sequence seq[0..63] of length 64 that contains exactly two copies of each integer 1..32, such that the two copies of every value v are exactly v+1 positions apart (their indices differ by v+1). Example: L(2,3) = [2, 3, 1, 2, 1, 3].
Find a Langford sequence L(2,32).
Answer format: {"se... | {"n": 32, "fixed": [], "family": "mc_langford", "subset": "construct"} | null | null | null | {"seq": [26, 21, 23, 14, 17, 13, 32, 16, 25, 20, 1, 19, 1, 22, 2, 4, 27, 2, 14, 13, 4, 31, 17, 21, 16, 15, 23, 26, 30, 28, 20, 19, 12, 29, 25, 11, 22, 24, 10, 32, 9, 15, 18, 8, 27, 12, 7, 11, 6, 10, 9, 5, 8, 31, 7, 6, 3, 5, 28, 30, 3, 18, 24, 29]} | 1 |
construct-mc-langford-l5-s1 | construct | mc_langford | langford_pairing | combinatorics | competition | 5 | MathConstraint/langford | CC-BY-4.0 | [
"agentic_trivial",
"np_search"
] | A Langford sequence L(2,31) is a sequence seq[0..61] of length 62 that contains exactly two copies of each integer 1..31, such that the two copies of every value v are exactly v+1 positions apart (their indices differ by v+1). Example: L(2,3) = [2, 3, 1, 2, 1, 3].
Find a Langford sequence L(2,31).
Answer format: {"se... | {"n": 31, "fixed": [], "family": "mc_langford", "subset": "construct"} | null | null | null | {"seq": [31, 28, 6, 3, 29, 4, 11, 3, 2, 6, 4, 2, 16, 5, 26, 30, 22, 18, 11, 5, 17, 13, 14, 23, 27, 1, 24, 1, 19, 16, 28, 21, 31, 25, 29, 13, 18, 14, 17, 22, 20, 26, 15, 12, 10, 8, 30, 23, 19, 7, 9, 24, 27, 21, 8, 10, 12, 7, 15, 25, 9, 20]} | 1 |
construct-mc-langford-l5-s2 | construct | mc_langford | langford_pairing | combinatorics | competition | 5 | MathConstraint/langford | CC-BY-4.0 | [
"agentic_trivial",
"np_search"
] | A Langford sequence L(2,36) is a sequence seq[0..71] of length 72 that contains exactly two copies of each integer 1..36, such that the two copies of every value v are exactly v+1 positions apart (their indices differ by v+1). Example: L(2,3) = [2, 3, 1, 2, 1, 3].
Find a Langford sequence L(2,36).
Answer format: {"se... | {"n": 36, "fixed": [], "family": "mc_langford", "subset": "construct"} | null | null | null | {"seq": [11, 13, 29, 35, 31, 34, 36, 17, 33, 18, 5, 2, 11, 6, 2, 13, 5, 19, 30, 32, 6, 28, 23, 24, 9, 17, 14, 16, 18, 21, 22, 25, 29, 26, 9, 27, 31, 19, 20, 35, 34, 14, 33, 36, 16, 1, 23, 1, 24, 30, 28, 21, 32, 22, 15, 10, 8, 25, 12, 20, 26, 7, 4, 27, 3, 8, 10, 4, 3, 7, 15, 12]} | 1 |
construct-mc-langford-l5-s3 | construct | mc_langford | langford_pairing | combinatorics | competition | 5 | MathConstraint/langford | CC-BY-4.0 | [
"agentic_trivial",
"np_search"
] | A Langford sequence L(2,35) is a sequence seq[0..69] of length 70 that contains exactly two copies of each integer 1..35, such that the two copies of every value v are exactly v+1 positions apart (their indices differ by v+1). Example: L(2,3) = [2, 3, 1, 2, 1, 3].
Find a Langford sequence L(2,35).
