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-ae-p52-erdos-squarefree-l4-s4 | construct | ae_p52_erdos_squarefree | erdos_ab_plus_1_never_squarefree | number_theory | research | 4 | AlphaEvolve-Repository-of-Problems/52-erdos-squarefree | CC-BY-4.0 | [
"exact_integer"
] | Erdos squarefree problem.
Let N = 2532. Find a set A of distinct integers in {1, 2, ..., N} with 102 <= |A| <= 224 such that for ALL a, b in A
(including a = b) the number a*b + 1 is NOT squarefree, i.e. a*b + 1 is divisible by p^2 for some prime p.
Answer format: {"A": [a_1, a_2, ..., a_m]}
Write your final answer ... | {"N": 2532, "t": 102, "family": "ae_p52_erdos_squarefree", "subset": "construct"} | null | null | null | {"A": [7, 32, 57, 82, 107, 132, 157, 182, 207, 232, 257, 282, 307, 332, 357, 382, 407, 432, 457, 482, 507, 532, 557, 582, 607, 632, 657, 682, 707, 732, 757, 782, 807, 832, 857, 882, 907, 932, 957, 982, 1007, 1032, 1057, 1082, 1107, 1132, 1157, 1182, 1207, 1232, 1257, 1282, 1307, 1332, 1357, 1382, 1407, 1432, 1457, 1482... | 1 |
construct-ae-p52-erdos-squarefree-l4-s5 | construct | ae_p52_erdos_squarefree | erdos_ab_plus_1_never_squarefree | number_theory | research | 4 | AlphaEvolve-Repository-of-Problems/52-erdos-squarefree | CC-BY-4.0 | [
"exact_integer"
] | Erdos squarefree problem.
Let N = 1796. Find a set A of distinct integers in {1, 2, ..., N} with 72 <= |A| <= 164 such that for ALL a, b in A
(including a = b) the number a*b + 1 is NOT squarefree, i.e. a*b + 1 is divisible by p^2 for some prime p.
Answer format: {"A": [a_1, a_2, ..., a_m]}
Write your final answer a... | {"N": 1796, "t": 72, "family": "ae_p52_erdos_squarefree", "subset": "construct"} | null | null | null | {"A": [7, 32, 57, 82, 107, 132, 157, 182, 207, 232, 257, 282, 307, 332, 357, 382, 407, 432, 457, 482, 507, 532, 557, 582, 607, 632, 657, 682, 707, 732, 757, 782, 807, 832, 857, 882, 907, 932, 957, 982, 1007, 1032, 1057, 1082, 1107, 1132, 1157, 1182, 1207, 1232, 1257, 1282, 1307, 1332, 1357, 1382, 1407, 1432, 1457, 1482... | 1 |
construct-ae-p52-erdos-squarefree-l4-s6 | construct | ae_p52_erdos_squarefree | erdos_ab_plus_1_never_squarefree | number_theory | research | 4 | AlphaEvolve-Repository-of-Problems/52-erdos-squarefree | CC-BY-4.0 | [
"exact_integer"
] | Erdos squarefree problem.
Let N = 1555. Find a set A of distinct integers in {1, 2, ..., N} with 62 <= |A| <= 144 such that for ALL a, b in A
(including a = b) the number a*b + 1 is NOT squarefree, i.e. a*b + 1 is divisible by p^2 for some prime p.
Answer format: {"A": [a_1, a_2, ..., a_m]}
Write your final answer a... | {"N": 1555, "t": 62, "family": "ae_p52_erdos_squarefree", "subset": "construct"} | null | null | null | {"A": [7, 32, 57, 82, 107, 132, 157, 182, 207, 232, 257, 282, 307, 332, 357, 382, 407, 432, 457, 482, 507, 532, 557, 582, 607, 632, 657, 682, 707, 732, 757, 782, 807, 832, 857, 882, 907, 932, 957, 982, 1007, 1032, 1057, 1082, 1107, 1132, 1157, 1182, 1207, 1232, 1257, 1282, 1307, 1332, 1357, 1382, 1407, 1432, 1457, 1482... | 1 |
construct-ae-p52-erdos-squarefree-l4-s7 | construct | ae_p52_erdos_squarefree | erdos_ab_plus_1_never_squarefree | number_theory | research | 4 | AlphaEvolve-Repository-of-Problems/52-erdos-squarefree | CC-BY-4.0 | [
"exact_integer"
] | Erdos squarefree problem.
Let N = 2983. Find a set A of distinct integers in {1, 2, ..., N} with 120 <= |A| <= 260 such that for ALL a, b in A
(including a = b) the number a*b + 1 is NOT squarefree, i.e. a*b + 1 is divisible by p^2 for some prime p.
Answer format: {"A": [a_1, a_2, ..., a_m]}
Write your final answer ... | {"N": 2983, "t": 120, "family": "ae_p52_erdos_squarefree", "subset": "construct"} | null | null | null | {"A": [7, 32, 57, 82, 107, 132, 157, 182, 207, 232, 257, 282, 307, 332, 357, 382, 407, 432, 457, 482, 507, 532, 557, 582, 607, 632, 657, 682, 707, 732, 757, 782, 807, 832, 857, 882, 907, 932, 957, 982, 1007, 1032, 1057, 1082, 1107, 1132, 1157, 1182, 1207, 1232, 1257, 1282, 1307, 1332, 1357, 1382, 1407, 1432, 1457, 1482... | 1 |
construct-ae-p52-erdos-squarefree-l4-s8 | construct | ae_p52_erdos_squarefree | erdos_ab_plus_1_never_squarefree | number_theory | research | 4 | AlphaEvolve-Repository-of-Problems/52-erdos-squarefree | CC-BY-4.0 | [
"exact_integer"
] | Erdos squarefree problem.
Let N = 1764. Find a set A of distinct integers in {1, 2, ..., N} with 71 <= |A| <= 162 such that for ALL a, b in A
(including a = b) the number a*b + 1 is NOT squarefree, i.e. a*b + 1 is divisible by p^2 for some prime p.
Answer format: {"A": [a_1, a_2, ..., a_m]}
Write your final answer a... | {"N": 1764, "t": 71, "family": "ae_p52_erdos_squarefree", "subset": "construct"} | null | null | null | {"A": [7, 32, 57, 82, 107, 132, 157, 182, 207, 232, 257, 282, 307, 332, 357, 382, 407, 432, 457, 482, 507, 532, 557, 582, 607, 632, 657, 682, 707, 732, 757, 782, 807, 832, 857, 882, 907, 932, 957, 982, 1007, 1032, 1057, 1082, 1107, 1132, 1157, 1182, 1207, 1232, 1257, 1282, 1307, 1332, 1357, 1382, 1407, 1432, 1457, 1482... | 1 |
construct-ae-p52-erdos-squarefree-l4-s9 | construct | ae_p52_erdos_squarefree | erdos_ab_plus_1_never_squarefree | number_theory | research | 4 | AlphaEvolve-Repository-of-Problems/52-erdos-squarefree | CC-BY-4.0 | [
"exact_integer"
] | Erdos squarefree problem.
