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-number-partitioning-l3-s2 | construct | mc_number_partitioning | equal_sum_partition_1_to_n | number_theory | competition | 3 | MathConstraint/number_partitioning | CC-BY-4.0 | [
"agentic_trivial"
] | Partition the integers 1, 2, ..., 24 into 3 disjoint subsets (numbered 0..2) that all have the same sum 100 (the total is 300).
Find such a partition.
Answer format: {"x": [x_1, ..., x_24]}: a list of 24 integers in 0..2, where the i-th entry (0-indexed) is the subset containing the integer i+1
Write your final answ... | {"n": 24, "k": 3, "family": "mc_number_partitioning", "subset": "construct"} | null | null | null | {"x": [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 1, 2, 2, 0, 1, 2]} | 1 |
construct-mc-number-partitioning-l3-s3 | construct | mc_number_partitioning | equal_sum_partition_1_to_n | number_theory | competition | 3 | MathConstraint/number_partitioning | CC-BY-4.0 | [
"agentic_trivial"
] | Partition the integers 1, 2, ..., 14 into 5 disjoint subsets (numbered 0..4) that all have the same sum 21 (the total is 105).
Find such a partition.
Answer format: {"x": [x_1, ..., x_14]}: a list of 14 integers in 0..4, where the i-th entry (0-indexed) is the subset containing the integer i+1
Write your final answe... | {"n": 14, "k": 5, "family": "mc_number_partitioning", "subset": "construct"} | null | null | null | {"x": [0, 0, 0, 0, 0, 0, 1, 2, 3, 4, 4, 3, 2, 1]} | 1 |
construct-mc-number-partitioning-l3-s4 | construct | mc_number_partitioning | equal_sum_partition_1_to_n | number_theory | competition | 3 | MathConstraint/number_partitioning | CC-BY-4.0 | [
"agentic_trivial"
] | Partition the integers 1, 2, ..., 16 into 4 disjoint subsets (numbered 0..3) that all have the same sum 34 (the total is 136).
Find such a partition.
Answer format: {"x": [x_1, ..., x_16]}: a list of 16 integers in 0..3, where the i-th entry (0-indexed) is the subset containing the integer i+1
Write your final answe... | {"n": 16, "k": 4, "family": "mc_number_partitioning", "subset": "construct"} | null | null | null | {"x": [0, 3, 2, 1, 1, 0, 2, 2, 3, 3, 1, 0, 3, 1, 0, 2]} | 1 |
construct-mc-number-partitioning-l3-s5 | construct | mc_number_partitioning | equal_sum_partition_1_to_n | number_theory | competition | 3 | MathConstraint/number_partitioning | CC-BY-4.0 | [
"agentic_trivial"
] | Partition the integers 1, 2, ..., 19 into 5 disjoint subsets (numbered 0..4) that all have the same sum 38 (the total is 190).
Find such a partition.
Answer format: {"x": [x_1, ..., x_19]}: a list of 19 integers in 0..4, where the i-th entry (0-indexed) is the subset containing the integer i+1
Write your final answe... | {"n": 19, "k": 5, "family": "mc_number_partitioning", "subset": "construct"} | null | null | null | {"x": [0, 2, 2, 3, 0, 2, 4, 1, 1, 1, 1, 2, 0, 4, 2, 3, 4, 3, 0]} | 1 |
construct-mc-number-partitioning-l3-s6 | construct | mc_number_partitioning | equal_sum_partition_1_to_n | number_theory | competition | 3 | MathConstraint/number_partitioning | CC-BY-4.0 | [
"agentic_trivial"
] | Partition the integers 1, 2, ..., 24 into 4 disjoint subsets (numbered 0..3) that all have the same sum 75 (the total is 300).
Find such a partition.
Answer format: {"x": [x_1, ..., x_24]}: a list of 24 integers in 0..3, where the i-th entry (0-indexed) is the subset containing the integer i+1
Write your final answe... | {"n": 24, "k": 4, "family": "mc_number_partitioning", "subset": "construct"} | null | null | null | {"x": [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 2, 2, 1, 3, 3, 3, 0, 3, 2, 1, 2]} | 1 |
construct-mc-number-partitioning-l3-s7 | construct | mc_number_partitioning | equal_sum_partition_1_to_n | number_theory | competition | 3 | MathConstraint/number_partitioning | CC-BY-4.0 | [
"agentic_trivial"
] | Partition the integers 1, 2, ..., 20 into 3 disjoint subsets (numbered 0..2) that all have the same sum 70 (the total is 210).
Find such a partition.
Answer format: {"x": [x_1, ..., x_20]}: a list of 20 integers in 0..2, where the i-th entry (0-indexed) is the subset containing the integer i+1
Write your final answe... | {"n": 20, "k": 3, "family": "mc_number_partitioning", "subset": "construct"} | null | null | null | {"x": [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 2, 2, 2, 2, 1]} | 1 |
construct-mc-number-partitioning-l3-s8 | construct | mc_number_partitioning | equal_sum_partition_1_to_n | number_theory | competition | 3 | MathConstraint/number_partitioning | CC-BY-4.0 | [
"agentic_trivial"
] | Partition the integers 1, 2, ..., 21 into 3 disjoint subsets (numbered 0..2) that all have the same sum 77 (the total is 231).
Find such a partition.
Answer format: {"x": [x_1, ..., x_21]}: a list of 21 integers in 0..2, where the i-th entry (0-indexed) is the subset containing the integer i+1
Write your final answe... | {"n": 21, "k": 3, "family": "mc_number_partitioning", "subset": "construct"} | null | null | null | {"x": [0, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 2, 1, 1, 0, 0, 2, 0, 0]} | 1 |
construct-mc-number-partitioning-l3-s9 | construct | mc_number_partitioning | equal_sum_partition_1_to_n | number_theory | competition | 3 | MathConstraint/number_partitioning | CC-BY-4.0 | [
"agentic_trivial"
] | Partition the integers 1, 2, ..., 18 into 3 disjoint subsets (numbered 0..2) that all have the same sum 57 (the total is 171).
Find such a partition.
Answer format: {"x": [x_1, ..., x_18]}: a list of 18 integers in 0..2, where the i-th entry (0-indexed) is the subset containing the integer i+1
Write your final answe... | {"n": 18, "k": 3, "family": "mc_number_partitioning", "subset": "construct"} | null | null | null | {"x": [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 0, 2, 1, 2, 1, 1, 2]} | 1 |
construct-mc-number-partitioning-l4-s0 | construct | mc_number_partitioning | equal_sum_partition_1_to_n | number_theory | competition | 4 | MathConstraint/number_partitioning | CC-BY-4.0 | [
"agentic_trivial"
] | Partition the integers 1, 2, ..., 30 into 3 disjoint subsets (numbered 0..2) that all have the same sum 155 (the total is 465).
Find such a partition.
Answer format: {"x": [x_1, ..., x_30]}: a list of 30 integers in 0..2, where the i-th entry (0-indexed) is the subset containing the integer i+1
Write your final answ... | {"n": 30, "k": 3, "family": "mc_number_partitioning", "subset": "construct"} | null | null | null | {"x": [0, 1, 2, 2, 1, 0, 0, 1, 2, 2, 1, 0, 0, 1, 2, 2, 1, 0, 0, 1, 2, 2, 1, 0, 0, 1, 2, 2, 1, 0]} | 1 |
construct-mc-number-partitioning-l4-s1 | construct | mc_number_partitioning | equal_sum_partition_1_to_n | number_theory | competition | 4 | MathConstraint/number_partitioning | CC-BY-4.0 | [
"agentic_trivial"
] | Partition the integers 1, 2, ..., 27 into 3 disjoint subsets (numbered 0..2) that all have the same sum 126 (the total is 378).
Find such a partition.
Answer format: {"x": [x_1, ..., x_27]}: a list of 27 integers in 0..2, where the i-th entry (0-indexed) is the subset containing the integer i+1
Write your final answ... | {"n": 27, "k": 3, "family": "mc_number_partitioning", "subset": "construct"} | null | null | null | {"x": [0, 2, 1, 1, 0, 2, 2, 1, 0, 0, 1, 2, 2, 1, 0, 0, 1, 2, 2, 1, 0, 0, 1, 2, 2, 1, 0]} | 1 |
construct-mc-number-partitioning-l4-s2 | construct | mc_number_partitioning | equal_sum_partition_1_to_n | number_theory | competition | 4 | MathConstraint/number_partitioning | CC-BY-4.0 | [
"agentic_trivial"
] | Partition the integers 1, 2, ..., 27 into 6 disjoint subsets (numbered 0..5) that all have the same sum 63 (the total is 378).
Find such a partition.
Answer format: {"x": [x_1, ..., x_27]}: a list of 27 integers in 0..5, where the i-th entry (0-indexed) is the subset containing the integer i+1
Write your final answe... | {"n": 27, "k": 6, "family": "mc_number_partitioning", "subset": "construct"} | null | null | null | {"x": [5, 4, 2, 2, 0, 1, 4, 3, 5, 5, 4, 3, 2, 1, 0, 0, 1, 2, 3, 4, 5, 5, 4, 3, 2, 1, 0]} | 1 |
construct-mc-number-partitioning-l4-s3 | construct | mc_number_partitioning | equal_sum_partition_1_to_n | number_theory | competition | 4 | MathConstraint/number_partitioning | CC-BY-4.0 | [
"agentic_trivial"
] | Partition the integers 1, 2, ..., 39 into 5 disjoint subsets (numbered 0..4) that all have the same sum 156 (the total is 780).
Find such a partition.
Answer format: {"x": [x_1, ..., x_39]}: a list of 39 integers in 0..4, where the i-th entry (0-indexed) is the subset containing the integer i+1
Write your final answ... | {"n": 39, "k": 5, "family": "mc_number_partitioning", "subset": "construct"} | null | null | null | {"x": [1, 2, 3, 4, 4, 3, 2, 1, 0, 0, 1, 2, 3, 4, 4, 3, 2, 1, 0, 0, 1, 2, 3, 4, 4, 3, 2, 1, 0, 0, 1, 2, 3, 4, 4, 3, 2, 1, 0]} | 1 |
construct-mc-number-partitioning-l4-s4 | construct | mc_number_partitioning | equal_sum_partition_1_to_n | number_theory | competition | 4 | MathConstraint/number_partitioning | CC-BY-4.0 | [
"agentic_trivial"
] | Partition the integers 1, 2, ..., 35 into 5 disjoint subsets (numbered 0..4) that all have the same sum 126 (the total is 630).
Find such a partition.
Answer format: {"x": [x_1, ..., x_35]}: a list of 35 integers in 0..4, where the i-th entry (0-indexed) is the subset containing the integer i+1
Write your final answ... | {"n": 35, "k": 5, "family": "mc_number_partitioning", "subset": "construct"} | null | null | null | {"x": [0, 2, 4, 1, 3, 1, 3, 0, 2, 4, 4, 3, 2, 1, 0, 0, 1, 2, 3, 4, 4, 3, 2, 1, 0, 0, 1, 2, 3, 4, 4, 3, 2, 1, 0]} | 1 |
construct-mc-number-partitioning-l4-s5 | construct | mc_number_partitioning | equal_sum_partition_1_to_n | number_theory | competition | 4 | MathConstraint/number_partitioning | CC-BY-4.0 | [
"agentic_trivial"
] | Partition the integers 1, 2, ..., 39 into 3 disjoint subsets (numbered 0..2) that all have the same sum 260 (the total is 780).
Find such a partition.
Answer format: {"x": [x_1, ..., x_39]}: a list of 39 integers in 0..2, where the i-th entry (0-indexed) is the subset containing the integer i+1
Write your final answ... | {"n": 39, "k": 3, "family": "mc_number_partitioning", "subset": "construct"} | null | null | null | {"x": [0, 2, 1, 1, 0, 2, 2, 1, 0, 0, 1, 2, 2, 1, 0, 0, 1, 2, 2, 1, 0, 0, 1, 2, 2, 1, 0, 0, 1, 2, 2, 1, 0, 0, 1, 2, 2, 1, 0]} | 1 |
construct-mc-number-partitioning-l4-s6 | construct | mc_number_partitioning | equal_sum_partition_1_to_n | number_theory | competition | 4 | MathConstraint/number_partitioning | CC-BY-4.0 | [
"agentic_trivial"
] | Partition the integers 1, 2, ..., 39 into 4 disjoint subsets (numbered 0..3) that all have the same sum 195 (the total is 780).
Find such a partition.
Answer format: {"x": [x_1, ..., x_39]}: a list of 39 integers in 0..3, where the i-th entry (0-indexed) is the subset containing the integer i+1
Write your final answ... | {"n": 39, "k": 4, "family": "mc_number_partitioning", "subset": "construct"} | null | null | null | {"x": [1, 2, 3, 3, 2, 1, 0, 0, 1, 2, 3, 3, 2, 1, 0, 0, 1, 2, 3, 3, 2, 1, 0, 0, 1, 2, 3, 3, 2, 1, 0, 0, 1, 2, 3, 3, 2, 1, 0]} | 1 |
construct-mc-number-partitioning-l4-s7 | construct | mc_number_partitioning | equal_sum_partition_1_to_n | number_theory | competition | 4 | MathConstraint/number_partitioning | CC-BY-4.0 | [
"agentic_trivial"
] | Partition the integers 1, 2, ..., 31 into 4 disjoint subsets (numbered 0..3) that all have the same sum 124 (the total is 496).
Find such a partition.