Answer format: {"se... | {"n": 35, "fixed": [], "family": "mc_langford", "subset": "construct"} | null | null | null | {"seq": [26, 30, 31, 29, 24, 34, 3, 20, 9, 15, 3, 2, 7, 8, 2, 10, 28, 35, 9, 18, 7, 33, 8, 25, 32, 15, 10, 26, 20, 24, 27, 22, 30, 29, 31, 23, 11, 1, 18, 1, 34, 14, 19, 6, 21, 28, 13, 16, 11, 25, 6, 17, 12, 35, 22, 33, 14, 32, 27, 23, 13, 5, 19, 4, 16, 12, 21, 5, 4, 17]} | 1 |
construct-mc-langford-l6-s0 | construct | mc_langford | langford_pairing | combinatorics | competition | 6 | MathConstraint/langford | CC-BY-4.0 | [
"agentic_trivial",
"np_search"
] | A Langford sequence L(2,39) is a sequence seq[0..77] of length 78 that contains exactly two copies of each integer 1..39, such that the two copies of every value v are exactly v+1 positions apart (their indices differ by v+1). Example: L(2,3) = [2, 3, 1, 2, 1, 3].
Find a Langford sequence L(2,39).
Answer format: {"se... | {"n": 39, "fixed": [], "family": "mc_langford", "subset": "construct"} | null | null | null | {"seq": [28, 38, 39, 13, 5, 20, 17, 11, 30, 36, 5, 21, 24, 1, 8, 1, 3, 13, 26, 11, 3, 37, 27, 8, 17, 22, 20, 19, 29, 28, 34, 2, 35, 21, 2, 31, 16, 24, 33, 30, 38, 14, 39, 32, 25, 26, 36, 19, 22, 7, 27, 23, 10, 16, 9, 18, 14, 7, 29, 37, 12, 15, 6, 10, 9, 34, 4, 31, 35, 6, 25, 4, 33, 12, 18, 23, 32, 15]} | 1 |
construct-mc-langford-l6-s1 | construct | mc_langford | langford_pairing | combinatorics | competition | 6 | MathConstraint/langford | CC-BY-4.0 | [
"agentic_trivial",
"np_search"
] | A Langford sequence L(2,40) is a sequence seq[0..79] of length 80 that contains exactly two copies of each integer 1..40, such that the two copies of every value v are exactly v+1 positions apart (their indices differ by v+1). Example: L(2,3) = [2, 3, 1, 2, 1, 3].
Find a Langford sequence L(2,40).
Answer format: {"se... | {"n": 40, "fixed": [], "family": "mc_langford", "subset": "construct"} | null | null | null | {"seq": [20, 5, 28, 15, 19, 17, 22, 5, 24, 32, 35, 14, 1, 33, 1, 34, 11, 26, 21, 15, 27, 20, 30, 17, 19, 37, 14, 13, 11, 22, 39, 28, 4, 24, 40, 25, 36, 4, 18, 38, 21, 13, 32, 23, 26, 31, 35, 33, 27, 29, 34, 12, 7, 30, 10, 16, 9, 18, 3, 8, 7, 25, 3, 37, 12, 10, 9, 23, 8, 6, 39, 2, 16, 36, 2, 40, 6, 31, 38, 29]} | 1 |
construct-mc-langford-l6-s2 | construct | mc_langford | langford_pairing | combinatorics | competition | 6 | MathConstraint/langford | CC-BY-4.0 | [
"agentic_trivial",
"np_search"
] | A Langford sequence L(2,43) is a sequence seq[0..85] of length 86 that contains exactly two copies of each integer 1..43, such that the two copies of every value v are exactly v+1 positions apart (their indices differ by v+1). Example: L(2,3) = [2, 3, 1, 2, 1, 3].
Find a Langford sequence L(2,43).
Answer format: {"se... | {"n": 43, "fixed": [], "family": "mc_langford", "subset": "construct"} | null | null | null | {"seq": [39, 33, 30, 42, 25, 28, 43, 24, 18, 9, 31, 14, 11, 29, 38, 7, 34, 27, 37, 9, 26, 36, 32, 7, 11, 22, 14, 18, 20, 1, 25, 1, 24, 30, 28, 33, 41, 35, 23, 40, 39, 17, 31, 29, 16, 27, 42, 26, 22, 20, 43, 34, 13, 38, 12, 32, 37, 21, 36, 17, 10, 16, 23, 19, 5, 8, 13, 12, 6, 15, 5, 10, 3, 35, 8, 6, 3, 4, 41, 21, 40, 2,... | 1 |
construct-mc-langford-l6-s3 | construct | mc_langford | langford_pairing | combinatorics | competition | 6 | MathConstraint/langford | CC-BY-4.0 | [
"agentic_trivial",
"np_search"
] | A Langford sequence L(2,44) is a sequence seq[0..87] of length 88 that contains exactly two copies of each integer 1..44, such that the two copies of every value v are exactly v+1 positions apart (their indices differ by v+1). Example: L(2,3) = [2, 3, 1, 2, 1, 3].