Let N = 3697. Find a set A of distinct integers in {1, 2, ..., N} with 148 <= |A| <= 316 such that for ALL a, b in A
(including a = b) the number a*b + 1 is NOT squarefree, i.e. a*b + 1 is divisible by p^2 for some prime p.
Answer format: {"A": [a_1, a_2, ..., a_m]}
Write your final answer ... | {"N": 3697, "t": 148, "family": "ae_p52_erdos_squarefree", "subset": "construct"} | null | null | null | {"A": [7, 32, 57, 82, 107, 132, 157, 182, 207, 232, 257, 282, 307, 332, 357, 382, 407, 432, 457, 482, 507, 532, 557, 582, 607, 632, 657, 682, 707, 732, 757, 782, 807, 832, 857, 882, 907, 932, 957, 982, 1007, 1032, 1057, 1082, 1107, 1132, 1157, 1182, 1207, 1232, 1257, 1282, 1307, 1332, 1357, 1382, 1407, 1432, 1457, 1482... | 1 |
construct-ae-p52-erdos-squarefree-l5-s0 | construct | ae_p52_erdos_squarefree | erdos_ab_plus_1_never_squarefree | number_theory | research | 5 | AlphaEvolve-Repository-of-Problems/52-erdos-squarefree | CC-BY-4.0 | [
"exact_integer"
] | Erdos squarefree problem.
Let N = 9076. Find a set A of distinct integers in {1, 2, ..., N} with 363 <= |A| <= 746 such that for ALL a, b in A
(including a = b) the number a*b + 1 is NOT squarefree, i.e. a*b + 1 is divisible by p^2 for some prime p.
Answer format: {"A": [a_1, a_2, ..., a_m]}
Write your final answer ... | {"N": 9076, "t": 363, "family": "ae_p52_erdos_squarefree", "subset": "construct"} | null | null | null | {"A": [7, 32, 57, 82, 107, 132, 157, 182, 207, 232, 257, 282, 307, 332, 357, 382, 407, 432, 457, 482, 507, 532, 557, 582, 607, 632, 657, 682, 707, 732, 757, 782, 807, 832, 857, 882, 907, 932, 957, 982, 1007, 1032, 1057, 1082, 1107, 1132, 1157, 1182, 1207, 1232, 1257, 1282, 1307, 1332, 1357, 1382, 1407, 1432, 1457, 1482... | 1 |
construct-ae-p52-erdos-squarefree-l5-s1 | construct | ae_p52_erdos_squarefree | erdos_ab_plus_1_never_squarefree | number_theory | research | 5 | AlphaEvolve-Repository-of-Problems/52-erdos-squarefree | CC-BY-4.0 | [
"exact_integer"
] | Erdos squarefree problem.
Let N = 8984. Find a set A of distinct integers in {1, 2, ..., N} with 360 <= |A| <= 740 such that for ALL a, b in A
(including a = b) the number a*b + 1 is NOT squarefree, i.e. a*b + 1 is divisible by p^2 for some prime p.
Answer format: {"A": [a_1, a_2, ..., a_m]}
Write your final answer ... | {"N": 8984, "t": 360, "family": "ae_p52_erdos_squarefree", "subset": "construct"} | null | null | null | {"A": [7, 32, 57, 82, 107, 132, 157, 182, 207, 232, 257, 282, 307, 332, 357, 382, 407, 432, 457, 482, 507, 532, 557, 582, 607, 632, 657, 682, 707, 732, 757, 782, 807, 832, 857, 882, 907, 932, 957, 982, 1007, 1032, 1057, 1082, 1107, 1132, 1157, 1182, 1207, 1232, 1257, 1282, 1307, 1332, 1357, 1382, 1407, 1432, 1457, 1482... | 1 |
construct-ae-p52-erdos-squarefree-l5-s2 | construct | ae_p52_erdos_squarefree | erdos_ab_plus_1_never_squarefree | number_theory | research | 5 | AlphaEvolve-Repository-of-Problems/52-erdos-squarefree | CC-BY-4.0 | [
"exact_integer"
] | Erdos squarefree problem.
Let N = 8705. Find a set A of distinct integers in {1, 2, ..., N} with 348 <= |A| <= 716 such that for ALL a, b in A
(including a = b) the number a*b + 1 is NOT squarefree, i.e. a*b + 1 is divisible by p^2 for some prime p.
Answer format: {"A": [a_1, a_2, ..., a_m]}
Write your final answer ... | {"N": 8705, "t": 348, "family": "ae_p52_erdos_squarefree", "subset": "construct"} | null | null | null | {"A": [7, 32, 57, 82, 107, 132, 157, 182, 207, 232, 257, 282, 307, 332, 357, 382, 407, 432, 457, 482, 507, 532, 557, 582, 607, 632, 657, 682, 707, 732, 757, 782, 807, 832, 857, 882, 907, 932, 957, 982, 1007, 1032, 1057, 1082, 1107, 1132, 1157, 1182, 1207, 1232, 1257, 1282, 1307, 1332, 1357, 1382, 1407, 1432, 1457, 1482... | 1 |
construct-ae-p52-erdos-squarefree-l5-s3 | construct | ae_p52_erdos_squarefree | erdos_ab_plus_1_never_squarefree | number_theory | research | 5 | AlphaEvolve-Repository-of-Problems/52-erdos-squarefree | CC-BY-4.0 | [
"exact_integer"
] | Erdos squarefree problem.
Let N = 7068. Find a set A of distinct integers in {1, 2, ..., N} with 283 <= |A| <= 586 such that for ALL a, b in A
(including a = b) the number a*b + 1 is NOT squarefree, i.e. a*b + 1 is divisible by p^2 for some prime p.