Answer format: {"x": [x_1, ..., x_31]}: a list of 31 integers in 0..3, where the i-th entry (0-indexed) is the subset containing the integer i+1
Write your final answ... | {"n": 31, "k": 4, "family": "mc_number_partitioning", "subset": "construct"} | null | null | null | {"x": [1, 2, 3, 3, 2, 1, 0, 0, 1, 2, 3, 3, 2, 1, 0, 0, 1, 2, 3, 3, 2, 1, 0, 0, 1, 2, 3, 3, 2, 1, 0]} | 1 |
construct-mc-number-partitioning-l4-s8 | construct | mc_number_partitioning | equal_sum_partition_1_to_n | number_theory | competition | 4 | MathConstraint/number_partitioning | CC-BY-4.0 | [
"agentic_trivial"
] | Partition the integers 1, 2, ..., 29 into 3 disjoint subsets (numbered 0..2) that all have the same sum 145 (the total is 435).
Find such a partition.
Answer format: {"x": [x_1, ..., x_29]}: a list of 29 integers in 0..2, where the i-th entry (0-indexed) is the subset containing the integer i+1
Write your final answ... | {"n": 29, "k": 3, "family": "mc_number_partitioning", "subset": "construct"} | null | null | null | {"x": [1, 2, 2, 1, 0, 0, 1, 2, 2, 1, 0, 0, 1, 2, 2, 1, 0, 0, 1, 2, 2, 1, 0, 0, 1, 2, 2, 1, 0]} | 1 |
construct-mc-number-partitioning-l4-s9 | construct | mc_number_partitioning | equal_sum_partition_1_to_n | number_theory | competition | 4 | MathConstraint/number_partitioning | CC-BY-4.0 | [
"agentic_trivial"
] | Partition the integers 1, 2, ..., 34 into 7 disjoint subsets (numbered 0..6) that all have the same sum 85 (the total is 595).
Find such a partition.
Answer format: {"x": [x_1, ..., x_34]}: a list of 34 integers in 0..6, where the i-th entry (0-indexed) is the subset containing the integer i+1
Write your final answe... | {"n": 34, "k": 7, "family": "mc_number_partitioning", "subset": "construct"} | null | null | null | {"x": [6, 6, 5, 2, 4, 3, 3, 2, 4, 0, 1, 5, 6, 6, 5, 4, 3, 2, 1, 0, 0, 1, 2, 3, 4, 5, 6, 6, 5, 4, 3, 2, 1, 0]} | 1 |
construct-mc-number-partitioning-l5-s0 | construct | mc_number_partitioning | equal_sum_partition_1_to_n | number_theory | competition | 5 | MathConstraint/number_partitioning | CC-BY-4.0 | [
"agentic_trivial"
] | Partition the integers 1, 2, ..., 47 into 8 disjoint subsets (numbered 0..7) that all have the same sum 141 (the total is 1128).
Find such a partition.
Answer format: {"x": [x_1, ..., x_47]}: a list of 47 integers in 0..7, where the i-th entry (0-indexed) is the subset containing the integer i+1
Write your final ans... | {"n": 47, "k": 8, "family": "mc_number_partitioning", "subset": "construct"} | null | null | null | {"x": [1, 2, 3, 4, 5, 6, 7, 7, 6, 5, 4, 3, 2, 1, 0, 0, 1, 2, 3, 4, 5, 6, 7, 7, 6, 5, 4, 3, 2, 1, 0, 0, 1, 2, 3, 4, 5, 6, 7, 7, 6, 5, 4, 3, 2, 1, 0]} | 1 |
construct-mc-number-partitioning-l5-s1 | construct | mc_number_partitioning | equal_sum_partition_1_to_n | number_theory | competition | 5 | MathConstraint/number_partitioning | CC-BY-4.0 | [
"agentic_trivial"
] | Partition the integers 1, 2, ..., 69 into 3 disjoint subsets (numbered 0..2) that all have the same sum 805 (the total is 2415).
Find such a partition.
Answer format: {"x": [x_1, ..., x_69]}: a list of 69 integers in 0..2, where the i-th entry (0-indexed) is the subset containing the integer i+1
Write your final ans... | {"n": 69, "k": 3, "family": "mc_number_partitioning", "subset": "construct"} | null | null | null | {"x": [0, 2, 1, 1, 0, 2, 2, 1, 0, 0, 1, 2, 2, 1, 0, 0, 1, 2, 2, 1, 0, 0, 1, 2, 2, 1, 0, 0, 1, 2, 2, 1, 0, 0, 1, 2, 2, 1, 0, 0, 1, 2, 2, 1, 0, 0, 1, 2, 2, 1, 0, 0, 1, 2, 2, 1, 0, 0, 1, 2, 2, 1, 0, 0, 1, 2, 2, 1, 0]} | 1 |
construct-mc-number-partitioning-l5-s2 | construct | mc_number_partitioning | equal_sum_partition_1_to_n | number_theory | competition | 5 | MathConstraint/number_partitioning | CC-BY-4.0 | [
"agentic_trivial"
] | Partition the integers 1, 2, ..., 53 into 3 disjoint subsets (numbered 0..2) that all have the same sum 477 (the total is 1431).
Find such a partition.
Answer format: {"x": [x_1, ..., x_53]}: a list of 53 integers in 0..2, where the i-th entry (0-indexed) is the subset containing the integer i+1
Write your final ans... | {"n": 53, "k": 3, "family": "mc_number_partitioning", "subset": "construct"} | null | null | null | {"x": [1, 2, 2, 1, 0, 0, 1, 2, 2, 1, 0, 0, 1, 2, 2, 1, 0, 0, 1, 2, 2, 1, 0, 0, 1, 2, 2, 1, 0, 0, 1, 2, 2, 1, 0, 0, 1, 2, 2, 1, 0, 0, 1, 2, 2, 1, 0, 0, 1, 2, 2, 1, 0]} | 1 |
construct-mc-number-partitioning-l5-s3 | construct | mc_number_partitioning | equal_sum_partition_1_to_n | number_theory | competition | 5 | MathConstraint/number_partitioning | CC-BY-4.0 | [
"agentic_trivial"
] | Partition the integers 1, 2, ..., 60 into 6 disjoint subsets (numbered 0..5) that all have the same sum 305 (the total is 1830).
Find such a partition.
Answer format: {"x": [x_1, ..., x_60]}: a list of 60 integers in 0..5, where the i-th entry (0-indexed) is the subset containing the integer i+1
Write your final ans... | {"n": 60, "k": 6, "family": "mc_number_partitioning", "subset": "construct"} | null | null | null | {"x": [0, 1, 2, 3, 4, 5, 5, 4, 3, 2, 1, 0, 0, 1, 2, 3, 4, 5, 5, 4, 3, 2, 1, 0, 0, 1, 2, 3, 4, 5, 5, 4, 3, 2, 1, 0, 0, 1, 2, 3, 4, 5, 5, 4, 3, 2, 1, 0, 0, 1, 2, 3, 4, 5, 5, 4, 3, 2, 1, 0]} | 1 |
construct-mc-number-partitioning-l5-s4 | construct | mc_number_partitioning | equal_sum_partition_1_to_n | number_theory | competition | 5 | MathConstraint/number_partitioning | CC-BY-4.0 | [
"agentic_trivial"
] | Partition the integers 1, 2, ..., 44 into 3 disjoint subsets (numbered 0..2) that all have the same sum 330 (the total is 990).
Find such a partition.
Answer format: {"x": [x_1, ..., x_44]}: a list of 44 integers in 0..2, where the i-th entry (0-indexed) is the subset containing the integer i+1
Write your final answ... | {"n": 44, "k": 3, "family": "mc_number_partitioning", "subset": "construct"} | null | null | null | {"x": [2, 1, 1, 0, 2, 2, 1, 0, 0, 1, 2, 2, 1, 0, 0, 1, 2, 2, 1, 0, 0, 1, 2, 2, 1, 0, 0, 1, 2, 2, 1, 0, 0, 1, 2, 2, 1, 0, 0, 1, 2, 2, 1, 0]} | 1 |
construct-mc-number-partitioning-l5-s5 | construct | mc_number_partitioning | equal_sum_partition_1_to_n | number_theory | competition | 5 | MathConstraint/number_partitioning | CC-BY-4.0 | [
"agentic_trivial"
] | Partition the integers 1, 2, ..., 66 into 3 disjoint subsets (numbered 0..2) that all have the same sum 737 (the total is 2211).
Find such a partition.
Answer format: {"x": [x_1, ..., x_66]}: a list of 66 integers in 0..2, where the i-th entry (0-indexed) is the subset containing the integer i+1
Write your final ans... | {"n": 66, "k": 3, "family": "mc_number_partitioning", "subset": "construct"} | null | null | null | {"x": [0, 1, 2, 2, 1, 0, 0, 1, 2, 2, 1, 0, 0, 1, 2, 2, 1, 0, 0, 1, 2, 2, 1, 0, 0, 1, 2, 2, 1, 0, 0, 1, 2, 2, 1, 0, 0, 1, 2, 2, 1, 0, 0, 1, 2, 2, 1, 0, 0, 1, 2, 2, 1, 0, 0, 1, 2, 2, 1, 0, 0, 1, 2, 2, 1, 0]} | 1 |
construct-mc-number-partitioning-l5-s6 | construct | mc_number_partitioning | equal_sum_partition_1_to_n | number_theory | competition | 5 | MathConstraint/number_partitioning | CC-BY-4.0 | [
"agentic_trivial"
] | Partition the integers 1, 2, ..., 50 into 5 disjoint subsets (numbered 0..4) that all have the same sum 255 (the total is 1275).
Find such a partition.
Answer format: {"x": [x_1, ..., x_50]}: a list of 50 integers in 0..4, where the i-th entry (0-indexed) is the subset containing the integer i+1
Write your final ans... | {"n": 50, "k": 5, "family": "mc_number_partitioning", "subset": "construct"} | null | null | null | {"x": [0, 1, 2, 3, 4, 4, 3, 2, 1, 0, 0, 1, 2, 3, 4, 4, 3, 2, 1, 0, 0, 1, 2, 3, 4, 4, 3, 2, 1, 0, 0, 1, 2, 3, 4, 4, 3, 2, 1, 0, 0, 1, 2, 3, 4, 4, 3, 2, 1, 0]} | 1 |
construct-mc-number-partitioning-l5-s7 | construct | mc_number_partitioning | equal_sum_partition_1_to_n | number_theory | competition | 5 | MathConstraint/number_partitioning | CC-BY-4.0 | [
"agentic_trivial"
] | Partition the integers 1, 2, ..., 62 into 7 disjoint subsets (numbered 0..6) that all have the same sum 279 (the total is 1953).
Find such a partition.
Answer format: {"x": [x_1, ..., x_62]}: a list of 62 integers in 0..6, where the i-th entry (0-indexed) is the subset containing the integer i+1
Write your final ans... | {"n": 62, "k": 7, "family": "mc_number_partitioning", "subset": "construct"} | null | null | null | {"x": [6, 6, 5, 2, 4, 3, 3, 2, 4, 0, 1, 5, 6, 6, 5, 4, 3, 2, 1, 0, 0, 1, 2, 3, 4, 5, 6, 6, 5, 4, 3, 2, 1, 0, 0, 1, 2, 3, 4, 5, 6, 6, 5, 4, 3, 2, 1, 0, 0, 1, 2, 3, 4, 5, 6, 6, 5, 4, 3, 2, 1, 0]} | 1 |
construct-mc-number-partitioning-l5-s8 | construct | mc_number_partitioning | equal_sum_partition_1_to_n | number_theory | competition | 5 | MathConstraint/number_partitioning | CC-BY-4.0 | [
"agentic_trivial"
] | Partition the integers 1, 2, ..., 68 into 3 disjoint subsets (numbered 0..2) that all have the same sum 782 (the total is 2346).
Find such a partition.
Answer format: {"x": [x_1, ..., x_68]}: a list of 68 integers in 0..2, where the i-th entry (0-indexed) is the subset containing the integer i+1
Write your final ans... | {"n": 68, "k": 3, "family": "mc_number_partitioning", "subset": "construct"} | null | null | null | {"x": [2, 1, 1, 0, 2, 2, 1, 0, 0, 1, 2, 2, 1, 0, 0, 1, 2, 2, 1, 0, 0, 1, 2, 2, 1, 0, 0, 1, 2, 2, 1, 0, 0, 1, 2, 2, 1, 0, 0, 1, 2, 2, 1, 0, 0, 1, 2, 2, 1, 0, 0, 1, 2, 2, 1, 0, 0, 1, 2, 2, 1, 0, 0, 1, 2, 2, 1, 0]} | 1 |
construct-mc-number-partitioning-l5-s9 | construct | mc_number_partitioning | equal_sum_partition_1_to_n | number_theory | competition | 5 | MathConstraint/number_partitioning | CC-BY-4.0 | [
"agentic_trivial"
] | Partition the integers 1, 2, ..., 44 into 5 disjoint subsets (numbered 0..4) that all have the same sum 198 (the total is 990).
Find such a partition.
Answer format: {"x": [x_1, ..., x_44]}: a list of 44 integers in 0..4, where the i-th entry (0-indexed) is the subset containing the integer i+1
Write your final answ... | {"n": 44, "k": 5, "family": "mc_number_partitioning", "subset": "construct"} | null | null | null | {"x": [2, 4, 1, 3, 1, 3, 0, 2, 4, 4, 3, 2, 1, 0, 0, 1, 2, 3, 4, 4, 3, 2, 1, 0, 0, 1, 2, 3, 4, 4, 3, 2, 1, 0, 0, 1, 2, 3, 4, 4, 3, 2, 1, 0]} | 1 |
construct-mc-number-partitioning-l6-s0 | construct | mc_number_partitioning | equal_sum_partition_1_to_n | number_theory | competition | 6 | MathConstraint/number_partitioning | CC-BY-4.0 | [
"agentic_trivial"
] | Partition the integers 1, 2, ..., 99 into 5 disjoint subsets (numbered 0..4) that all have the same sum 990 (the total is 4950).