Find a Langford sequence L(2,44).
Answer format: {"se... | {"n": 44, "fixed": [], "family": "mc_langford", "subset": "construct"} | null | null | null | {"seq": [35, 24, 4, 10, 30, 9, 23, 4, 38, 21, 1, 43, 1, 19, 10, 9, 33, 20, 26, 39, 16, 42, 34, 29, 3, 6, 24, 44, 3, 28, 23, 21, 6, 19, 40, 30, 35, 16, 20, 22, 13, 41, 31, 17, 32, 26, 37, 38, 36, 15, 33, 14, 27, 29, 13, 43, 12, 34, 28, 39, 25, 17, 22, 7, 42, 15, 14, 8, 18, 12, 11, 7, 44, 5, 31, 40, 8, 32, 2, 5, 27, 2, 1... | 1 |
construct-mc-langford-l6-s4 | construct | mc_langford | langford_pairing | combinatorics | competition | 6 | MathConstraint/langford | CC-BY-4.0 | [
"agentic_trivial",
"np_search"
] | A Langford sequence L(2,47) is a sequence seq[0..93] of length 94 that contains exactly two copies of each integer 1..47, such that the two copies of every value v are exactly v+1 positions apart (their indices differ by v+1). Example: L(2,3) = [2, 3, 1, 2, 1, 3].
Find a Langford sequence L(2,47).
Answer format: {"se... | {"n": 47, "fixed": [], "family": "mc_langford", "subset": "construct"} | null | null | null | {"seq": [20, 33, 28, 46, 21, 35, 1, 36, 1, 23, 4, 22, 19, 42, 2, 4, 5, 2, 26, 7, 3, 20, 5, 24, 3, 27, 21, 7, 25, 34, 32, 28, 19, 23, 22, 33, 41, 38, 44, 47, 40, 35, 43, 45, 36, 26, 37, 18, 24, 17, 46, 39, 16, 27, 25, 15, 42, 14, 29, 30, 13, 31, 12, 32, 34, 11, 18, 17, 10, 16, 9, 15, 14, 8, 13, 12, 38, 11, 41, 10, 9, 40... | 1 |
construct-mc-langford-l6-s5 | construct | mc_langford | langford_pairing | combinatorics | competition | 6 | MathConstraint/langford | CC-BY-4.0 | [
"agentic_trivial",
"np_search"
] | A Langford sequence L(2,48) is a sequence seq[0..95] of length 96 that contains exactly two copies of each integer 1..48, such that the two copies of every value v are exactly v+1 positions apart (their indices differ by v+1). Example: L(2,3) = [2, 3, 1, 2, 1, 3].
Find a Langford sequence L(2,48).
Answer format: {"se... | {"n": 48, "fixed": [], "family": "mc_langford", "subset": "construct"} | null | null | null | {"seq": [44, 21, 32, 43, 26, 27, 29, 36, 46, 20, 23, 9, 6, 11, 3, 1, 5, 1, 3, 6, 35, 9, 5, 21, 38, 11, 34, 39, 24, 30, 20, 26, 7, 27, 23, 32, 29, 45, 48, 40, 7, 37, 47, 41, 36, 44, 19, 43, 42, 18, 31, 17, 25, 24, 16, 46, 35, 15, 33, 14, 30, 34, 13, 38, 12, 28, 19, 39, 18, 17, 10, 16, 22, 15, 14, 8, 13, 12, 25, 37, 40, ... | 1 |
construct-mc-low-autocorrelation-l1-s0 | construct | mc_low_autocorrelation | low_autocorrelation_binary_sequence | combinatorics | competition | 1 | MathConstraint/low_autocorrelation | CC-BY-4.0 | [
"np_search"
] | For a sequence seq[0..10] with entries in {-1, +1}, define the aperiodic autocorrelations C_k = sum_{i=0}^{11-k-1} seq[i]*seq[i+k] for k = 1..10 and the energy E = sum_k C_k^2.