Answer format: {"A": [a_1, a_2, ..., a_m]}
Write your final answer ... | {"N": 7068, "t": 283, "family": "ae_p52_erdos_squarefree", "subset": "construct"} | null | null | null | {"A": [7, 32, 57, 82, 107, 132, 157, 182, 207, 232, 257, 282, 307, 332, 357, 382, 407, 432, 457, 482, 507, 532, 557, 582, 607, 632, 657, 682, 707, 732, 757, 782, 807, 832, 857, 882, 907, 932, 957, 982, 1007, 1032, 1057, 1082, 1107, 1132, 1157, 1182, 1207, 1232, 1257, 1282, 1307, 1332, 1357, 1382, 1407, 1432, 1457, 1482... | 1 |
construct-ae-p52-erdos-squarefree-l5-s4 | construct | ae_p52_erdos_squarefree | erdos_ab_plus_1_never_squarefree | number_theory | research | 5 | AlphaEvolve-Repository-of-Problems/52-erdos-squarefree | CC-BY-4.0 | [
"exact_integer"
] | Erdos squarefree problem.
Let N = 7124. Find a set A of distinct integers in {1, 2, ..., N} with 285 <= |A| <= 590 such that for ALL a, b in A
(including a = b) the number a*b + 1 is NOT squarefree, i.e. a*b + 1 is divisible by p^2 for some prime p.
Answer format: {"A": [a_1, a_2, ..., a_m]}
Write your final answer ... | {"N": 7124, "t": 285, "family": "ae_p52_erdos_squarefree", "subset": "construct"} | null | null | null | {"A": [7, 32, 57, 82, 107, 132, 157, 182, 207, 232, 257, 282, 307, 332, 357, 382, 407, 432, 457, 482, 507, 532, 557, 582, 607, 632, 657, 682, 707, 732, 757, 782, 807, 832, 857, 882, 907, 932, 957, 982, 1007, 1032, 1057, 1082, 1107, 1132, 1157, 1182, 1207, 1232, 1257, 1282, 1307, 1332, 1357, 1382, 1407, 1432, 1457, 1482... | 1 |
construct-ae-p52-erdos-squarefree-l5-s5 | construct | ae_p52_erdos_squarefree | erdos_ab_plus_1_never_squarefree | number_theory | research | 5 | AlphaEvolve-Repository-of-Problems/52-erdos-squarefree | CC-BY-4.0 | [
"exact_integer"
] | Erdos squarefree problem.
Let N = 9722. Find a set A of distinct integers in {1, 2, ..., N} with 389 <= |A| <= 798 such that for ALL a, b in A
(including a = b) the number a*b + 1 is NOT squarefree, i.e. a*b + 1 is divisible by p^2 for some prime p.
Answer format: {"A": [a_1, a_2, ..., a_m]}
Write your final answer ... | {"N": 9722, "t": 389, "family": "ae_p52_erdos_squarefree", "subset": "construct"} | null | null | null | {"A": [7, 32, 57, 82, 107, 132, 157, 182, 207, 232, 257, 282, 307, 332, 357, 382, 407, 432, 457, 482, 507, 532, 557, 582, 607, 632, 657, 682, 707, 732, 757, 782, 807, 832, 857, 882, 907, 932, 957, 982, 1007, 1032, 1057, 1082, 1107, 1132, 1157, 1182, 1207, 1232, 1257, 1282, 1307, 1332, 1357, 1382, 1407, 1432, 1457, 1482... | 1 |
construct-ae-p52-erdos-squarefree-l5-s6 | construct | ae_p52_erdos_squarefree | erdos_ab_plus_1_never_squarefree | number_theory | research | 5 | AlphaEvolve-Repository-of-Problems/52-erdos-squarefree | CC-BY-4.0 | [
"exact_integer"
] | Erdos squarefree problem.
Let N = 4172. Find a set A of distinct integers in {1, 2, ..., N} with 167 <= |A| <= 354 such that for ALL a, b in A
(including a = b) the number a*b + 1 is NOT squarefree, i.e. a*b + 1 is divisible by p^2 for some prime p.
Answer format: {"A": [a_1, a_2, ..., a_m]}
Write your final answer ... | {"N": 4172, "t": 167, "family": "ae_p52_erdos_squarefree", "subset": "construct"} | null | null | null | {"A": [7, 32, 57, 82, 107, 132, 157, 182, 207, 232, 257, 282, 307, 332, 357, 382, 407, 432, 457, 482, 507, 532, 557, 582, 607, 632, 657, 682, 707, 732, 757, 782, 807, 832, 857, 882, 907, 932, 957, 982, 1007, 1032, 1057, 1082, 1107, 1132, 1157, 1182, 1207, 1232, 1257, 1282, 1307, 1332, 1357, 1382, 1407, 1432, 1457, 1482... | 1 |
construct-ae-p52-erdos-squarefree-l5-s7 | construct | ae_p52_erdos_squarefree | erdos_ab_plus_1_never_squarefree | number_theory | research | 5 | AlphaEvolve-Repository-of-Problems/52-erdos-squarefree | CC-BY-4.0 | [
"exact_integer"
] | Erdos squarefree problem.
Let N = 6132. Find a set A of distinct integers in {1, 2, ..., N} with 246 <= |A| <= 512 such that for ALL a, b in A
(including a = b) the number a*b + 1 is NOT squarefree, i.e. a*b + 1 is divisible by p^2 for some prime p.
Answer format: {"A": [a_1, a_2, ..., a_m]}
Write your final answer ... | {"N": 6132, "t": 246, "family": "ae_p52_erdos_squarefree", "subset": "construct"} | null | null | null | {"A": [7, 32, 57, 82, 107, 132, 157, 182, 207, 232, 257, 282, 307, 332, 357, 382, 407, 432, 457, 482, 507, 532, 557, 582, 607, 632, 657, 682, 707, 732, 757, 782, 807, 832, 857, 882, 907, 932, 957, 982, 1007, 1032, 1057, 1082, 1107, 1132, 1157, 1182, 1207, 1232, 1257, 1282, 1307, 1332, 1357, 1382, 1407, 1432, 1457, 1482... | 1 |
construct-ae-p52-erdos-squarefree-l5-s8 | construct | ae_p52_erdos_squarefree | erdos_ab_plus_1_never_squarefree | number_theory | research | 5 | AlphaEvolve-Repository-of-Problems/52-erdos-squarefree | CC-BY-4.0 | [
"exact_integer"
] | Erdos squarefree problem.
Let N = 5020. Find a set A of distinct integers in {1, 2, ..., N} with 201 <= |A| <= 422 such that for ALL a, b in A
(including a = b) the number a*b + 1 is NOT squarefree, i.e. a*b + 1 is divisible by p^2 for some prime p.