Find such a partition.
Answer format: {"x": [x_1, ..., x_99]}: a list of 99 integers in 0..4, where the i-th entry (0-indexed) is the subset containing the integer i+1
Write your final ans... | {"n": 99, "k": 5, "family": "mc_number_partitioning", "subset": "construct"} | null | null | null | {"x": [1, 2, 3, 4, 4, 3, 2, 1, 0, 0, 1, 2, 3, 4, 4, 3, 2, 1, 0, 0, 1, 2, 3, 4, 4, 3, 2, 1, 0, 0, 1, 2, 3, 4, 4, 3, 2, 1, 0, 0, 1, 2, 3, 4, 4, 3, 2, 1, 0, 0, 1, 2, 3, 4, 4, 3, 2, 1, 0, 0, 1, 2, 3, 4, 4, 3, 2, 1, 0, 0, 1, 2, 3, 4, 4, 3, 2, 1, 0, 0, 1, 2, 3, 4, 4, 3, 2, 1, 0, 0, 1, 2, 3, 4, 4, 3, 2, 1, 0]} | 1 |
construct-mc-number-partitioning-l6-s1 | construct | mc_number_partitioning | equal_sum_partition_1_to_n | number_theory | competition | 6 | MathConstraint/number_partitioning | CC-BY-4.0 | [
"agentic_trivial"
] | Partition the integers 1, 2, ..., 107 into 6 disjoint subsets (numbered 0..5) that all have the same sum 963 (the total is 5778).
Find such a partition.
Answer format: {"x": [x_1, ..., x_107]}: a list of 107 integers in 0..5, where the i-th entry (0-indexed) is the subset containing the integer i+1
Write your final ... | {"n": 107, "k": 6, "family": "mc_number_partitioning", "subset": "construct"} | null | null | null | {"x": [1, 2, 3, 4, 5, 5, 4, 3, 2, 1, 0, 0, 1, 2, 3, 4, 5, 5, 4, 3, 2, 1, 0, 0, 1, 2, 3, 4, 5, 5, 4, 3, 2, 1, 0, 0, 1, 2, 3, 4, 5, 5, 4, 3, 2, 1, 0, 0, 1, 2, 3, 4, 5, 5, 4, 3, 2, 1, 0, 0, 1, 2, 3, 4, 5, 5, 4, 3, 2, 1, 0, 0, 1, 2, 3, 4, 5, 5, 4, 3, 2, 1, 0, 0, 1, 2, 3, 4, 5, 5, 4, 3, 2, 1, 0, 0, 1, 2, 3, 4, 5, 5, 4, 3, 2... | 1 |
construct-mc-number-partitioning-l6-s2 | construct | mc_number_partitioning | equal_sum_partition_1_to_n | number_theory | competition | 6 | MathConstraint/number_partitioning | CC-BY-4.0 | [
"agentic_trivial"
] | Partition the integers 1, 2, ..., 120 into 4 disjoint subsets (numbered 0..3) that all have the same sum 1815 (the total is 7260).
Find such a partition.
Answer format: {"x": [x_1, ..., x_120]}: a list of 120 integers in 0..3, where the i-th entry (0-indexed) is the subset containing the integer i+1
Write your final... | {"n": 120, "k": 4, "family": "mc_number_partitioning", "subset": "construct"} | null | null | null | {"x": [0, 1, 2, 3, 3, 2, 1, 0, 0, 1, 2, 3, 3, 2, 1, 0, 0, 1, 2, 3, 3, 2, 1, 0, 0, 1, 2, 3, 3, 2, 1, 0, 0, 1, 2, 3, 3, 2, 1, 0, 0, 1, 2, 3, 3, 2, 1, 0, 0, 1, 2, 3, 3, 2, 1, 0, 0, 1, 2, 3, 3, 2, 1, 0, 0, 1, 2, 3, 3, 2, 1, 0, 0, 1, 2, 3, 3, 2, 1, 0, 0, 1, 2, 3, 3, 2, 1, 0, 0, 1, 2, 3, 3, 2, 1, 0, 0, 1, 2, 3, 3, 2, 1, 0, 0... | 1 |
construct-mc-number-partitioning-l6-s3 | construct | mc_number_partitioning | equal_sum_partition_1_to_n | number_theory | competition | 6 | MathConstraint/number_partitioning | CC-BY-4.0 | [
"agentic_trivial"
] | Partition the integers 1, 2, ..., 111 into 7 disjoint subsets (numbered 0..6) that all have the same sum 888 (the total is 6216).
Find such a partition.
Answer format: {"x": [x_1, ..., x_111]}: a list of 111 integers in 0..6, where the i-th entry (0-indexed) is the subset containing the integer i+1
Write your final ... | {"n": 111, "k": 7, "family": "mc_number_partitioning", "subset": "construct"} | null | null | null | {"x": [1, 2, 3, 4, 5, 6, 6, 5, 4, 3, 2, 1, 0, 0, 1, 2, 3, 4, 5, 6, 6, 5, 4, 3, 2, 1, 0, 0, 1, 2, 3, 4, 5, 6, 6, 5, 4, 3, 2, 1, 0, 0, 1, 2, 3, 4, 5, 6, 6, 5, 4, 3, 2, 1, 0, 0, 1, 2, 3, 4, 5, 6, 6, 5, 4, 3, 2, 1, 0, 0, 1, 2, 3, 4, 5, 6, 6, 5, 4, 3, 2, 1, 0, 0, 1, 2, 3, 4, 5, 6, 6, 5, 4, 3, 2, 1, 0, 0, 1, 2, 3, 4, 5, 6, 6... | 1 |
construct-mc-number-partitioning-l6-s4 | construct | mc_number_partitioning | equal_sum_partition_1_to_n | number_theory | competition | 6 | MathConstraint/number_partitioning | CC-BY-4.0 | [
"agentic_trivial"
] | Partition the integers 1, 2, ..., 118 into 7 disjoint subsets (numbered 0..6) that all have the same sum 1003 (the total is 7021).
Find such a partition.
Answer format: {"x": [x_1, ..., x_118]}: a list of 118 integers in 0..6, where the i-th entry (0-indexed) is the subset containing the integer i+1
Write your final... | {"n": 118, "k": 7, "family": "mc_number_partitioning", "subset": "construct"} | null | null | null | {"x": [6, 6, 5, 2, 4, 3, 3, 2, 4, 0, 1, 5, 6, 6, 5, 4, 3, 2, 1, 0, 0, 1, 2, 3, 4, 5, 6, 6, 5, 4, 3, 2, 1, 0, 0, 1, 2, 3, 4, 5, 6, 6, 5, 4, 3, 2, 1, 0, 0, 1, 2, 3, 4, 5, 6, 6, 5, 4, 3, 2, 1, 0, 0, 1, 2, 3, 4, 5, 6, 6, 5, 4, 3, 2, 1, 0, 0, 1, 2, 3, 4, 5, 6, 6, 5, 4, 3, 2, 1, 0, 0, 1, 2, 3, 4, 5, 6, 6, 5, 4, 3, 2, 1, 0, 0... | 1 |
construct-mc-number-partitioning-l6-s5 | construct | mc_number_partitioning | equal_sum_partition_1_to_n | number_theory | competition | 6 | MathConstraint/number_partitioning | CC-BY-4.0 | [
"agentic_trivial"
] | Partition the integers 1, 2, ..., 96 into 4 disjoint subsets (numbered 0..3) that all have the same sum 1164 (the total is 4656).
Find such a partition.
Answer format: {"x": [x_1, ..., x_96]}: a list of 96 integers in 0..3, where the i-th entry (0-indexed) is the subset containing the integer i+1
Write your final an... | {"n": 96, "k": 4, "family": "mc_number_partitioning", "subset": "construct"} | null | null | null | {"x": [0, 1, 2, 3, 3, 2, 1, 0, 0, 1, 2, 3, 3, 2, 1, 0, 0, 1, 2, 3, 3, 2, 1, 0, 0, 1, 2, 3, 3, 2, 1, 0, 0, 1, 2, 3, 3, 2, 1, 0, 0, 1, 2, 3, 3, 2, 1, 0, 0, 1, 2, 3, 3, 2, 1, 0, 0, 1, 2, 3, 3, 2, 1, 0, 0, 1, 2, 3, 3, 2, 1, 0, 0, 1, 2, 3, 3, 2, 1, 0, 0, 1, 2, 3, 3, 2, 1, 0, 0, 1, 2, 3, 3, 2, 1, 0]} | 1 |
construct-mc-number-partitioning-l6-s6 | construct | mc_number_partitioning | equal_sum_partition_1_to_n | number_theory | competition | 6 | MathConstraint/number_partitioning | CC-BY-4.0 | [
"agentic_trivial"
] | Partition the integers 1, 2, ..., 110 into 3 disjoint subsets (numbered 0..2) that all have the same sum 2035 (the total is 6105).
Find such a partition.
Answer format: {"x": [x_1, ..., x_110]}: a list of 110 integers in 0..2, where the i-th entry (0-indexed) is the subset containing the integer i+1
Write your final... | {"n": 110, "k": 3, "family": "mc_number_partitioning", "subset": "construct"} | null | null | null | {"x": [2, 1, 1, 0, 2, 2, 1, 0, 0, 1, 2, 2, 1, 0, 0, 1, 2, 2, 1, 0, 0, 1, 2, 2, 1, 0, 0, 1, 2, 2, 1, 0, 0, 1, 2, 2, 1, 0, 0, 1, 2, 2, 1, 0, 0, 1, 2, 2, 1, 0, 0, 1, 2, 2, 1, 0, 0, 1, 2, 2, 1, 0, 0, 1, 2, 2, 1, 0, 0, 1, 2, 2, 1, 0, 0, 1, 2, 2, 1, 0, 0, 1, 2, 2, 1, 0, 0, 1, 2, 2, 1, 0, 0, 1, 2, 2, 1, 0, 0, 1, 2, 2, 1, 0, 0... | 1 |
construct-mc-number-partitioning-l6-s7 | construct | mc_number_partitioning | equal_sum_partition_1_to_n | number_theory | competition | 6 | MathConstraint/number_partitioning | CC-BY-4.0 | [
"agentic_trivial"
] | Partition the integers 1, 2, ..., 95 into 6 disjoint subsets (numbered 0..5) that all have the same sum 760 (the total is 4560).
Find such a partition.
Answer format: {"x": [x_1, ..., x_95]}: a list of 95 integers in 0..5, where the i-th entry (0-indexed) is the subset containing the integer i+1
Write your final ans... | {"n": 95, "k": 6, "family": "mc_number_partitioning", "subset": "construct"} | null | null | null | {"x": [1, 2, 3, 4, 5, 5, 4, 3, 2, 1, 0, 0, 1, 2, 3, 4, 5, 5, 4, 3, 2, 1, 0, 0, 1, 2, 3, 4, 5, 5, 4, 3, 2, 1, 0, 0, 1, 2, 3, 4, 5, 5, 4, 3, 2, 1, 0, 0, 1, 2, 3, 4, 5, 5, 4, 3, 2, 1, 0, 0, 1, 2, 3, 4, 5, 5, 4, 3, 2, 1, 0, 0, 1, 2, 3, 4, 5, 5, 4, 3, 2, 1, 0, 0, 1, 2, 3, 4, 5, 5, 4, 3, 2, 1, 0]} | 1 |
construct-mc-number-partitioning-l6-s8 | construct | mc_number_partitioning | equal_sum_partition_1_to_n | number_theory | competition | 6 | MathConstraint/number_partitioning | CC-BY-4.0 | [
"agentic_trivial"
] | Partition the integers 1, 2, ..., 119 into 5 disjoint subsets (numbered 0..4) that all have the same sum 1428 (the total is 7140).
Find such a partition.
Answer format: {"x": [x_1, ..., x_119]}: a list of 119 integers in 0..4, where the i-th entry (0-indexed) is the subset containing the integer i+1
Write your final... | {"n": 119, "k": 5, "family": "mc_number_partitioning", "subset": "construct"} | null | null | null | {"x": [1, 2, 3, 4, 4, 3, 2, 1, 0, 0, 1, 2, 3, 4, 4, 3, 2, 1, 0, 0, 1, 2, 3, 4, 4, 3, 2, 1, 0, 0, 1, 2, 3, 4, 4, 3, 2, 1, 0, 0, 1, 2, 3, 4, 4, 3, 2, 1, 0, 0, 1, 2, 3, 4, 4, 3, 2, 1, 0, 0, 1, 2, 3, 4, 4, 3, 2, 1, 0, 0, 1, 2, 3, 4, 4, 3, 2, 1, 0, 0, 1, 2, 3, 4, 4, 3, 2, 1, 0, 0, 1, 2, 3, 4, 4, 3, 2, 1, 0, 0, 1, 2, 3, 4, 4... | 1 |
construct-mc-number-partitioning-l6-s9 | construct | mc_number_partitioning | equal_sum_partition_1_to_n | number_theory | competition | 6 | MathConstraint/number_partitioning | CC-BY-4.0 | [
"agentic_trivial"
] | Partition the integers 1, 2, ..., 119 into 4 disjoint subsets (numbered 0..3) that all have the same sum 1785 (the total is 7140).
Find such a partition.