Find a sequence of length 11 with E <= 23.
Some values are fixed in advance and your answer must agree with them:
seq[1] = 1, seq[8] = 1, c[6... | {"n": 11, "bound": 23, "fixed": [["seq", 1, 1], ["seq", 8, 1], ["c", 6, 0], ["c", 9, 1]], "family": "mc_low_autocorrelation", "subset": "construct"} | null | null | null | {"seq": [-1, 1, -1, 1, 1, -1, 1, 1, 1, -1, -1]} | 1 |
construct-mc-low-autocorrelation-l1-s1 | construct | mc_low_autocorrelation | low_autocorrelation_binary_sequence | combinatorics | competition | 1 | MathConstraint/low_autocorrelation | CC-BY-4.0 | [
"np_search"
] | For a sequence seq[0..11] with entries in {-1, +1}, define the aperiodic autocorrelations C_k = sum_{i=0}^{12-k-1} seq[i]*seq[i+k] for k = 1..11 and the energy E = sum_k C_k^2.
Find a sequence of length 12 with E <= 25.
Answer format: {"seq": [s_0, s_1, ..., s_11]} with every s_i equal to -1 or 1
Write your final an... | {"n": 12, "bound": 25, "fixed": [], "family": "mc_low_autocorrelation", "subset": "construct"} | null | null | null | {"seq": [-1, 1, 1, -1, 1, 1, 1, 1, -1, -1, -1, 1]} | 1 |
construct-mc-low-autocorrelation-l1-s2 | construct | mc_low_autocorrelation | low_autocorrelation_binary_sequence | combinatorics | competition | 1 | MathConstraint/low_autocorrelation | CC-BY-4.0 | [
"np_search"
] | For a sequence seq[0..9] with entries in {-1, +1}, define the aperiodic autocorrelations C_k = sum_{i=0}^{10-k-1} seq[i]*seq[i+k] for k = 1..9 and the energy E = sum_k C_k^2.
Find a sequence of length 10 with E <= 20.
Some values are fixed in advance and your answer must agree with them:
seq[0] = -1, seq[8] = 1, c[6]... | {"n": 10, "bound": 20, "fixed": [["seq", 0, -1], ["seq", 8, 1], ["c", 6, -1]], "family": "mc_low_autocorrelation", "subset": "construct"} | null | null | null | {"seq": [-1, -1, 1, 1, -1, 1, -1, 1, 1, 1]} | 1 |
construct-mc-low-autocorrelation-l2-s0 | construct | mc_low_autocorrelation | low_autocorrelation_binary_sequence | combinatorics | competition | 2 | MathConstraint/low_autocorrelation | CC-BY-4.0 | [
"np_search"
] | For a sequence seq[0..15] with entries in {-1, +1}, define the aperiodic autocorrelations C_k = sum_{i=0}^{16-k-1} seq[i]*seq[i+k] for k = 1..15 and the energy E = sum_k C_k^2.
Find a sequence of length 16 with E <= 37.
Answer format: {"seq": [s_0, s_1, ..., s_15]} with every s_i equal to -1 or 1
Write your final an... | {"n": 16, "bound": 37, "fixed": [], "family": "mc_low_autocorrelation", "subset": "construct"} | null | null | null | {"seq": [1, 1, -1, -1, -1, -1, -1, -1, 1, 1, -1, -1, 1, -1, 1, -1]} | 1 |
construct-mc-low-autocorrelation-l2-s1 | construct | mc_low_autocorrelation | low_autocorrelation_binary_sequence | combinatorics | competition | 2 | MathConstraint/low_autocorrelation | CC-BY-4.0 | [
"np_search"
] | For a sequence seq[0..16] with entries in {-1, +1}, define the aperiodic autocorrelations C_k = sum_{i=0}^{17-k-1} seq[i]*seq[i+k] for k = 1..16 and the energy E = sum_k C_k^2.