Answer format: {"A": [a_1, a_2, ..., a_m]}
Write your final answer ... | {"N": 5020, "t": 201, "family": "ae_p52_erdos_squarefree", "subset": "construct"} | null | null | null | {"A": [7, 32, 57, 82, 107, 132, 157, 182, 207, 232, 257, 282, 307, 332, 357, 382, 407, 432, 457, 482, 507, 532, 557, 582, 607, 632, 657, 682, 707, 732, 757, 782, 807, 832, 857, 882, 907, 932, 957, 982, 1007, 1032, 1057, 1082, 1107, 1132, 1157, 1182, 1207, 1232, 1257, 1282, 1307, 1332, 1357, 1382, 1407, 1432, 1457, 1482... | 1 |
construct-ae-p52-erdos-squarefree-l5-s9 | construct | ae_p52_erdos_squarefree | erdos_ab_plus_1_never_squarefree | number_theory | research | 5 | AlphaEvolve-Repository-of-Problems/52-erdos-squarefree | CC-BY-4.0 | [
"exact_integer"
] | Erdos squarefree problem.
Let N = 8175. Find a set A of distinct integers in {1, 2, ..., N} with 327 <= |A| <= 674 such that for ALL a, b in A
(including a = b) the number a*b + 1 is NOT squarefree, i.e. a*b + 1 is divisible by p^2 for some prime p.
Answer format: {"A": [a_1, a_2, ..., a_m]}
Write your final answer ... | {"N": 8175, "t": 327, "family": "ae_p52_erdos_squarefree", "subset": "construct"} | null | null | null | {"A": [7, 32, 57, 82, 107, 132, 157, 182, 207, 232, 257, 282, 307, 332, 357, 382, 407, 432, 457, 482, 507, 532, 557, 582, 607, 632, 657, 682, 707, 732, 757, 782, 807, 832, 857, 882, 907, 932, 957, 982, 1007, 1032, 1057, 1082, 1107, 1132, 1157, 1182, 1207, 1232, 1257, 1282, 1307, 1332, 1357, 1382, 1407, 1432, 1457, 1482... | 1 |
construct-ae-p54-touching-cylinders-l1-s0 | construct | ae_p54_touching_cylinders | mutually_touching_infinite_cylinders | discrete_geometry | research | 1 | AlphaEvolve-Repository-of-Problems/54-pairwise-touching-cylinders | CC-BY-4.0 | [
"float_tolerance",
"nonlinear_system"
] | Seven pairwise touching unit cylinders.
Find 7 infinite circular cylinders of radius 1 in R^3 such that every two of them touch, i.e. the distance
between the axes of every pair of cylinders equals exactly 2 (checked with absolute tolerance 1e-09).
Describe cylinder i by a point (x, y, z) on its axis and an axis dire... | {"n": 7, "unit_radius": true, "tol": 1e-09, "family": "ae_p54_touching_cylinders", "subset": "construct"} | null | null | null | {"cylinders": [[-0.895079798222949, -0.218667037637932, -2.698674434206914, 0.455691112272712, -0.886598452747669, -0.079301915368401], [2.312489793725001, 3.147856283569415, 0.748107205326668, -0.664105297845157, 0.595346549216158, -0.452246215805514], [3.170115696452898, -1.572941214905496, 0.275241501569553, 0.10117... | 1 |
construct-ae-p54-touching-cylinders-l2-s0 | construct | ae_p54_touching_cylinders | mutually_touching_infinite_cylinders | discrete_geometry | research | 2 | AlphaEvolve-Repository-of-Problems/54-pairwise-touching-cylinders | CC-BY-4.0 | [
"float_tolerance",
"nonlinear_system"
] | Nine pairwise touching cylinders of arbitrary radii.
Find 9 infinite circular cylinders in R^3 with radii r_i in [0.1, 10] such that every two of them touch
externally, i.e. for every pair the distance between the axes equals r_i + r_j (checked with absolute tolerance
1e-09).
Describe cylinder i by a point (x, y, z) ... | {"n": 9, "unit_radius": false, "tol": 1e-09, "r_min": 0.1, "r_max": 10.0, "family": "ae_p54_touching_cylinders", "subset": "construct"} | null | null | null | {"cylinders": [[0.19857821545445875, -0.23831984674253506, -0.24522717314179707, 0.6511120386651232, -0.2084217497676763, 0.7298037320602897, 0.1525803323841557], [-0.045817225700147575, -0.6222633532305163, -0.4434641824479314, 0.19047945804717148, -0.5789996892270514, 0.7927653725643129, 0.10952216244488278], [0.0451... | 1 |
construct-ae-p58-happy-ending-l1-s0 | construct | ae_p58_happy_ending | erdos_szekeres_no_convex_k_gon_2pow_k_minus_2 | discrete_geometry | research | 1 | AlphaEvolve-Repository-of-Problems/58-erdos-szekeres-happy-ending | CC-BY-4.0 | [
"exact_integer",
"np_search"
] | Erdos-Szekeres happy ending problem (lower-bound construction).
Place n = 8 distinct points with integer coordinates (|x|, |y| <= 10^18) in the plane such that
1. no three of the points are collinear, and
2. no 5 of the points are in convex position (i.e. the points contain no convex 5-gon: no 5-point
subset whose ... | {"n": 8, "k": 5, "max_abs": 1000000000000000000, "family": "ae_p58_happy_ending", "subset": "construct"} | null | null | null | {"points": [[0, 0], [15000, -15000000], [15001, -14999998], [15002, -14999990], [30000, -60000000], [30001, -59999990], [30002, -59999988], [45000, -135000000]]} | 1 |
construct-ae-p58-happy-ending-l2-s0 | construct | ae_p58_happy_ending | erdos_szekeres_no_convex_k_gon_2pow_k_minus_2 | discrete_geometry | research | 2 | AlphaEvolve-Repository-of-Problems/58-erdos-szekeres-happy-ending | CC-BY-4.0 | [
"exact_integer",
"np_search"
] | Erdos-Szekeres happy ending problem (lower-bound construction).
Place n = 16 distinct points with integer coordinates (|x|, |y| <= 10^18) in the plane such that
1. no three of the points are collinear, and
2. no 6 of the points are in convex position (i.e. the points contain no convex 6-gon: no 6-point
subset whose... | {"n": 16, "k": 6, "max_abs": 1000000000000000000, "family": "ae_p58_happy_ending", "subset": "construct"} | null | null | null | {"points": [[0, 0], [92000, -92000000], [92001, -91999998], [92002, -91999990], [92003, -91999954], [184000, -368000000], [184001, -367999990], [184002, -367999988], [184003, -367999924], [184004, -367999922], [184005, -367999914], [276000, -828000000], [276001, -827999944], [276002, -827999934], [276003, -827999932], ... | 1 |
construct-ae-p58-happy-ending-l3-s0 | construct | ae_p58_happy_ending | erdos_szekeres_no_convex_k_gon_2pow_k_minus_2 | discrete_geometry | research | 3 | AlphaEvolve-Repository-of-Problems/58-erdos-szekeres-happy-ending | CC-BY-4.0 | [
"exact_integer",
"np_search"
] | Erdos-Szekeres happy ending problem (lower-bound construction).