Answer format: {"x": [x_1, ..., x_119]}: a list of 119 integers in 0..3, where the i-th entry (0-indexed) is the subset containing the integer i+1
Write your final... | {"n": 119, "k": 4, "family": "mc_number_partitioning", "subset": "construct"} | null | null | null | {"x": [1, 2, 3, 3, 2, 1, 0, 0, 1, 2, 3, 3, 2, 1, 0, 0, 1, 2, 3, 3, 2, 1, 0, 0, 1, 2, 3, 3, 2, 1, 0, 0, 1, 2, 3, 3, 2, 1, 0, 0, 1, 2, 3, 3, 2, 1, 0, 0, 1, 2, 3, 3, 2, 1, 0, 0, 1, 2, 3, 3, 2, 1, 0, 0, 1, 2, 3, 3, 2, 1, 0, 0, 1, 2, 3, 3, 2, 1, 0, 0, 1, 2, 3, 3, 2, 1, 0, 0, 1, 2, 3, 3, 2, 1, 0, 0, 1, 2, 3, 3, 2, 1, 0, 0, 1... | 1 |
construct-mc-ortholatin-l1-s0 | construct | mc_ortholatin | orthogonal_latin_squares | combinatorics | competition | 1 | MathConstraint/ortholatin | CC-BY-4.0 | [
"np_search"
] | Construct a pair of orthogonal Latin squares of order 3: two 3x3 arrays X and Y with entries in 0..2 such that every row and every column of X is a permutation of 0..2, the same holds for Y, and the 9 ordered pairs (X[i][j], Y[i][j]) are all distinct.
Answer format: {"X": [[row 0], ..., [row 2]], "Y": [[row 0], ..., [... | {"n": 3, "family": "mc_ortholatin", "subset": "construct"} | null | null | null | {"X": [[0, 1, 2], [1, 2, 0], [2, 0, 1]], "Y": [[0, 2, 1], [1, 0, 2], [2, 1, 0]]} | 1 |
construct-mc-ortholatin-l1-s1 | construct | mc_ortholatin | orthogonal_latin_squares | combinatorics | competition | 1 | MathConstraint/ortholatin | CC-BY-4.0 | [
"np_search"
] | Construct a pair of orthogonal Latin squares of order 4: two 4x4 arrays X and Y with entries in 0..3 such that every row and every column of X is a permutation of 0..3, the same holds for Y, and the 16 ordered pairs (X[i][j], Y[i][j]) are all distinct.
Answer format: {"X": [[row 0], ..., [row 3]], "Y": [[row 0], ..., ... | {"n": 4, "family": "mc_ortholatin", "subset": "construct"} | null | null | null | {"X": [[0, 1, 2, 3], [1, 0, 3, 2], [2, 3, 0, 1], [3, 2, 1, 0]], "Y": [[0, 1, 2, 3], [2, 3, 0, 1], [3, 2, 1, 0], [1, 0, 3, 2]]} | 1 |
construct-mc-ortholatin-l1-s2 | construct | mc_ortholatin | orthogonal_latin_squares | combinatorics | competition | 1 | MathConstraint/ortholatin | CC-BY-4.0 | [
"np_search"
] | Construct a pair of orthogonal Latin squares of order 5: two 5x5 arrays X and Y with entries in 0..4 such that every row and every column of X is a permutation of 0..4, the same holds for Y, and the 25 ordered pairs (X[i][j], Y[i][j]) are all distinct.
Answer format: {"X": [[row 0], ..., [row 4]], "Y": [[row 0], ..., ... | {"n": 5, "family": "mc_ortholatin", "subset": "construct"} | null | null | null | {"X": [[0, 1, 2, 3, 4], [1, 2, 3, 4, 0], [2, 3, 4, 0, 1], [3, 4, 0, 1, 2], [4, 0, 1, 2, 3]], "Y": [[0, 2, 4, 1, 3], [1, 3, 0, 2, 4], [2, 4, 1, 3, 0], [3, 0, 2, 4, 1], [4, 1, 3, 0, 2]]} | 1 |
construct-mc-ortholatin-l2-s0 | construct | mc_ortholatin | orthogonal_latin_squares | combinatorics | competition | 2 | MathConstraint/ortholatin | CC-BY-4.0 | [
"np_search"
] | Construct a pair of orthogonal Latin squares of order 8: two 8x8 arrays X and Y with entries in 0..7 such that every row and every column of X is a permutation of 0..7, the same holds for Y, and the 64 ordered pairs (X[i][j], Y[i][j]) are all distinct.
Answer format: {"X": [[row 0], ..., [row 7]], "Y": [[row 0], ..., ... | {"n": 8, "family": "mc_ortholatin", "subset": "construct"} | null | null | null | {"X": [[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, 2, 3], [5, 4, 7, 6, 1, 0, 3, 2], [6, 7, 4, 5, 2, 3, 0, 1], [7, 6, 5, 4, 3, 2, 1, 0]], "Y": [[0, 1, 2, 3, 4, 5, 6, 7], [2, 3, 0, 1, 6, 7, 4, 5], [4, 7, 6, 5, 0, 1, 2, 3], [6, 5, 4, 7, 2, 3, 0... | 1 |
construct-mc-ortholatin-l2-s1 | construct | mc_ortholatin | orthogonal_latin_squares | combinatorics | competition | 2 | MathConstraint/ortholatin | CC-BY-4.0 | [
"np_search"
] | Construct a pair of orthogonal Latin squares of order 9: two 9x9 arrays X and Y with entries in 0..8 such that every row and every column of X is a permutation of 0..8, the same holds for Y, and the 81 ordered pairs (X[i][j], Y[i][j]) are all distinct.
Answer format: {"X": [[row 0], ..., [row 8]], "Y": [[row 0], ..., ... | {"n": 9, "family": "mc_ortholatin", "subset": "construct"} | null | null | null | {"X": [[0, 1, 2, 3, 4, 5, 6, 7, 8], [1, 2, 3, 4, 5, 6, 7, 8, 0], [2, 3, 4, 5, 6, 7, 8, 0, 1], [3, 4, 5, 6, 7, 8, 0, 1, 2], [4, 5, 6, 7, 8, 0, 1, 2, 3], [5, 6, 7, 8, 0, 1, 2, 3, 4], [6, 7, 8, 0, 1, 2, 3, 4, 5], [7, 8, 0, 1, 2, 3, 4, 5, 6], [8, 0, 1, 2, 3, 4, 5, 6, 7]], "Y": [[0, 2, 4, 6, 8, 1, 3, 5, 7], [1, 3, 5, 7, 0, ... | 1 |
construct-mc-ortholatin-l2-s2 | construct | mc_ortholatin | orthogonal_latin_squares | combinatorics | competition | 2 | MathConstraint/ortholatin | CC-BY-4.0 | [
"np_search"
] | Construct a pair of orthogonal Latin squares of order 7: two 7x7 arrays X and Y with entries in 0..6 such that every row and every column of X is a permutation of 0..6, the same holds for Y, and the 49 ordered pairs (X[i][j], Y[i][j]) are all distinct.
Answer format: {"X": [[row 0], ..., [row 6]], "Y": [[row 0], ..., ... | {"n": 7, "family": "mc_ortholatin", "subset": "construct"} | null | null | null | {"X": [[0, 1, 2, 3, 4, 5, 6], [1, 2, 3, 4, 5, 6, 0], [2, 3, 4, 5, 6, 0, 1], [3, 4, 5, 6, 0, 1, 2], [4, 5, 6, 0, 1, 2, 3], [5, 6, 0, 1, 2, 3, 4], [6, 0, 1, 2, 3, 4, 5]], "Y": [[0, 2, 4, 6, 1, 3, 5], [1, 3, 5, 0, 2, 4, 6], [2, 4, 6, 1, 3, 5, 0], [3, 5, 0, 2, 4, 6, 1], [4, 6, 1, 3, 5, 0, 2], [5, 0, 2, 4, 6, 1, 3], [6, 1, ... | 1 |
construct-mc-ortholatin-l3-s0 | construct | mc_ortholatin | orthogonal_latin_squares | combinatorics | competition | 3 | MathConstraint/ortholatin | CC-BY-4.0 | [
"np_search"
] | Construct a pair of orthogonal Latin squares of order 10: two 10x10 arrays X and Y with entries in 0..9 such that every row and every column of X is a permutation of 0..9, the same holds for Y, and the 100 ordered pairs (X[i][j], Y[i][j]) are all distinct.
Answer format: {"X": [[row 0], ..., [row 9]], "Y": [[row 0], .... | {"n": 10, "family": "mc_ortholatin", "subset": "construct"} | null | null | null | {"X": [[0, 6, 2, 3, 4, 5, 1, 7, 8, 9], [1, 7, 8, 9, 0, 6, 2, 3, 4, 5], [7, 8, 4, 0, 6, 2, 3, 9, 5, 1], [8, 9, 5, 1, 2, 3, 4, 0, 6, 7], [9, 0, 1, 7, 8, 4, 5, 6, 2, 3], [5, 1, 7, 8, 9, 0, 6, 2, 3, 4], [6, 2, 3, 4, 5, 1, 7, 8, 9, 0], [2, 3, 9, 5, 1, 7, 8, 4, 0, 6], [3, 4, 0, 6, 7, 8, 9, 5, 1, 2], [4, 5, 6, 2, 3, 9, 0, 1, ... | 1 |
construct-mc-ortholatin-l3-s1 | construct | mc_ortholatin | orthogonal_latin_squares | combinatorics | competition | 3 | MathConstraint/ortholatin | CC-BY-4.0 | [
"np_search"
] | Construct a pair of orthogonal Latin squares of order 13: two 13x13 arrays X and Y with entries in 0..12 such that every row and every column of X is a permutation of 0..12, the same holds for Y, and the 169 ordered pairs (X[i][j], Y[i][j]) are all distinct.
Answer format: {"X": [[row 0], ..., [row 12]], "Y": [[row 0]... | {"n": 13, "family": "mc_ortholatin", "subset": "construct"} | null | null | null | {"X": [[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12], [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 0], [2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 0, 1], [3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 0, 1, 2], [4, 5, 6, 7, 8, 9, 10, 11, 12, 0, 1, 2, 3], [5, 6, 7, 8, 9, 10, 11, 12, 0, 1, 2, 3, 4], [6, 7, 8, 9, 10, 11, 12, 0, 1, 2, 3, 4, 5], [7, 8... | 1 |
construct-mc-ortholatin-l3-s2 | construct | mc_ortholatin | orthogonal_latin_squares | combinatorics | competition | 3 | MathConstraint/ortholatin | CC-BY-4.0 | [
"np_search"
] | Construct a pair of orthogonal Latin squares of order 11: two 11x11 arrays X and Y with entries in 0..10 such that every row and every column of X is a permutation of 0..10, the same holds for Y, and the 121 ordered pairs (X[i][j], Y[i][j]) are all distinct.
Answer format: {"X": [[row 0], ..., [row 10]], "Y": [[row 0]... | {"n": 11, "family": "mc_ortholatin", "subset": "construct"} | null | null | null | {"X": [[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10], [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 0], [2, 3, 4, 5, 6, 7, 8, 9, 10, 0, 1], [3, 4, 5, 6, 7, 8, 9, 10, 0, 1, 2], [4, 5, 6, 7, 8, 9, 10, 0, 1, 2, 3], [5, 6, 7, 8, 9, 10, 0, 1, 2, 3, 4], [6, 7, 8, 9, 10, 0, 1, 2, 3, 4, 5], [7, 8, 9, 10, 0, 1, 2, 3, 4, 5, 6], [8, 9, 10, 0, 1, 2, 3, 4,... | 1 |
construct-mc-ortholatin-l3-s3 | construct | mc_ortholatin | orthogonal_latin_squares | combinatorics | competition | 3 | MathConstraint/ortholatin | CC-BY-4.0 | [
"np_search"
] | Construct a pair of orthogonal Latin squares of order 12: two 12x12 arrays X and Y with entries in 0..11 such that every row and every column of X is a permutation of 0..11, the same holds for Y, and the 144 ordered pairs (X[i][j], Y[i][j]) are all distinct.
Answer format: {"X": [[row 0], ..., [row 11]], "Y": [[row 0]... | {"n": 12, "family": "mc_ortholatin", "subset": "construct"} | null | null | null | {"X": [[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], [1, 2, 0, 4, 5, 3, 7, 8, 6, 10, 11, 9], [2, 0, 1, 5, 3, 4, 8, 6, 7, 11, 9, 10], [3, 4, 5, 0, 1, 2, 9, 10, 11, 6, 7, 8], [4, 5, 3, 1, 2, 0, 10, 11, 9, 7, 8, 6], [5, 3, 4, 2, 0, 1, 11, 9, 10, 8, 6, 7], [6, 7, 8, 9, 10, 11, 0, 1, 2, 3, 4, 5], [7, 8, 6, 10, 11, 9, 1, 2, 0, 4, ... | 1 |
construct-mc-ortholatin-l4-s0 | construct | mc_ortholatin | orthogonal_latin_squares | combinatorics | competition | 4 | MathConstraint/ortholatin | CC-BY-4.0 | [
"np_search"
] | Construct a pair of orthogonal Latin squares of order 17: two 17x17 arrays X and Y with entries in 0..16 such that every row and every column of X is a permutation of 0..16, the same holds for Y, and the 289 ordered pairs (X[i][j], Y[i][j]) are all distinct.