Find a sequence of length 17 with E <= 40.
Some values are fixed in advance and your answer must agree with them:
seq[1] = -1, seq[6] = 1, se... | {"n": 17, "bound": 40, "fixed": [["seq", 1, -1], ["seq", 6, 1], ["seq", 9, -1], ["c", 7, 3], ["c", 8, -2], ["c", 12, 0]], "family": "mc_low_autocorrelation", "subset": "construct"} | null | null | null | {"seq": [-1, -1, -1, -1, 1, -1, 1, -1, -1, -1, 1, 1, 1, -1, 1, 1, -1]} | 1 |
construct-mc-low-autocorrelation-l2-s2 | construct | mc_low_autocorrelation | low_autocorrelation_binary_sequence | combinatorics | competition | 2 | MathConstraint/low_autocorrelation | CC-BY-4.0 | [
"np_search"
] | For a sequence seq[0..12] with entries in {-1, +1}, define the aperiodic autocorrelations C_k = sum_{i=0}^{13-k-1} seq[i]*seq[i+k] for k = 1..12 and the energy E = sum_k C_k^2.
Find a sequence of length 13 with E <= 28.
Some values are fixed in advance and your answer must agree with them:
seq[8] = 1, seq[10] = -1, c... | {"n": 13, "bound": 28, "fixed": [["seq", 8, 1], ["seq", 10, -1], ["c", 4, 2], ["c", 5, -1]], "family": "mc_low_autocorrelation", "subset": "construct"} | null | null | null | {"seq": [1, -1, 1, -1, -1, -1, -1, 1, 1, -1, -1, 1, 1]} | 1 |
construct-mc-low-autocorrelation-l3-s0 | construct | mc_low_autocorrelation | low_autocorrelation_binary_sequence | combinatorics | competition | 3 | MathConstraint/low_autocorrelation | CC-BY-4.0 | [
"np_search"
] | For a sequence seq[0..30] with entries in {-1, +1}, define the aperiodic autocorrelations C_k = sum_{i=0}^{31-k-1} seq[i]*seq[i+k] for k = 1..30 and the energy E = sum_k C_k^2.
Find a sequence of length 31 with E <= 96.
Answer format: {"seq": [s_0, s_1, ..., s_30]} with every s_i equal to -1 or 1
Write your final an... | {"n": 31, "bound": 96, "fixed": [], "family": "mc_low_autocorrelation", "subset": "construct"} | null | null | null | {"seq": [1, -1, -1, 1, 1, -1, 1, -1, 1, 1, -1, -1, 1, 1, 1, -1, 1, -1, -1, 1, 1, 1, -1, 1, -1, -1, -1, -1, -1, -1, -1]} | 1 |
construct-mc-low-autocorrelation-l3-s1 | construct | mc_low_autocorrelation | low_autocorrelation_binary_sequence | combinatorics | competition | 3 | MathConstraint/low_autocorrelation | CC-BY-4.0 | [
"np_search"
] | For a sequence seq[0..18] with entries in {-1, +1}, define the aperiodic autocorrelations C_k = sum_{i=0}^{19-k-1} seq[i]*seq[i+k] for k = 1..18 and the energy E = sum_k C_k^2.
Find a sequence of length 19 with E <= 46.
Some values are fixed in advance and your answer must agree with them:
seq[4] = -1, seq[12] = 1, s... | {"n": 19, "bound": 46, "fixed": [["seq", 4, -1], ["seq", 12, 1], ["seq", 13, -1], ["c", 1, -1], ["c", 2, 0], ["c", 7, -3]], "family": "mc_low_autocorrelation", "subset": "construct"} | null | null | null | {"seq": [1, -1, -1, 1, -1, -1, 1, 1, -1, -1, -1, -1, 1, -1, 1, -1, 1, 1, 1]} | 1 |
construct-mc-low-autocorrelation-l3-s2 | construct | mc_low_autocorrelation | low_autocorrelation_binary_sequence | combinatorics | competition | 3 | MathConstraint/low_autocorrelation | CC-BY-4.0 | [
"np_search"
] | For a sequence seq[0..23] with entries in {-1, +1}, define the aperiodic autocorrelations C_k = sum_{i=0}^{24-k-1} seq[i]*seq[i+k] for k = 1..23 and the energy E = sum_k C_k^2.