Place n = 32 distinct points with integer coordinates (|x|, |y| <= 10^18) in the plane such that
1. no three of the points are collinear, and
2. no 7 of the points are in convex position (i.e. the points contain no convex 7-gon: no 7-point
subset whose... | {"n": 32, "k": 7, "max_abs": 1000000000000000000, "family": "ae_p58_happy_ending", "subset": "construct"} | null | null | null | {"points": [[0, 0], [846000, -846000000], [846001, -845999998], [846002, -845999990], [846003, -845999954], [846004, -845999762], [1692000, -3384000000], [1692001, -3383999990], [1692002, -3383999988], [1692003, -3383999924], [1692004, -3383999922], [1692005, -3383999914], [1692006, -3383999250], [1692007, -3383999248]... | 1 |
construct-ae-p58-happy-ending-l4-s0 | construct | ae_p58_happy_ending | erdos_szekeres_no_convex_k_gon_2pow_k_minus_2 | discrete_geometry | research | 4 | AlphaEvolve-Repository-of-Problems/58-erdos-szekeres-happy-ending | CC-BY-4.0 | [
"exact_integer",
"np_search"
] | Erdos-Szekeres happy ending problem (lower-bound construction).
Place n = 64 distinct points with integer coordinates (|x|, |y| <= 10^18) in the plane such that
1. no three of the points are collinear, and
2. no 8 of the points are in convex position (i.e. the points contain no convex 8-gon: no 8-point
subset whose... | {"n": 64, "k": 8, "max_abs": 1000000000000000000, "family": "ae_p58_happy_ending", "subset": "construct"} | null | null | null | {"points": [[0, 0], [15448000, -15448000000], [15448001, -15447999998], [15448002, -15447999990], [15448003, -15447999954], [15448004, -15447999762], [15448005, -15447998562], [30896000, -61792000000], [30896001, -61791999990], [30896002, -61791999988], [30896003, -61791999924], [30896004, -61791999922], [30896005, -61... | 1 |
construct-ae-p58-happy-ending-l5-s0 | construct | ae_p58_happy_ending | erdos_szekeres_no_convex_k_gon_2pow_k_minus_2 | discrete_geometry | research | 5 | AlphaEvolve-Repository-of-Problems/58-erdos-szekeres-happy-ending | CC-BY-4.0 | [
"exact_integer",
"np_search"
] | Erdos-Szekeres happy ending problem (lower-bound construction).
Place n = 128 distinct points with integer coordinates (|x|, |y| <= 10^18) in the plane such that
1. no three of the points are collinear, and
2. no 9 of the points are in convex position (i.e. the points contain no convex 9-gon: no 9-point
subset whos... | {"n": 128, "k": 9, "max_abs": 1000000000000000000, "family": "ae_p58_happy_ending", "subset": "construct"} | null | null | null | {"points": [[0, 0], [515385000, -515385000000], [515385001, -515384999998], [515385002, -515384999990], [515385003, -515384999954], [515385004, -515384999762], [515385005, -515384998562], [515385006, -515384989922], [1030770000, -2061540000000], [1030770001, -2061539999990], [1030770002, -2061539999988], [1030770003, -... | 1 |
construct-ae-p65-imo2025-p6-tiling-l1-s0 | construct | ae_p65_imo2025_p6_tiling | imo2025_p6_min_tiles | combinatorics | competition | 1 | AlphaEvolve-Repository-of-Problems/65-imo-2025-p6 | CC-BY-4.0 | [
"exact_integer"
] | Tiling a grid with one hole per row and column (IMO 2025 Problem 6, n = 9).
Consider an 9 x 9 grid of unit squares, rows and columns numbered 0..8. Place rectangular tiles whose
sides lie on grid lines, no two tiles overlapping (each unit square is covered by at most one tile), so that
every row and every column conta... | {"n": 9, "max_tiles": 12, "family": "ae_p65_imo2025_p6_tiling", "subset": "construct"} | null | null | null | {"tiles": [[0, 0, 3, 2], [0, 3, 1, 6], [1, 2, 3, 3], [1, 6, 1, 3], [2, 5, 3, 3], [3, 0, 3, 1], [3, 8, 6, 1], [4, 1, 3, 3], [5, 4, 3, 3], [6, 7, 3, 1], [7, 0, 2, 3], [8, 3, 1, 3]]} | 1 |
construct-ae-p65-imo2025-p6-tiling-l2-s0 | construct | ae_p65_imo2025_p6_tiling | imo2025_p6_min_tiles | combinatorics | competition | 2 | AlphaEvolve-Repository-of-Problems/65-imo-2025-p6 | CC-BY-4.0 | [
"exact_integer"
] | Tiling a grid with one hole per row and column (IMO 2025 Problem 6, n = 25).
Consider an 25 x 25 grid of unit squares, rows and columns numbered 0..24. Place rectangular tiles whose
sides lie on grid lines, no two tiles overlapping (each unit square is covered by at most one tile), so that
every row and every column c... | {"n": 25, "max_tiles": 32, "family": "ae_p65_imo2025_p6_tiling", "subset": "construct"} | null | null | null | {"tiles": [[0, 0, 5, 4], [0, 5, 1, 20], [1, 4, 5, 5], [1, 10, 1, 15], [2, 9, 5, 5], [2, 15, 1, 10], [3, 14, 5, 5], [3, 20, 1, 5], [4, 19, 5, 5], [5, 0, 5, 3], [5, 24, 20, 1], [6, 3, 5, 5], [7, 8, 5, 5], [8, 13, 5, 5], [9, 18, 5, 5], [10, 0, 5, 2], [10, 23, 15, 1], [11, 2, 5, 5], [12, 7, 5, 5], [13, 12, 5, 5], [14, 17, ... | 1 |
construct-ae-p65-imo2025-p6-tiling-l3-s0 | construct | ae_p65_imo2025_p6_tiling | imo2025_p6_min_tiles | combinatorics | competition | 3 | AlphaEvolve-Repository-of-Problems/65-imo-2025-p6 | CC-BY-4.0 | [
"exact_integer"
] | Tiling a grid with one hole per row and column (IMO 2025 Problem 6, n = 64).