Answer format: {"X": [[row 0], ..., [row 16]], "Y": [[row 0]... | {"n": 17, "family": "mc_ortholatin", "subset": "construct"} | null | null | null | {"X": [[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16], [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 0], [2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 0, 1], [3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 0, 1, 2], [4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 0, 1, 2, 3], [5, 6, 7, 8, ... | 1 |
construct-mc-ortholatin-l4-s1 | construct | mc_ortholatin | orthogonal_latin_squares | combinatorics | competition | 4 | MathConstraint/ortholatin | CC-BY-4.0 | [
"np_search"
] | Construct a pair of orthogonal Latin squares of order 15: two 15x15 arrays X and Y with entries in 0..14 such that every row and every column of X is a permutation of 0..14, the same holds for Y, and the 225 ordered pairs (X[i][j], Y[i][j]) are all distinct.
Answer format: {"X": [[row 0], ..., [row 14]], "Y": [[row 0]... | {"n": 15, "family": "mc_ortholatin", "subset": "construct"} | null | null | null | {"X": [[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14], [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 0], [2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 0, 1], [3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 0, 1, 2], [4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 0, 1, 2, 3], [5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 0, 1, 2, 3, 4], [... | 1 |
construct-mc-ortholatin-l4-s2 | construct | mc_ortholatin | orthogonal_latin_squares | combinatorics | competition | 4 | MathConstraint/ortholatin | CC-BY-4.0 | [
"np_search"
] | Construct a pair of orthogonal Latin squares of order 16: two 16x16 arrays X and Y with entries in 0..15 such that every row and every column of X is a permutation of 0..15, the same holds for Y, and the 256 ordered pairs (X[i][j], Y[i][j]) are all distinct.
Answer format: {"X": [[row 0], ..., [row 15]], "Y": [[row 0]... | {"n": 16, "family": "mc_ortholatin", "subset": "construct"} | null | null | null | {"X": [[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15], [1, 0, 3, 2, 5, 4, 7, 6, 9, 8, 11, 10, 13, 12, 15, 14], [2, 3, 0, 1, 6, 7, 4, 5, 10, 11, 8, 9, 14, 15, 12, 13], [3, 2, 1, 0, 7, 6, 5, 4, 11, 10, 9, 8, 15, 14, 13, 12], [4, 5, 6, 7, 0, 1, 2, 3, 12, 13, 14, 15, 8, 9, 10, 11], [5, 4, 7, 6, 1, 0, 3, 2, 13, 12, ... | 1 |
construct-mc-ortholatin-l5-s0 | construct | mc_ortholatin | orthogonal_latin_squares | combinatorics | competition | 5 | MathConstraint/ortholatin | CC-BY-4.0 | [
"np_search"
] | Construct a pair of orthogonal Latin squares of order 20: two 20x20 arrays X and Y with entries in 0..19 such that every row and every column of X is a permutation of 0..19, the same holds for Y, and the 400 ordered pairs (X[i][j], Y[i][j]) are all distinct.
Answer format: {"X": [[row 0], ..., [row 19]], "Y": [[row 0]... | {"n": 20, "family": "mc_ortholatin", "subset": "construct"} | null | null | null | {"X": [[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19], [1, 2, 3, 4, 0, 6, 7, 8, 9, 5, 11, 12, 13, 14, 10, 16, 17, 18, 19, 15], [2, 3, 4, 0, 1, 7, 8, 9, 5, 6, 12, 13, 14, 10, 11, 17, 18, 19, 15, 16], [3, 4, 0, 1, 2, 8, 9, 5, 6, 7, 13, 14, 10, 11, 12, 18, 19, 15, 16, 17], [4, 0, 1, 2, 3, 9, 5, 6, ... | 1 |
construct-mc-ortholatin-l5-s1 | construct | mc_ortholatin | orthogonal_latin_squares | combinatorics | competition | 5 | MathConstraint/ortholatin | CC-BY-4.0 | [
"np_search"
] | Construct a pair of orthogonal Latin squares of order 19: two 19x19 arrays X and Y with entries in 0..18 such that every row and every column of X is a permutation of 0..18, the same holds for Y, and the 361 ordered pairs (X[i][j], Y[i][j]) are all distinct.
Answer format: {"X": [[row 0], ..., [row 18]], "Y": [[row 0]... | {"n": 19, "family": "mc_ortholatin", "subset": "construct"} | null | null | null | {"X": [[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18], [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 0], [2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 0, 1], [3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 0, 1, 2], [4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15... | 1 |
construct-mc-ortholatin-l5-s2 | construct | mc_ortholatin | orthogonal_latin_squares | combinatorics | competition | 5 | MathConstraint/ortholatin | CC-BY-4.0 | [
"np_search"
] | Construct a pair of orthogonal Latin squares of order 21: two 21x21 arrays X and Y with entries in 0..20 such that every row and every column of X is a permutation of 0..20, the same holds for Y, and the 441 ordered pairs (X[i][j], Y[i][j]) are all distinct.
Answer format: {"X": [[row 0], ..., [row 20]], "Y": [[row 0]... | {"n": 21, "family": "mc_ortholatin", "subset": "construct"} | null | null | null | {"X": [[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20], [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 0], [2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 0, 1], [3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 0, 1, 2], [4, 5, 6,... | 1 |
construct-mc-ortholatin-l5-s3 | construct | mc_ortholatin | orthogonal_latin_squares | combinatorics | competition | 5 | MathConstraint/ortholatin | CC-BY-4.0 | [
"np_search"
] | Construct a pair of orthogonal Latin squares of order 23: two 23x23 arrays X and Y with entries in 0..22 such that every row and every column of X is a permutation of 0..22, the same holds for Y, and the 529 ordered pairs (X[i][j], Y[i][j]) are all distinct.
Answer format: {"X": [[row 0], ..., [row 22]], "Y": [[row 0]... | {"n": 23, "family": "mc_ortholatin", "subset": "construct"} | null | null | null | {"X": [[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22], [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 0], [2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 0, 1], [3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19,... | 1 |
construct-mc-ortholatin-l6-s0 | construct | mc_ortholatin | orthogonal_latin_squares | combinatorics | competition | 6 | MathConstraint/ortholatin | CC-BY-4.0 | [
"np_search"
] | Construct a pair of orthogonal Latin squares of order 28: two 28x28 arrays X and Y with entries in 0..27 such that every row and every column of X is a permutation of 0..27, the same holds for Y, and the 784 ordered pairs (X[i][j], Y[i][j]) are all distinct.
Answer format: {"X": [[row 0], ..., [row 27]], "Y": [[row 0]... | {"n": 28, "family": "mc_ortholatin", "subset": "construct"} | null | null | null | {"X": [[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27], [1, 2, 3, 4, 5, 6, 0, 8, 9, 10, 11, 12, 13, 7, 15, 16, 17, 18, 19, 20, 14, 22, 23, 24, 25, 26, 27, 21], [2, 3, 4, 5, 6, 0, 1, 9, 10, 11, 12, 13, 7, 8, 16, 17, 18, 19, 20, 14, 15, 23, 24, 25, 26, 27, 21, 22], [... | 1 |
construct-mc-ortholatin-l6-s1 | construct | mc_ortholatin | orthogonal_latin_squares | combinatorics | competition | 6 | MathConstraint/ortholatin | CC-BY-4.0 | [
"np_search"
] | Construct a pair of orthogonal Latin squares of order 24: two 24x24 arrays X and Y with entries in 0..23 such that every row and every column of X is a permutation of 0..23, the same holds for Y, and the 576 ordered pairs (X[i][j], Y[i][j]) are all distinct.
Answer format: {"X": [[row 0], ..., [row 23]], "Y": [[row 0]... | {"n": 24, "family": "mc_ortholatin", "subset": "construct"} | null | null | null | {"X": [[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23], [1, 2, 0, 4, 5, 3, 7, 8, 6, 10, 11, 9, 13, 14, 12, 16, 17, 15, 19, 20, 18, 22, 23, 21], [2, 0, 1, 5, 3, 4, 8, 6, 7, 11, 9, 10, 14, 12, 13, 17, 15, 16, 20, 18, 19, 23, 21, 22], [3, 4, 5, 0, 1, 2, 9, 10, 11, 6, 7, 8, 15, 16, 17... | 1 |
construct-mc-ortholatin-l6-s2 | construct | mc_ortholatin | orthogonal_latin_squares | combinatorics | competition | 6 | MathConstraint/ortholatin | CC-BY-4.0 | [
"np_search"
] | Construct a pair of orthogonal Latin squares of order 25: two 25x25 arrays X and Y with entries in 0..24 such that every row and every column of X is a permutation of 0..24, the same holds for Y, and the 625 ordered pairs (X[i][j], Y[i][j]) are all distinct.
Answer format: {"X": [[row 0], ..., [row 24]], "Y": [[row 0]... | {"n": 25, "family": "mc_ortholatin", "subset": "construct"} | null | null | null | {"X": [[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24], [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 0], [2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 0, 1], [3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,... | 1 |
construct-mc-ortholatin-l6-s3 | construct | mc_ortholatin | orthogonal_latin_squares | combinatorics | competition | 6 | MathConstraint/ortholatin | CC-BY-4.0 | [
"np_search"
] | Construct a pair of orthogonal Latin squares of order 27: two 27x27 arrays X and Y with entries in 0..26 such that every row and every column of X is a permutation of 0..26, the same holds for Y, and the 729 ordered pairs (X[i][j], Y[i][j]) are all distinct.
Answer format: {"X": [[row 0], ..., [row 26]], "Y": [[row 0]... | {"n": 27, "family": "mc_ortholatin", "subset": "construct"} | null | null | null | {"X": [[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26], [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 0], [2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 0, 1], [3, 4, 5, 6, ... | 1 |
construct-mc-pysms-chromatic-girth-l1-s0 | construct | mc_pysms_chromatic_girth | graph_existence_chromatic_girth | graph_theory | competition | 1 | MathConstraint/pysms_chromatic_girth | CC-BY-4.0 | [
"np_search"
] | Construct a simple undirected graph on the 9 vertices 0..8 such that:
- the graph has at least 9 edges
- the chromatic number is at most 5: the vertices can be coloured with colours 0..4 so that adjacent vertices get different colours (you must also give such a colouring)
- the girth is at least 5: the graph has ... | {"vertices": 9, "required_edges": [[4, 8]], "max_chromatic_number": 5, "min_edges": 9, "min_girth": 5, "family": "mc_pysms_chromatic_girth", "subset": "construct"} | null | null | null | {"edges": [[0, 8], [1, 8], [2, 7], [3, 6], [3, 8], [4, 5], [4, 8], [5, 6], [7, 8]], "coloring": [1, 1, 0, 1, 1, 0, 2, 1, 0]} | 1 |
construct-mc-pysms-chromatic-girth-l1-s1 | construct | mc_pysms_chromatic_girth | graph_existence_chromatic_girth | graph_theory | competition | 1 | MathConstraint/pysms_chromatic_girth | CC-BY-4.0 | [
"np_search"
] | Construct a simple undirected graph on the 13 vertices 0..12 such that:
- the graph has at least 8 edges
- the chromatic number is at most 2: the vertices can be coloured with colours 0..1 so that adjacent vertices get different colours (you must also give such a colouring)
- the girth is at least 5: the graph ha... | {"vertices": 13, "required_edges": [[0, 1], [0, 8]], "max_chromatic_number": 2, "min_edges": 8, "min_girth": 5, "family": "mc_pysms_chromatic_girth", "subset": "construct"} | null | null | null | {"edges": [[0, 1], [0, 2], [0, 3], [0, 4], [0, 5], [0, 6], [0, 7], [0, 8], [0, 9], [0, 10], [0, 11], [0, 12]], "coloring": [0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]} | 1 |
construct-mc-pysms-chromatic-girth-l1-s2 | construct | mc_pysms_chromatic_girth | graph_existence_chromatic_girth | graph_theory | competition | 1 | MathConstraint/pysms_chromatic_girth | CC-BY-4.0 | [
"np_search"
] | Construct a simple undirected graph on the 13 vertices 0..12 such that:
- the graph has at least 10 edges
- the chromatic number is at most 5: the vertices can be coloured with colours 0..4 so that adjacent vertices get different colours (you must also give such a colouring)
- the girth is at least 5: the graph h... | {"vertices": 13, "required_edges": [[0, 2], [0, 4]], "max_chromatic_number": 5, "min_edges": 10, "min_girth": 5, "family": "mc_pysms_chromatic_girth", "subset": "construct"} | null | null | null | {"edges": [[0, 1], [0, 2], [0, 3], [0, 4], [0, 5], [0, 6], [0, 7], [0, 8], [0, 9], [0, 10], [0, 11], [0, 12]], "coloring": [0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]} | 1 |
construct-mc-pysms-chromatic-girth-l1-s3 | construct | mc_pysms_chromatic_girth | graph_existence_chromatic_girth | graph_theory | competition | 1 | MathConstraint/pysms_chromatic_girth | CC-BY-4.0 | [
"np_search"
] | Construct a simple undirected graph on the 14 vertices 0..13 such that:
- the graph has at least 16 edges
- the chromatic number is at most 4: the vertices can be coloured with colours 0..3 so that adjacent vertices get different colours (you must also give such a colouring)
- the girth is at least 4: the graph h... | {"vertices": 14, "required_edges": [], "max_chromatic_number": 4, "min_edges": 16, "min_girth": 4, "family": "mc_pysms_chromatic_girth", "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]], "coloring": [0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]} | 1 |
construct-mc-pysms-chromatic-girth-l2-s0 | construct | mc_pysms_chromatic_girth | graph_existence_chromatic_girth | graph_theory | competition | 2 | MathConstraint/pysms_chromatic_girth | CC-BY-4.0 | [
"np_search"
] | Construct a simple undirected graph on the 15 vertices 0..14 such that:
- the graph has at least 10 edges
- the chromatic number is at most 5: the vertices can be coloured with colours 0..4 so that adjacent vertices get different colours (you must also give such a colouring)
- the girth is at least 7: the graph h... | {"vertices": 15, "required_edges": [], "max_chromatic_number": 5, "min_edges": 10, "min_girth": 7, "family": "mc_pysms_chromatic_girth", "subset": "construct"} | null | null | null | {"edges": [[0, 1], [0, 2], [0, 3], [0, 4], [0, 5], [0, 6], [0, 7], [0, 8], [0, 9], [0, 10], [0, 11], [0, 12], [0, 13], [0, 14]], "coloring": [0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]} | 1 |
construct-mc-pysms-chromatic-girth-l2-s1 | construct | mc_pysms_chromatic_girth | graph_existence_chromatic_girth | graph_theory | competition | 2 | MathConstraint/pysms_chromatic_girth | CC-BY-4.0 | [
"np_search"
] | Construct a simple undirected graph on the 15 vertices 0..14 such that:
- the graph has at least 19 edges
- the chromatic number is at most 2: the vertices can be coloured with colours 0..1 so that adjacent vertices get different colours (you must also give such a colouring)
- the girth is at least 4: the graph h... | {"vertices": 15, "required_edges": [], "max_chromatic_number": 2, "min_edges": 19, "min_girth": 4, "family": "mc_pysms_chromatic_girth", "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], [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]], "coloring": [0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]} | 1 |
construct-mc-pysms-chromatic-girth-l2-s2 | construct | mc_pysms_chromatic_girth | graph_existence_chromatic_girth | graph_theory | competition | 2 | MathConstraint/pysms_chromatic_girth | CC-BY-4.0 | [
"np_search"
] | Construct a simple undirected graph on the 15 vertices 0..14 such that:
- the graph has at least 16 edges
- the chromatic number is at most 2: the vertices can be coloured with colours 0..1 so that adjacent vertices get different colours (you must also give such a colouring)
- the girth is at least 6: the graph h... | {"vertices": 15, "required_edges": [], "max_chromatic_number": 2, "min_edges": 16, "min_girth": 6, "family": "mc_pysms_chromatic_girth", "subset": "construct"} | null | null | null | {"edges": [[0, 13], [0, 14], [1, 11], [1, 12], [2, 10], [2, 12], [2, 14], [3, 9], [3, 12], [3, 13], [4, 9], [4, 10], [4, 11], [5, 8], [5, 11], [5, 14], [6, 8], [6, 10], [6, 13], [7, 8], [7, 9]], "coloring": [0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1]} | 1 |
construct-mc-pysms-chromatic-girth-l2-s3 | construct | mc_pysms_chromatic_girth | graph_existence_chromatic_girth | graph_theory | competition | 2 | MathConstraint/pysms_chromatic_girth | CC-BY-4.0 | [
"np_search"
] | Construct a simple undirected graph on the 14 vertices 0..13 such that:
- the graph has at least 16 edges
- the chromatic number is at most 5: the vertices can be coloured with colours 0..4 so that adjacent vertices get different colours (you must also give such a colouring)
- the girth is at least 5: the graph h... | {"vertices": 14, "required_edges": [], "max_chromatic_number": 5, "min_edges": 16, "min_girth": 5, "family": "mc_pysms_chromatic_girth", "subset": "construct"} | null | null | null | {"edges": [[0, 11], [0, 12], [0, 13], [1, 9], [1, 10], [1, 13], [2, 8], [2, 10], [2, 12], [3, 6], [3, 7], [3, 13], [4, 5], [4, 7], [4, 12], [5, 6], [5, 11], [6, 8], [7, 10], [8, 9], [9, 11]], "coloring": [0, 0, 0, 0, 0, 1, 2, 1, 1, 2, 2, 3, 1, 1]} | 1 |
construct-mc-pysms-chromatic-girth-l3-s0 | construct | mc_pysms_chromatic_girth | graph_existence_chromatic_girth | graph_theory | competition | 3 | MathConstraint/pysms_chromatic_girth | CC-BY-4.0 | [
"np_search"
] | Construct a simple undirected graph on the 23 vertices 0..22 such that:
- the graph has at least 44 edges
- the chromatic number is at most 3: the vertices can be coloured with colours 0..2 so that adjacent vertices get different colours (you must also give such a colouring)
- the girth is at least 5: the graph h... | {"vertices": 23, "required_edges": [], "max_chromatic_number": 3, "min_edges": 44, "min_girth": 5, "family": "mc_pysms_chromatic_girth", "subset": "construct"} | null | null | null | {"edges": [[0, 20], [0, 21], [0, 22], [1, 17], [1, 18], [1, 19], [2, 15], [2, 16], [2, 19], [2, 22], [3, 13], [3, 14], [3, 19], [3, 21], [4, 11], [4, 12], [4, 18], [4, 20], [5, 10], [5, 12], [5, 16], [5, 21], [6, 9], [6, 12], [6, 14], [6, 15], [7, 8], [7, 11], [7, 13], [7, 15], [8, 10], [8, 14], [8, 22], [9, 10], [9, 1... | 1 |
construct-mc-pysms-chromatic-girth-l3-s1 | construct | mc_pysms_chromatic_girth | graph_existence_chromatic_girth | graph_theory | competition | 3 | MathConstraint/pysms_chromatic_girth | CC-BY-4.0 | [
"np_search"
] | Construct a simple undirected graph on the 22 vertices 0..21 such that:
- the graph has at least 17 edges
- the chromatic number is at most 4: the vertices can be coloured with colours 0..3 so that adjacent vertices get different colours (you must also give such a colouring)
- the girth is at least 7: the graph h... | {"vertices": 22, "required_edges": [], "max_chromatic_number": 4, "min_edges": 17, "min_girth": 7, "family": "mc_pysms_chromatic_girth", "subset": "construct"} | null | null | null | {"edges": [[0, 1], [0, 2], [0, 3], [0, 4], [0, 5], [0, 6], [0, 7], [0, 8], [0, 9], [0, 10], [0, 11], [0, 12], [0, 13], [0, 14], [0, 15], [0, 16], [0, 17], [0, 18], [0, 19], [0, 20], [0, 21]], "coloring": [0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]} | 1 |
construct-mc-pysms-chromatic-girth-l3-s2 | construct | mc_pysms_chromatic_girth | graph_existence_chromatic_girth | graph_theory | competition | 3 | MathConstraint/pysms_chromatic_girth | CC-BY-4.0 | [
"np_search"
] | Construct a simple undirected graph on the 14 vertices 0..13 such that:
- the graph has at least 20 edges
- the chromatic number is at most 3: the vertices can be coloured with colours 0..2 so that adjacent vertices get different colours (you must also give such a colouring)
- the girth is at least 6: the graph h... | {"vertices": 14, "required_edges": [], "max_chromatic_number": 3, "min_edges": 20, "min_girth": 6, "family": "mc_pysms_chromatic_girth", "subset": "construct"} | null | null | null | {"edges": [[0, 11], [0, 12], [0, 13], [1, 9], [1, 10], [1, 13], [2, 8], [2, 10], [2, 12], [3, 8], [3, 9], [3, 11], [4, 7], [4, 10], [4, 11], [5, 7], [5, 9], [5, 12], [6, 7], [6, 8], [6, 13]], "coloring": [0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1]} | 1 |
construct-mc-pysms-chromatic-girth-l3-s3 | construct | mc_pysms_chromatic_girth | graph_existence_chromatic_girth | graph_theory | competition | 3 | MathConstraint/pysms_chromatic_girth | CC-BY-4.0 | [
"np_search"
] | Construct a simple undirected graph on the 19 vertices 0..18 such that:
- the graph has at least 25 edges
- the chromatic number is at most 5: the vertices can be coloured with colours 0..4 so that adjacent vertices get different colours (you must also give such a colouring)
- the girth is at least 5: the graph h... | {"vertices": 19, "required_edges": [], "max_chromatic_number": 5, "min_edges": 25, "min_girth": 5, "family": "mc_pysms_chromatic_girth", "subset": "construct"} | null | null | null | {"edges": [[0, 18], [1, 18], [2, 16], [2, 17], [3, 14], [3, 15], [3, 18], [4, 12], [4, 13], [4, 17], [5, 10], [5, 11], [5, 16], [6, 9], [6, 11], [6, 13], [7, 8], [7, 11], [7, 12], [8, 10], [8, 13], [9, 10], [9, 12], [11, 15], [13, 14], [14, 16], [15, 17]], "coloring": [0, 0, 1, 0, 1, 1, 1, 1, 2, 0, 3, 0, 2, 0, 1, 1, 0,... | 1 |
construct-mc-pysms-chromatic-girth-l4-s0 | construct | mc_pysms_chromatic_girth | graph_existence_chromatic_girth | graph_theory | competition | 4 | MathConstraint/pysms_chromatic_girth | CC-BY-4.0 | [
"np_search"
] | Construct a simple undirected graph on the 23 vertices 0..22 such that:
- the graph has at least 26 edges
- the chromatic number is at most 4: the vertices can be coloured with colours 0..3 so that adjacent vertices get different colours (you must also give such a colouring)
- the girth is at least 6: the graph h... | {"vertices": 23, "required_edges": [], "max_chromatic_number": 4, "min_edges": 26, "min_girth": 6, "family": "mc_pysms_chromatic_girth", "subset": "construct"} | null | null | null | {"edges": [[0, 8], [0, 9], [0, 10], [0, 11], [0, 12], [0, 13], [0, 14], [0, 15], [0, 16], [0, 17], [0, 18], [0, 19], [0, 20], [0, 21], [0, 22], [1, 7], [1, 22], [2, 21], [3, 7], [3, 21], [4, 7], [4, 20], [5, 7], [5, 19], [6, 7], [6, 18]], "coloring": [0, 1, 0, 2, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 1, 2]... | 1 |
construct-mc-pysms-chromatic-girth-l4-s1 | construct | mc_pysms_chromatic_girth | graph_existence_chromatic_girth | graph_theory | competition | 4 | MathConstraint/pysms_chromatic_girth | CC-BY-4.0 | [
"np_search"
] | Construct a simple undirected graph on the 24 vertices 0..23 such that:
- the graph has at least 29 edges
- the chromatic number is at most 3: the vertices can be coloured with colours 0..2 so that adjacent vertices get different colours (you must also give such a colouring)
- the girth is at least 7: the graph h... | {"vertices": 24, "required_edges": [], "max_chromatic_number": 3, "min_edges": 29, "min_girth": 7, "family": "mc_pysms_chromatic_girth", "subset": "construct"} | null | null | null | {"edges": [[0, 22], [0, 23], [1, 20], [1, 21], [2, 18], [2, 19], [3, 16], [3, 17], [4, 14], [4, 15], [4, 23], [5, 13], [5, 15], [5, 21], [6, 12], [6, 14], [6, 20], [7, 11], [7, 13], [7, 19], [8, 10], [8, 12], [8, 18], [9, 10], [9, 11], [9, 23], [10, 21], [11, 17], [12, 22], [13, 22], [14, 19], [15, 16], [16, 18], [17, ... | 1 |
construct-mc-pysms-chromatic-girth-l4-s2 | construct | mc_pysms_chromatic_girth | graph_existence_chromatic_girth | graph_theory | competition | 4 | MathConstraint/pysms_chromatic_girth | CC-BY-4.0 | [
"np_search"
] | Construct a simple undirected graph on the 21 vertices 0..20 such that:
- the graph has at least 21 edges
- the chromatic number is at most 3: the vertices can be coloured with colours 0..2 so that adjacent vertices get different colours (you must also give such a colouring)
- the girth is at least 7: the graph h... | {"vertices": 21, "required_edges": [], "max_chromatic_number": 3, "min_edges": 21, "min_girth": 7, "family": "mc_pysms_chromatic_girth", "subset": "construct"} | null | null | null | {"edges": [[0, 5], [0, 6], [0, 7], [0, 8], [0, 9], [0, 10], [0, 11], [0, 12], [0, 13], [0, 14], [0, 15], [0, 16], [0, 17], [0, 18], [0, 19], [0, 20], [1, 3], [1, 4], [2, 4], [2, 20], [3, 19]], "coloring": [0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1]} | 1 |
construct-mc-pysms-chromatic-girth-l4-s3 | construct | mc_pysms_chromatic_girth | graph_existence_chromatic_girth | graph_theory | competition | 4 | MathConstraint/pysms_chromatic_girth | CC-BY-4.0 | [
"np_search"
] | Construct a simple undirected graph on the 20 vertices 0..19 such that:
- the graph has at least 21 edges
- the chromatic number is at most 3: the vertices can be coloured with colours 0..2 so that adjacent vertices get different colours (you must also give such a colouring)
- the girth is at least 7: the graph h... | {"vertices": 20, "required_edges": [], "max_chromatic_number": 3, "min_edges": 21, "min_girth": 7, "family": "mc_pysms_chromatic_girth", "subset": "construct"} | null | null | null | {"edges": [[0, 7], [0, 8], [0, 9], [0, 10], [0, 11], [0, 12], [0, 13], [0, 14], [0, 15], [0, 16], [0, 17], [0, 18], [0, 19], [1, 6], [1, 19], [2, 5], [2, 18], [3, 4], [3, 17], [4, 5], [4, 6]], "coloring": [0, 0, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1]} | 1 |