Find a sequence of length 24 with E <= 62.
Some values are fixed in advance and your answer must agree with them:
seq[9] = -1, seq[14] = 1, s... | {"n": 24, "bound": 62, "fixed": [["seq", 9, -1], ["seq", 14, 1], ["seq", 15, -1], ["seq", 22, -1], ["c", 3, 0], ["c", 9, -2], ["c", 14, -1], ["c", 19, 0]], "family": "mc_low_autocorrelation", "subset": "construct"} | null | null | null | {"seq": [-1, 1, 1, -1, -1, 1, 1, -1, 1, -1, 1, 1, 1, -1, 1, -1, 1, 1, 1, 1, -1, -1, -1, -1]} | 1 |
construct-mc-low-autocorrelation-l3-s3 | construct | mc_low_autocorrelation | low_autocorrelation_binary_sequence | combinatorics | competition | 3 | MathConstraint/low_autocorrelation | CC-BY-4.0 | [
"np_search"
] | For a sequence seq[0..20] with entries in {-1, +1}, define the aperiodic autocorrelations C_k = sum_{i=0}^{21-k-1} seq[i]*seq[i+k] for k = 1..20 and the energy E = sum_k C_k^2.
Find a sequence of length 21 with E <= 52.
Some values are fixed in advance and your answer must agree with them:
seq[5] = -1, seq[12] = -1, ... | {"n": 21, "bound": 52, "fixed": [["seq", 5, -1], ["seq", 12, -1], ["seq", 17, 1], ["seq", 20, 1], ["c", 0, 2], ["c", 1, -1], ["c", 8, 2], ["c", 19, -1]], "family": "mc_low_autocorrelation", "subset": "construct"} | null | null | null | {"seq": [-1, 1, 1, -1, -1, -1, 1, 1, 1, -1, 1, -1, -1, -1, -1, -1, -1, 1, -1, -1, 1]} | 1 |
construct-mc-low-autocorrelation-l3-s4 | construct | mc_low_autocorrelation | low_autocorrelation_binary_sequence | combinatorics | competition | 3 | MathConstraint/low_autocorrelation | CC-BY-4.0 | [
"np_search"
] | For a sequence seq[0..21] with entries in {-1, +1}, define the aperiodic autocorrelations C_k = sum_{i=0}^{22-k-1} seq[i]*seq[i+k] for k = 1..21 and the energy E = sum_k C_k^2.
Find a sequence of length 22 with E <= 56.
Answer format: {"seq": [s_0, s_1, ..., s_21]} with every s_i equal to -1 or 1
Write your final an... | {"n": 22, "bound": 56, "fixed": [], "family": "mc_low_autocorrelation", "subset": "construct"} | null | null | null | {"seq": [1, -1, 1, -1, 1, 1, -1, -1, 1, -1, -1, 1, 1, 1, -1, -1, -1, -1, 1, -1, -1, -1]} | 1 |
construct-mc-low-autocorrelation-l3-s5 | construct | mc_low_autocorrelation | low_autocorrelation_binary_sequence | combinatorics | competition | 3 | MathConstraint/low_autocorrelation | CC-BY-4.0 | [
"np_search"
] | For a sequence seq[0..29] with entries in {-1, +1}, define the aperiodic autocorrelations C_k = sum_{i=0}^{30-k-1} seq[i]*seq[i+k] for k = 1..29 and the energy E = sum_k C_k^2.
Find a sequence of length 30 with E <= 90.
Answer format: {"seq": [s_0, s_1, ..., s_29]} with every s_i equal to -1 or 1
Write your final an... | {"n": 30, "bound": 90, "fixed": [], "family": "mc_low_autocorrelation", "subset": "construct"} | null | null | null | {"seq": [-1, 1, -1, 1, -1, -1, 1, -1, 1, -1, 1, 1, 1, -1, 1, 1, -1, -1, 1, -1, -1, -1, -1, -1, 1, 1, 1, -1, -1, -1]} | 1 |
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