Consider an 64 x 64 grid of unit squares, rows and columns numbered 0..63. Place rectangular tiles whose
sides lie on grid lines, no two tiles overlapping (each unit square is covered by at most one tile), so that
every row and every column c... | {"n": 64, "max_tiles": 77, "family": "ae_p65_imo2025_p6_tiling", "subset": "construct"} | null | null | null | {"tiles": [[0, 0, 8, 7], [0, 8, 1, 56], [1, 7, 8, 8], [1, 16, 1, 48], [2, 15, 8, 8], [2, 24, 1, 40], [3, 23, 8, 8], [3, 32, 1, 32], [4, 31, 8, 8], [4, 40, 1, 24], [5, 39, 8, 8], [5, 48, 1, 16], [6, 47, 8, 8], [6, 56, 1, 8], [7, 55, 8, 8], [8, 0, 8, 6], [8, 63, 56, 1], [9, 6, 8, 8], [10, 14, 8, 8], [11, 22, 8, 8], [12, ... | 1 |
construct-ae-p65-imo2025-p6-tiling-l4-s0 | construct | ae_p65_imo2025_p6_tiling | imo2025_p6_min_tiles | combinatorics | competition | 4 | AlphaEvolve-Repository-of-Problems/65-imo-2025-p6 | CC-BY-4.0 | [
"exact_integer"
] | Tiling a grid with one hole per row and column (IMO 2025 Problem 6, n = 225).
Consider an 225 x 225 grid of unit squares, rows and columns numbered 0..224. Place rectangular tiles whose
sides lie on grid lines, no two tiles overlapping (each unit square is covered by at most one tile), so that
every row and every colu... | {"n": 225, "max_tiles": 252, "family": "ae_p65_imo2025_p6_tiling", "subset": "construct"} | null | null | null | {"tiles": [[0, 0, 15, 14], [0, 15, 1, 210], [1, 14, 15, 15], [1, 30, 1, 195], [2, 29, 15, 15], [2, 45, 1, 180], [3, 44, 15, 15], [3, 60, 1, 165], [4, 59, 15, 15], [4, 75, 1, 150], [5, 74, 15, 15], [5, 90, 1, 135], [6, 89, 15, 15], [6, 105, 1, 120], [7, 104, 15, 15], [7, 120, 1, 105], [8, 119, 15, 15], [8, 135, 1, 90], ... | 1 |
construct-ae-p65-imo2025-p6-tiling-l5-s0 | construct | ae_p65_imo2025_p6_tiling | imo2025_p6_min_tiles | combinatorics | competition | 5 | AlphaEvolve-Repository-of-Problems/65-imo-2025-p6 | CC-BY-4.0 | [
"exact_integer"
] | Tiling a grid with one hole per row and column (IMO 2025 Problem 6, n = 900).
Consider an 900 x 900 grid of unit squares, rows and columns numbered 0..899. Place rectangular tiles whose
sides lie on grid lines, no two tiles overlapping (each unit square is covered by at most one tile), so that
every row and every colu... | {"n": 900, "max_tiles": 957, "family": "ae_p65_imo2025_p6_tiling", "subset": "construct"} | null | null | null | {"tiles": [[0, 0, 30, 29], [0, 30, 1, 870], [1, 29, 30, 30], [1, 60, 1, 840], [2, 59, 30, 30], [2, 90, 1, 810], [3, 89, 30, 30], [3, 120, 1, 780], [4, 119, 30, 30], [4, 150, 1, 750], [5, 149, 30, 30], [5, 180, 1, 720], [6, 179, 30, 30], [6, 210, 1, 690], [7, 209, 30, 30], [7, 240, 1, 660], [8, 239, 30, 30], [8, 270, 1,... | 1 |
construct-ae-p65-imo2025-p6-tiling-l6-s0 | construct | ae_p65_imo2025_p6_tiling | imo2025_p6_min_tiles | combinatorics | competition | 6 | AlphaEvolve-Repository-of-Problems/65-imo-2025-p6 | CC-BY-4.0 | [
"exact_integer"
] | Tiling a grid with one hole per row and column (IMO 2025 Problem 6, n = 2025).
Consider an 2025 x 2025 grid of unit squares, rows and columns numbered 0..2024. Place rectangular tiles whose
sides lie on grid lines, no two tiles overlapping (each unit square is covered by at most one tile), so that
every row and every ... | {"n": 2025, "max_tiles": 2112, "family": "ae_p65_imo2025_p6_tiling", "subset": "construct"} | null | null | null | {"tiles": [[0, 0, 45, 44], [0, 45, 1, 1980], [1, 44, 45, 45], [1, 90, 1, 1935], [2, 89, 45, 45], [2, 135, 1, 1890], [3, 134, 45, 45], [3, 180, 1, 1845], [4, 179, 45, 45], [4, 225, 1, 1800], [5, 224, 45, 45], [5, 270, 1, 1755], [6, 269, 45, 45], [6, 315, 1, 1710], [7, 314, 45, 45], [7, 360, 1, 1665], [8, 359, 45, 45], [... | 1 |
construct-mc-all-interval-l1-s0 | construct | mc_all_interval | all_interval_series | combinatorics | competition | 1 | MathConstraint/all_interval | CC-BY-4.0 | [
"agentic_trivial"
] | An all-interval series of size 7 is a permutation x[0..6] of 0..6 such that the absolute differences d[i] = |x[i+1] - x[i]| (i = 0..5) form a permutation of 1..6.
Find an all-interval series of size 7.
Answer format: {"x": [x_0, x_1, ..., x_6]}
Write your final answer as JSON to `/workdir/answer.json`. The instance ... | {"n": 7, "fixed": [], "family": "mc_all_interval", "subset": "construct"} | null | null | null | {"x": [0, 6, 1, 5, 2, 4, 3]} | 1 |
construct-mc-all-interval-l1-s1 | construct | mc_all_interval | all_interval_series | combinatorics | competition | 1 | MathConstraint/all_interval | CC-BY-4.0 | [
"agentic_trivial"
] | An all-interval series of size 4 is a permutation x[0..3] of 0..3 such that the absolute differences d[i] = |x[i+1] - x[i]| (i = 0..2) form a permutation of 1..3.
Find an all-interval series of size 4.
Answer format: {"x": [x_0, x_1, ..., x_3]}
Write your final answer as JSON to `/workdir/answer.json`. The instance ... | {"n": 4, "fixed": [], "family": "mc_all_interval", "subset": "construct"} | null | null | null | {"x": [0, 3, 1, 2]} | 1 |
construct-mc-all-interval-l1-s2 | construct | mc_all_interval | all_interval_series | combinatorics | competition | 1 | MathConstraint/all_interval | CC-BY-4.0 | [
"agentic_trivial"
] | An all-interval series of size 5 is a permutation x[0..4] of 0..4 such that the absolute differences d[i] = |x[i+1] - x[i]| (i = 0..3) form a permutation of 1..4.
Find an all-interval series of size 5.