construct-mc-pysms-chromatic-girth-l5-s0 | construct | mc_pysms_chromatic_girth | graph_existence_chromatic_girth | graph_theory | competition | 5 | MathConstraint/pysms_chromatic_girth | CC-BY-4.0 | [
"np_search"
] | Construct a simple undirected graph on the 24 vertices 0..23 such that:
- the graph has at least 33 edges
- the chromatic number is at most 3: the vertices can be coloured with colours 0..2 so that adjacent vertices get different colours (you must also give such a colouring)
- the girth is at least 7: the graph h... | {"vertices": 24, "required_edges": [], "max_chromatic_number": 3, "min_edges": 33, "min_girth": 7, "family": "mc_pysms_chromatic_girth", "subset": "construct"} | null | null | null | {"edges": [[0, 22], [0, 23], [1, 21], [1, 23], [2, 20], [2, 23], [3, 19], [3, 22], [4, 18], [4, 19], [4, 21], [5, 17], [5, 18], [6, 15], [6, 16], [7, 13], [7, 14], [8, 12], [8, 14], [8, 16], [9, 11], [9, 13], [9, 15], [10, 11], [10, 12], [10, 21], [11, 22], [12, 17], [13, 20], [14, 19], [15, 18], [16, 23], [17, 20]], "... | 1 |
construct-mc-pysms-chromatic-girth-l5-s1 | construct | mc_pysms_chromatic_girth | graph_existence_chromatic_girth | graph_theory | competition | 5 | MathConstraint/pysms_chromatic_girth | CC-BY-4.0 | [
"np_search"
] | Construct a simple undirected graph on the 30 vertices 0..29 such that:
- the graph has at least 33 edges
- the chromatic number is at most 3: the vertices can be coloured with colours 0..2 so that adjacent vertices get different colours (you must also give such a colouring)
- the girth is at least 7: the graph h... | {"vertices": 30, "required_edges": [], "max_chromatic_number": 3, "min_edges": 33, "min_girth": 7, "family": "mc_pysms_chromatic_girth", "subset": "construct"} | null | null | null | {"edges": [[0, 12], [0, 13], [0, 14], [0, 15], [0, 16], [0, 17], [0, 18], [0, 19], [0, 20], [0, 21], [0, 22], [0, 23], [0, 24], [0, 25], [0, 26], [0, 27], [0, 28], [0, 29], [1, 11], [1, 29], [2, 8], [2, 9], [2, 10], [2, 28], [3, 6], [3, 7], [3, 27], [4, 5], [4, 7], [5, 26], [6, 10], [7, 11], [9, 11]], "coloring": [0, 1... | 1 |
construct-mc-pysms-chromatic-girth-l5-s2 | construct | mc_pysms_chromatic_girth | graph_existence_chromatic_girth | graph_theory | competition | 5 | MathConstraint/pysms_chromatic_girth | CC-BY-4.0 | [
"np_search"
] | Construct a simple undirected graph on the 24 vertices 0..23 such that:
- the graph has at least 33 edges
- the chromatic number is at most 5: the vertices can be coloured with colours 0..4 so that adjacent vertices get different colours (you must also give such a colouring)
- the girth is at least 7: the graph h... | {"vertices": 24, "required_edges": [], "max_chromatic_number": 5, "min_edges": 33, "min_girth": 7, "family": "mc_pysms_chromatic_girth", "subset": "construct"} | null | null | null | {"edges": [[0, 21], [0, 22], [0, 23], [1, 19], [1, 20], [1, 23], [2, 17], [2, 18], [2, 23], [3, 15], [3, 16], [3, 22], [4, 14], [4, 16], [4, 20], [5, 13], [5, 16], [5, 18], [6, 12], [6, 15], [6, 19], [7, 11], [7, 14], [7, 17], [8, 10], [8, 12], [8, 18], [9, 10], [9, 11], [9, 22], [10, 20], [11, 13], [12, 21], [13, 19],... | 1 |
construct-mc-pysms-chromatic-girth-l5-s3 | construct | mc_pysms_chromatic_girth | graph_existence_chromatic_girth | graph_theory | competition | 5 | MathConstraint/pysms_chromatic_girth | CC-BY-4.0 | [
"np_search"
] | Construct a simple undirected graph on the 22 vertices 0..21 such that:
- the graph has at least 27 edges
- the chromatic number is at most 3: the vertices can be coloured with colours 0..2 so that adjacent vertices get different colours (you must also give such a colouring)
- the girth is at least 7: the graph h... | {"vertices": 22, "required_edges": [], "max_chromatic_number": 3, "min_edges": 27, "min_girth": 7, "family": "mc_pysms_chromatic_girth", "subset": "construct"} | null | null | null | {"edges": [[0, 20], [0, 21], [1, 19], [1, 21], [2, 18], [2, 21], [3, 16], [3, 17], [4, 15], [4, 17], [4, 21], [5, 14], [5, 16], [5, 20], [6, 13], [6, 16], [6, 19], [7, 12], [7, 15], [8, 11], [8, 14], [9, 10], [9, 13], [9, 18], [10, 11], [10, 17], [12, 13], [14, 15]], "coloring": [1, 1, 1, 2, 1, 0, 0, 1, 0, 0, 1, 2, 0, ... | 1 |
construct-mc-pysms-chromatic-girth-l6-s0 | construct | mc_pysms_chromatic_girth | graph_existence_chromatic_girth | graph_theory | competition | 6 | MathConstraint/pysms_chromatic_girth | CC-BY-4.0 | [
"np_search"
] | Construct a simple undirected graph on the 21 vertices 0..20 such that:
- the graph has at least 27 edges
- the chromatic number is at most 4: the vertices can be coloured with colours 0..3 so that adjacent vertices get different colours (you must also give such a colouring)
- the girth is at least 8: the graph h... | {"vertices": 21, "required_edges": [], "max_chromatic_number": 4, "min_edges": 27, "min_girth": 8, "family": "mc_pysms_chromatic_girth", "subset": "construct"} | null | null | null | {"edges": [[0, 19], [0, 20], [1, 18], [1, 20], [2, 17], [2, 19], [3, 16], [3, 18], [4, 15], [4, 17], [5, 14], [5, 17], [5, 18], [6, 13], [6, 16], [7, 13], [7, 15], [7, 20], [8, 13], [8, 14], [9, 12], [9, 16], [9, 19], [10, 12], [10, 15], [11, 12], [11, 14]], "coloring": [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, ... | 1 |
construct-mc-pysms-chromatic-girth-l6-s1 | construct | mc_pysms_chromatic_girth | graph_existence_chromatic_girth | graph_theory | competition | 6 | MathConstraint/pysms_chromatic_girth | CC-BY-4.0 | [
"np_search"
] | Construct a simple undirected graph on the 24 vertices 0..23 such that:
- the graph has at least 34 edges
- the chromatic number is at most 4: the vertices can be coloured with colours 0..3 so that adjacent vertices get different colours (you must also give such a colouring)
- the girth is at least 7: the graph h... | {"vertices": 24, "required_edges": [], "max_chromatic_number": 4, "min_edges": 34, "min_girth": 7, "family": "mc_pysms_chromatic_girth", "subset": "construct"} | null | null | null | {"edges": [[0, 21], [0, 22], [0, 23], [1, 19], [1, 20], [1, 23], [2, 17], [2, 18], [2, 23], [3, 15], [3, 16], [3, 22], [4, 14], [4, 16], [4, 20], [5, 13], [5, 16], [5, 18], [6, 12], [6, 15], [6, 19], [7, 11], [7, 14], [7, 17], [8, 10], [8, 12], [8, 18], [9, 10], [9, 11], [9, 22], [10, 20], [11, 13], [12, 21], [13, 19],... | 1 |
construct-mc-pysms-chromatic-girth-l6-s2 | construct | mc_pysms_chromatic_girth | graph_existence_chromatic_girth | graph_theory | competition | 6 | MathConstraint/pysms_chromatic_girth | CC-BY-4.0 | [
"np_search"
] | Construct a simple undirected graph on the 25 vertices 0..24 such that:
- the graph has at least 34 edges
- the chromatic number is at most 5: the vertices can be coloured with colours 0..4 so that adjacent vertices get different colours (you must also give such a colouring)
- the girth is at least 7: the graph h... | {"vertices": 25, "required_edges": [], "max_chromatic_number": 5, "min_edges": 34, "min_girth": 7, "family": "mc_pysms_chromatic_girth", "subset": "construct"} | null | null | null | {"edges": [[0, 23], [0, 24], [1, 21], [1, 22], [2, 19], [2, 20], [3, 17], [3, 18], [4, 15], [4, 16], [5, 13], [5, 14], [5, 24], [6, 12], [6, 14], [6, 22], [7, 11], [7, 13], [7, 20], [8, 10], [8, 12], [8, 18], [9, 10], [9, 11], [9, 16], [10, 21], [11, 17], [12, 23], [13, 15], [14, 19], [15, 18], [16, 19], [17, 22], [20,... | 1 |
construct-mc-pysms-chromatic-girth-l6-s3 | construct | mc_pysms_chromatic_girth | graph_existence_chromatic_girth | graph_theory | competition | 6 | MathConstraint/pysms_chromatic_girth | CC-BY-4.0 | [
"np_search"
] | Construct a simple undirected graph on the 25 vertices 0..24 such that:
- the graph has at least 31 edges
- the chromatic number is at most 4: the vertices can be coloured with colours 0..3 so that adjacent vertices get different colours (you must also give such a colouring)
- the girth is at least 7: the graph h... | {"vertices": 25, "required_edges": [], "max_chromatic_number": 4, "min_edges": 31, "min_girth": 7, "family": "mc_pysms_chromatic_girth", "subset": "construct"} | null | null | null | {"edges": [[0, 24], [1, 22], [1, 23], [2, 20], [2, 21], [3, 18], [3, 19], [4, 16], [4, 17], [4, 24], [5, 15], [5, 17], [5, 23], [6, 14], [6, 17], [6, 21], [7, 13], [7, 16], [7, 22], [8, 12], [8, 14], [8, 19], [9, 11], [9, 13], [9, 21], [10, 11], [10, 12], [10, 23], [11, 18], [12, 20], [13, 15], [14, 22], [15, 19], [16,... | 1 |
construct-mc-pysms-chromatic-girth-l6-s4 | construct | mc_pysms_chromatic_girth | graph_existence_chromatic_girth | graph_theory | competition | 6 | MathConstraint/pysms_chromatic_girth | CC-BY-4.0 | [
"np_search"
] | Construct a simple undirected graph on the 30 vertices 0..29 such that:
- the graph has at least 42 edges
- the chromatic number is at most 5: the vertices can be coloured with colours 0..4 so that adjacent vertices get different colours (you must also give such a colouring)
- the girth is at least 7: the graph h... | {"vertices": 30, "required_edges": [], "max_chromatic_number": 5, "min_edges": 42, "min_girth": 7, "family": "mc_pysms_chromatic_girth", "subset": "construct"} | null | null | null | {"edges": [[0, 28], [0, 29], [1, 27], [1, 29], [2, 26], [2, 28], [3, 26], [3, 27], [4, 24], [4, 25], [5, 23], [5, 25], [6, 22], [6, 24], [6, 29], [7, 21], [7, 24], [7, 26], [8, 20], [8, 23], [8, 29], [9, 19], [9, 22], [10, 18], [10, 20], [11, 17], [11, 19], [12, 17], [12, 18], [12, 24], [13, 16], [13, 18], [13, 28], [1... | 1 |
construct-mc-pysms-clique-coloring-l1-s0 | construct | mc_pysms_clique_coloring | graph_existence_clique_coloring | graph_theory | competition | 1 | MathConstraint/pysms_clique_coloring | CC-BY-4.0 | [
"np_search"
] | Construct a simple undirected graph on the 8 vertices 0..7 such that:
- every vertex has degree at least 1
- the graph contains no clique of size 5 (maximum clique size at most 4)
- the chromatic number is at most 2: the vertices can be coloured with colours 0..1 so that adjacent vertices get different colours (y... | {"vertices": 8, "required_edges": [[2, 7], [0, 5]], "max_chromatic_number": 2, "max_clique": 4, "min_degree": 1, "family": "mc_pysms_clique_coloring", "subset": "construct"} | null | null | null | {"edges": [[0, 5], [0, 6], [0, 7], [1, 4], [1, 6], [1, 7], [2, 4], [2, 5], [2, 6], [2, 7], [3, 4], [3, 5], [3, 6], [3, 7]], "coloring": [0, 0, 0, 0, 1, 1, 1, 1]} | 1 |
construct-mc-pysms-clique-coloring-l1-s1 | construct | mc_pysms_clique_coloring | graph_existence_clique_coloring | graph_theory | competition | 1 | MathConstraint/pysms_clique_coloring | CC-BY-4.0 | [
"np_search"
] | Construct a simple undirected graph on the 11 vertices 0..10 such that:
- every vertex has degree at least 4
- the graph contains no clique of size 6 (maximum clique size at most 5)
- the chromatic number is at most 4: the vertices can be coloured with colours 0..3 so that adjacent vertices get different colours ... | {"vertices": 11, "required_edges": [], "max_chromatic_number": 4, "max_clique": 5, "min_degree": 4, "family": "mc_pysms_clique_coloring", "subset": "construct"} | null | null | null | {"edges": [[0, 5], [0, 6], [0, 7], [0, 8], [0, 9], [0, 10], [1, 3], [1, 4], [1, 6], [1, 7], [1, 8], [1, 9], [1, 10], [2, 3], [2, 4], [2, 6], [2, 7], [2, 8], [2, 9], [2, 10], [3, 6], [3, 7], [3, 8], [3, 9], [3, 10], [4, 5], [4, 6], [4, 7], [4, 8], [4, 9], [4, 10], [5, 6], [5, 7], [5, 8], [5, 9], [5, 10], [7, 9], [7, 10]... | 1 |
construct-mc-pysms-clique-coloring-l1-s2 | construct | mc_pysms_clique_coloring | graph_existence_clique_coloring | graph_theory | competition | 1 | MathConstraint/pysms_clique_coloring | CC-BY-4.0 | [
"np_search"
] | Construct a simple undirected graph on the 11 vertices 0..10 such that:
- every vertex has degree at least 3
- the graph contains no clique of size 5 (maximum clique size at most 4)
- the chromatic number is at most 2: the vertices can be coloured with colours 0..1 so that adjacent vertices get different colours ... | {"vertices": 11, "required_edges": [[1, 10], [0, 4], [0, 8], [2, 9]], "max_chromatic_number": 2, "max_clique": 4, "min_degree": 3, "family": "mc_pysms_clique_coloring", "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]], "coloring": [0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1]} | 1 |
construct-mc-pysms-clique-coloring-l2-s0 | construct | mc_pysms_clique_coloring | graph_existence_clique_coloring | graph_theory | competition | 2 | MathConstraint/pysms_clique_coloring | CC-BY-4.0 | [
"np_search"
] | Construct a simple undirected graph on the 12 vertices 0..11 such that:
- every vertex has degree at least 3
- the graph contains no clique of size 6 (maximum clique size at most 5)
- the chromatic number is at most 3: the vertices can be coloured with colours 0..2 so that adjacent vertices get different colours ... | {"vertices": 12, "required_edges": [[1, 2], [0, 2], [1, 4], [2, 9], [2, 7]], "max_chromatic_number": 3, "max_clique": 5, "min_degree": 3, "family": "mc_pysms_clique_coloring", "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], [1, 2], [1, 3], [1, 4], [1, 5], [1, 6], [1, 7], [1, 8], [1, 9], [1, 10], [1, 11], [2, 3], [2, 4], [2, 5], [2, 6], [2, 7], [2, 8], [2, 9], [2, 10], [2, 11]], "coloring": [1, 1, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2]} | 1 |
construct-mc-pysms-clique-coloring-l2-s1 | construct | mc_pysms_clique_coloring | graph_existence_clique_coloring | graph_theory | competition | 2 | MathConstraint/pysms_clique_coloring | CC-BY-4.0 | [
"np_search"
] | Construct a simple undirected graph on the 13 vertices 0..12 such that:
- every vertex has degree at least 4
- the graph contains no clique of size 6 (maximum clique size at most 5)
- the chromatic number is at most 5: the vertices can be coloured with colours 0..4 so that adjacent vertices get different colours ... | {"vertices": 13, "required_edges": [[1, 3], [2, 7], [3, 11], [3, 10], [0, 12], [2, 10], [2, 4], [1, 11]], "max_chromatic_number": 5, "max_clique": 5, "min_degree": 4, "family": "mc_pysms_clique_coloring", "subset": "construct"} | null | null | null | {"edges": [[0, 1], [0, 2], [0, 3], [0, 4], [0, 5], [0, 6], [0, 7], [0, 8], [0, 9], [0, 10], [0, 11], [0, 12], [1, 2], [1, 3], [1, 4], [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, ... | 1 |
construct-mc-pysms-clique-coloring-l2-s2 | construct | mc_pysms_clique_coloring | graph_existence_clique_coloring | graph_theory | competition | 2 | MathConstraint/pysms_clique_coloring | CC-BY-4.0 | [
"np_search"
] | Construct a simple undirected graph on the 12 vertices 0..11 such that:
- every vertex has degree at least 4
- the graph contains no clique of size 3 (maximum clique size at most 2)
- the chromatic number is at most 2: the vertices can be coloured with colours 0..1 so that adjacent vertices get different colours ... | {"vertices": 12, "required_edges": [[2, 8], [1, 9], [0, 6], [3, 10], [0, 9], [3, 9]], "max_chromatic_number": 2, "max_clique": 2, "min_degree": 4, "family": "mc_pysms_clique_coloring", "subset": "construct"} | null | null | null | {"edges": [[0, 4], [0, 5], [0, 6], [0, 7], [0, 8], [0, 9], [0, 10], [0, 11], [1, 4], [1, 5], [1, 6], [1, 7], [1, 8], [1, 9], [1, 10], [1, 11], [2, 4], [2, 5], [2, 6], [2, 7], [2, 8], [2, 9], [2, 10], [2, 11], [3, 4], [3, 5], [3, 6], [3, 7], [3, 8], [3, 9], [3, 10], [3, 11]], "coloring": [0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1... | 1 |
construct-mc-pysms-clique-coloring-l3-s0 | construct | mc_pysms_clique_coloring | graph_existence_clique_coloring | graph_theory | competition | 3 | MathConstraint/pysms_clique_coloring | CC-BY-4.0 | [
"np_search"
] | Construct a simple undirected graph on the 14 vertices 0..13 such that:
- every vertex has degree at least 5
- the graph contains no clique of size 4 (maximum clique size at most 3)
- the chromatic number is at most 5: the vertices can be coloured with colours 0..4 so that adjacent vertices get different colours ... | {"vertices": 14, "required_edges": [], "max_chromatic_number": 5, "max_clique": 3, "min_degree": 5, "family": "mc_pysms_clique_coloring", "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, 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, 4], [3, 5], [3, 6], [3, 7], [3, 8], [3, 9], [3, 10], ... | 1 |
construct-mc-pysms-clique-coloring-l3-s1 | construct | mc_pysms_clique_coloring | graph_existence_clique_coloring | graph_theory | competition | 3 | MathConstraint/pysms_clique_coloring | CC-BY-4.0 | [
"np_search"
] | Construct a simple undirected graph on the 14 vertices 0..13 such that:
- every vertex has degree at least 1
- the graph contains no clique of size 5 (maximum clique size at most 4)
- the chromatic number is at most 5: the vertices can be coloured with colours 0..4 so that adjacent vertices get different colours ... | {"vertices": 14, "required_edges": [[1, 4], [1, 2], [1, 9], [0, 3]], "max_chromatic_number": 5, "max_clique": 4, "min_degree": 1, "family": "mc_pysms_clique_coloring", "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]], "coloring": [0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]} | 1 |
construct-mc-pysms-clique-coloring-l3-s2 | construct | mc_pysms_clique_coloring | graph_existence_clique_coloring | graph_theory | competition | 3 | MathConstraint/pysms_clique_coloring | CC-BY-4.0 | [
"np_search"
] | Construct a simple undirected graph on the 15 vertices 0..14 such that:
- every vertex has degree at least 3
- the graph contains no clique of size 3 (maximum clique size at most 2)
- the chromatic number is at most 5: the vertices can be coloured with colours 0..4 so that adjacent vertices get different colours ... | {"vertices": 15, "required_edges": [], "max_chromatic_number": 5, "max_clique": 2, "min_degree": 3, "family": "mc_pysms_clique_coloring", "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, 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]], "colo... | 1 |
construct-mc-pysms-clique-coloring-l4-s0 | construct | mc_pysms_clique_coloring | graph_existence_clique_coloring | graph_theory | competition | 4 | MathConstraint/pysms_clique_coloring | CC-BY-4.0 | [
"np_search"
] | Construct a simple undirected graph on the 16 vertices 0..15 such that:
- every vertex has degree at least 1
- the graph contains no clique of size 3 (maximum clique size at most 2)
- the chromatic number is at most 2: the vertices can be coloured with colours 0..1 so that adjacent vertices get different colours ... | {"vertices": 16, "required_edges": [], "max_chromatic_number": 2, "max_clique": 2, "min_degree": 1, "family": "mc_pysms_clique_coloring", "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], [0, 14], [0, 15], [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], [1, 15]], "coloring": [0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]} | 1 |
construct-mc-pysms-clique-coloring-l4-s1 | construct | mc_pysms_clique_coloring | graph_existence_clique_coloring | graph_theory | competition | 4 | MathConstraint/pysms_clique_coloring | CC-BY-4.0 | [
"np_search"
] | Construct a simple undirected graph on the 15 vertices 0..14 such that:
- every vertex has degree at least 5
- the graph contains no clique of size 5 (maximum clique size at most 4)
- the chromatic number is at most 4: the vertices can be coloured with colours 0..3 so that adjacent vertices get different colours ... | {"vertices": 15, "required_edges": [], "max_chromatic_number": 4, "max_clique": 4, "min_degree": 5, "family": "mc_pysms_clique_coloring", "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, 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], [3, 4]... | 1 |
construct-mc-pysms-clique-coloring-l4-s2 | construct | mc_pysms_clique_coloring | graph_existence_clique_coloring | graph_theory | competition | 4 | MathConstraint/pysms_clique_coloring | CC-BY-4.0 | [
"np_search"
] | Construct a simple undirected graph on the 15 vertices 0..14 such that:
- every vertex has degree at least 1
- the graph contains no clique of size 3 (maximum clique size at most 2)
- the chromatic number is at most 4: the vertices can be coloured with colours 0..3 so that adjacent vertices get different colours ... | {"vertices": 15, "required_edges": [[1, 8], [1, 9], [0, 10], [0, 6], [0, 5]], "max_chromatic_number": 4, "max_clique": 2, "min_degree": 1, "family": "mc_pysms_clique_coloring", "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], [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]], "coloring": [0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]} | 1 |
construct-mc-pysms-clique-coloring-l5-s0 | construct | mc_pysms_clique_coloring | graph_existence_clique_coloring | graph_theory | competition | 5 | MathConstraint/pysms_clique_coloring | CC-BY-4.0 | [
"np_search"
] | Construct a simple undirected graph on the 12 vertices 0..11 such that:
- every vertex has degree at least 4
- the graph contains no clique of size 5 (maximum clique size at most 4)
- the chromatic number is at most 5: the vertices can be coloured with colours 0..4 so that adjacent vertices get different colours ... | {"vertices": 12, "required_edges": [[0, 10], [0, 11], [0, 7], [3, 10], [2, 9], [1, 9], [3, 6]], "max_chromatic_number": 5, "max_clique": 4, "min_degree": 4, "family": "mc_pysms_clique_coloring", "subset": "construct"} | null | null | null | {"edges": [[0, 3], [0, 4], [0, 5], [0, 6], [0, 7], [0, 8], [0, 9], [0, 10], [0, 11], [1, 2], [1, 4], [1, 5], [1, 6], [1, 7], [1, 8], [1, 9], [1, 10], [1, 11], [2, 3], [2, 4], [2, 5], [2, 6], [2, 7], [2, 8], [2, 9], [2, 10], [2, 11], [3, 4], [3, 5], [3, 6], [3, 7], [3, 8], [3, 9], [3, 10], [3, 11]], "coloring": [0, 1, 0... | 1 |
construct-mc-pysms-clique-coloring-l5-s1 | construct | mc_pysms_clique_coloring | graph_existence_clique_coloring | graph_theory | competition | 5 | MathConstraint/pysms_clique_coloring | CC-BY-4.0 | [
"np_search"
] | Construct a simple undirected graph on the 19 vertices 0..18 such that:
- every vertex has degree at least 5
- the graph contains no clique of size 6 (maximum clique size at most 5)
- the chromatic number is at most 5: the vertices can be coloured with colours 0..4 so that adjacent vertices get different colours ... | {"vertices": 19, "required_edges": [], "max_chromatic_number": 5, "max_clique": 5, "min_degree": 5, "family": "mc_pysms_clique_coloring", "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], [0, 14], [0, 15], [0, 16], [0, 17], [0, 18], [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], [1, 15], [1, 16], [1, 17], [1, 18], [2, 3], [2, 4], [2,... | 1 |
construct-mc-pysms-clique-coloring-l5-s2 | construct | mc_pysms_clique_coloring | graph_existence_clique_coloring | graph_theory | competition | 5 | MathConstraint/pysms_clique_coloring | CC-BY-4.0 | [
"np_search"
] | Construct a simple undirected graph on the 20 vertices 0..19 such that:
- every vertex has degree at least 5
- the graph contains no clique of size 4 (maximum clique size at most 3)
- the chromatic number is at most 3: the vertices can be coloured with colours 0..2 so that adjacent vertices get different colours ... | {"vertices": 20, "required_edges": [], "max_chromatic_number": 3, "max_clique": 3, "min_degree": 5, "family": "mc_pysms_clique_coloring", "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], [0, 14], [0, 15], [0, 16], [0, 17], [0, 18], [0, 19], [1, 4], [1, 5], [1, 6], [1, 7], [1, 8], [1, 9], [1, 10], [1, 11], [1, 12], [1, 13], [1, 14], [1, 15], [1, 16], [1, 17], [1, 18], [1, 19], [2, 4], [2, 5], [2, 6], [2, 7], [... | 1 |
construct-mc-pysms-clique-coloring-l5-s3 | construct | mc_pysms_clique_coloring | graph_existence_clique_coloring | graph_theory | competition | 5 | MathConstraint/pysms_clique_coloring | CC-BY-4.0 | [
"np_search"
] | Construct a simple undirected graph on the 16 vertices 0..15 such that:
- every vertex has degree at least 1
- the graph contains no clique of size 4 (maximum clique size at most 3)
- the chromatic number is at most 4: the vertices can be coloured with colours 0..3 so that adjacent vertices get different colours ... | {"vertices": 16, "required_edges": [[1, 7], [1, 10], [0, 8], [0, 3], [1, 14]], "max_chromatic_number": 4, "max_clique": 3, "min_degree": 1, "family": "mc_pysms_clique_coloring", "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], [0, 14], [0, 15], [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], [1, 15]], "coloring": [0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]} | 1 |
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