Answer format: {"x": [x_0, x_1, ..., x_4]}
Write your final answer as JSON to `/workdir/answer.json`. The instance ... | {"n": 5, "fixed": [], "family": "mc_all_interval", "subset": "construct"} | null | null | null | {"x": [0, 4, 1, 3, 2]} | 1 |
construct-mc-all-interval-l1-s3 | construct | mc_all_interval | all_interval_series | combinatorics | competition | 1 | MathConstraint/all_interval | CC-BY-4.0 | [
"agentic_trivial"
] | An all-interval series of size 6 is a permutation x[0..5] of 0..5 such that the absolute differences d[i] = |x[i+1] - x[i]| (i = 0..4) form a permutation of 1..5.
Find an all-interval series of size 6.
Answer format: {"x": [x_0, x_1, ..., x_5]}
Write your final answer as JSON to `/workdir/answer.json`. The instance ... | {"n": 6, "fixed": [], "family": "mc_all_interval", "subset": "construct"} | null | null | null | {"x": [0, 5, 1, 4, 2, 3]} | 1 |
construct-mc-all-interval-l2-s0 | construct | mc_all_interval | all_interval_series | combinatorics | competition | 2 | MathConstraint/all_interval | CC-BY-4.0 | [
"agentic_trivial"
] | An all-interval series of size 8 is a permutation x[0..7] of 0..7 such that the absolute differences d[i] = |x[i+1] - x[i]| (i = 0..6) form a permutation of 1..7.
Find an all-interval series of size 8.
Some values are fixed in advance and your answer must agree with them:
x[4] = 2, d[5] = 2
Answer format: {"x": [x_0... | {"n": 8, "fixed": [["x", 4, 2], ["d", 5, 2]], "family": "mc_all_interval", "subset": "construct"} | null | null | null | {"x": [0, 7, 1, 6, 2, 5, 3, 4]} | 1 |
construct-mc-all-interval-l2-s1 | construct | mc_all_interval | all_interval_series | combinatorics | competition | 2 | MathConstraint/all_interval | CC-BY-4.0 | [
"agentic_trivial"
] | An all-interval series of size 10 is a permutation x[0..9] of 0..9 such that the absolute differences d[i] = |x[i+1] - x[i]| (i = 0..8) form a permutation of 1..9.
Find an all-interval series of size 10.
Answer format: {"x": [x_0, x_1, ..., x_9]}
Write your final answer as JSON to `/workdir/answer.json`. The instanc... | {"n": 10, "fixed": [], "family": "mc_all_interval", "subset": "construct"} | null | null | null | {"x": [0, 9, 1, 8, 2, 7, 3, 6, 4, 5]} | 1 |
construct-mc-all-interval-l2-s2 | construct | mc_all_interval | all_interval_series | combinatorics | competition | 2 | MathConstraint/all_interval | CC-BY-4.0 | [
"agentic_trivial"
] | An all-interval series of size 11 is a permutation x[0..10] of 0..10 such that the absolute differences d[i] = |x[i+1] - x[i]| (i = 0..9) form a permutation of 1..10.
Find an all-interval series of size 11.
Answer format: {"x": [x_0, x_1, ..., x_10]}
Write your final answer as JSON to `/workdir/answer.json`. The ins... | {"n": 11, "fixed": [], "family": "mc_all_interval", "subset": "construct"} | null | null | null | {"x": [0, 10, 1, 9, 2, 8, 3, 7, 4, 6, 5]} | 1 |
construct-mc-all-interval-l2-s3 | construct | mc_all_interval | all_interval_series | combinatorics | competition | 2 | MathConstraint/all_interval | CC-BY-4.0 | [
"agentic_trivial"
] | An all-interval series of size 9 is a permutation x[0..8] of 0..8 such that the absolute differences d[i] = |x[i+1] - x[i]| (i = 0..7) form a permutation of 1..8.
Find an all-interval series of size 9.
Answer format: {"x": [x_0, x_1, ..., x_8]}
Write your final answer as JSON to `/workdir/answer.json`. The instance ... | {"n": 9, "fixed": [], "family": "mc_all_interval", "subset": "construct"} | null | null | null | {"x": [0, 8, 1, 7, 2, 6, 3, 5, 4]} | 1 |
construct-mc-all-interval-l2-s4 | construct | mc_all_interval | all_interval_series | combinatorics | competition | 2 | MathConstraint/all_interval | CC-BY-4.0 | [
"agentic_trivial"
] | An all-interval series of size 10 is a permutation x[0..9] of 0..9 such that the absolute differences d[i] = |x[i+1] - x[i]| (i = 0..8) form a permutation of 1..9.
Find an all-interval series of size 10.
Some values are fixed in advance and your answer must agree with them:
x[0] = 0, x[3] = 8, d[1] = 8
Answer format... | {"n": 10, "fixed": [["x", 0, 0], ["x", 3, 8], ["d", 1, 8]], "family": "mc_all_interval", "subset": "construct"} | null | null | null | {"x": [0, 9, 1, 8, 2, 7, 3, 6, 4, 5]} | 1 |
construct-mc-all-interval-l2-s5 | construct | mc_all_interval | all_interval_series | combinatorics | competition | 2 | MathConstraint/all_interval | CC-BY-4.0 | [
"agentic_trivial"
] | An all-interval series of size 8 is a permutation x[0..7] of 0..7 such that the absolute differences d[i] = |x[i+1] - x[i]| (i = 0..6) form a permutation of 1..7.
Find an all-interval series of size 8.
Answer format: {"x": [x_0, x_1, ..., x_7]}
Write your final answer as JSON to `/workdir/answer.json`. The instance ... | {"n": 8, "fixed": [], "family": "mc_all_interval", "subset": "construct"} | null | null | null | {"x": [0, 7, 1, 6, 2, 5, 3, 4]} | 1 |
construct-mc-all-interval-l3-s0 | construct | mc_all_interval | all_interval_series | combinatorics | competition | 3 | MathConstraint/all_interval | CC-BY-4.0 | [
"agentic_trivial"
] | An all-interval series of size 14 is a permutation x[0..13] of 0..13 such that the absolute differences d[i] = |x[i+1] - x[i]| (i = 0..12) form a permutation of 1..13.
Find an all-interval series of size 14.
Some values are fixed in advance and your answer must agree with them:
x[6] = 3, x[12] = 6, d[3] = 10, d[11] =... | {"n": 14, "fixed": [["x", 6, 3], ["x", 12, 6], ["d", 3, 10], ["d", 11, 2]], "family": "mc_all_interval", "subset": "construct"} | null | null | null | {"x": [0, 13, 1, 12, 2, 11, 3, 10, 4, 9, 5, 8, 6, 7]} | 1 |
construct-mc-all-interval-l3-s1 | construct | mc_all_interval | all_interval_series | combinatorics | competition | 3 | MathConstraint/all_interval | CC-BY-4.0 | [
"agentic_trivial"
] | An all-interval series of size 13 is a permutation x[0..12] of 0..12 such that the absolute differences d[i] = |x[i+1] - x[i]| (i = 0..11) form a permutation of 1..12.
Find an all-interval series of size 13.
Answer format: {"x": [x_0, x_1, ..., x_12]}
Write your final answer as JSON to `/workdir/answer.json`. The in... | {"n": 13, "fixed": [], "family": "mc_all_interval", "subset": "construct"} | null | null | null | {"x": [0, 12, 1, 11, 2, 10, 3, 9, 4, 8, 5, 7, 6]} | 1 |
construct-mc-all-interval-l3-s2 | construct | mc_all_interval | all_interval_series | combinatorics | competition | 3 | MathConstraint/all_interval | CC-BY-4.0 | [
"agentic_trivial"
] | An all-interval series of size 12 is a permutation x[0..11] of 0..11 such that the absolute differences d[i] = |x[i+1] - x[i]| (i = 0..10) form a permutation of 1..11.
Find an all-interval series of size 12.
Answer format: {"x": [x_0, x_1, ..., x_11]}
Write your final answer as JSON to `/workdir/answer.json`. The in... | {"n": 12, "fixed": [], "family": "mc_all_interval", "subset": "construct"} | null | null | null | {"x": [0, 11, 1, 10, 2, 9, 3, 8, 4, 7, 5, 6]} | 1 |
construct-mc-all-interval-l3-s3 | construct | mc_all_interval | all_interval_series | combinatorics | competition | 3 | MathConstraint/all_interval | CC-BY-4.0 | [
"agentic_trivial"
] | An all-interval series of size 15 is a permutation x[0..14] of 0..14 such that the absolute differences d[i] = |x[i+1] - x[i]| (i = 0..13) form a permutation of 1..14.
Find an all-interval series of size 15.
Answer format: {"x": [x_0, x_1, ..., x_14]}
Write your final answer as JSON to `/workdir/answer.json`. The in... | {"n": 15, "fixed": [], "family": "mc_all_interval", "subset": "construct"} | null | null | null | {"x": [0, 14, 1, 13, 2, 12, 3, 11, 4, 10, 5, 9, 6, 8, 7]} | 1 |
construct-mc-all-interval-l3-s4 | construct | mc_all_interval | all_interval_series | combinatorics | competition | 3 | MathConstraint/all_interval | CC-BY-4.0 | [
"agentic_trivial"
] | An all-interval series of size 14 is a permutation x[0..13] of 0..13 such that the absolute differences d[i] = |x[i+1] - x[i]| (i = 0..12) form a permutation of 1..13.
Find an all-interval series of size 14.
Answer format: {"x": [x_0, x_1, ..., x_13]}
Write your final answer as JSON to `/workdir/answer.json`. The in... | {"n": 14, "fixed": [], "family": "mc_all_interval", "subset": "construct"} | null | null | null | {"x": [0, 13, 1, 12, 2, 11, 3, 10, 4, 9, 5, 8, 6, 7]} | 1 |
construct-mc-all-interval-l4-s0 | construct | mc_all_interval | all_interval_series | combinatorics | competition | 4 | MathConstraint/all_interval | CC-BY-4.0 | [
"agentic_trivial"
] | An all-interval series of size 16 is a permutation x[0..15] of 0..15 such that the absolute differences d[i] = |x[i+1] - x[i]| (i = 0..14) form a permutation of 1..15.
Find an all-interval series of size 16.
Answer format: {"x": [x_0, x_1, ..., x_15]}
Write your final answer as JSON to `/workdir/answer.json`. The in... | {"n": 16, "fixed": [], "family": "mc_all_interval", "subset": "construct"} | null | null | null | {"x": [0, 15, 1, 14, 2, 13, 3, 12, 4, 11, 5, 10, 6, 9, 7, 8]} | 1 |
construct-mc-all-interval-l4-s1 | construct | mc_all_interval | all_interval_series | combinatorics | competition | 4 | MathConstraint/all_interval | CC-BY-4.0 | [
"agentic_trivial"
] | An all-interval series of size 28 is a permutation x[0..27] of 0..27 such that the absolute differences d[i] = |x[i+1] - x[i]| (i = 0..26) form a permutation of 1..27.
Find an all-interval series of size 28.
Answer format: {"x": [x_0, x_1, ..., x_27]}
Write your final answer as JSON to `/workdir/answer.json`. The in... | {"n": 28, "fixed": [], "family": "mc_all_interval", "subset": "construct"} | null | null | null | {"x": [0, 27, 1, 26, 2, 25, 3, 24, 4, 23, 5, 22, 6, 21, 7, 20, 8, 19, 9, 18, 10, 17, 11, 16, 12, 15, 13, 14]} | 1 |
construct-mc-all-interval-l4-s2 | construct | mc_all_interval | all_interval_series | combinatorics | competition | 4 | MathConstraint/all_interval | CC-BY-4.0 | [
"agentic_trivial"
] | An all-interval series of size 24 is a permutation x[0..23] of 0..23 such that the absolute differences d[i] = |x[i+1] - x[i]| (i = 0..22) form a permutation of 1..23.
Find an all-interval series of size 24.
Answer format: {"x": [x_0, x_1, ..., x_23]}
Write your final answer as JSON to `/workdir/answer.json`. The in... | {"n": 24, "fixed": [], "family": "mc_all_interval", "subset": "construct"} | null | null | null | {"x": [0, 23, 1, 22, 2, 21, 3, 20, 4, 19, 5, 18, 6, 17, 7, 16, 8, 15, 9, 14, 10, 13, 11, 12]} | 1 |
construct-mc-all-interval-l4-s3 | construct | mc_all_interval | all_interval_series | combinatorics | competition | 4 | MathConstraint/all_interval | CC-BY-4.0 | [
"agentic_trivial"
] | An all-interval series of size 22 is a permutation x[0..21] of 0..21 such that the absolute differences d[i] = |x[i+1] - x[i]| (i = 0..20) form a permutation of 1..21.
Find an all-interval series of size 22.
Answer format: {"x": [x_0, x_1, ..., x_21]}
Write your final answer as JSON to `/workdir/answer.json`. The in... | {"n": 22, "fixed": [], "family": "mc_all_interval", "subset": "construct"} | null | null | null | {"x": [0, 21, 1, 20, 2, 19, 3, 18, 4, 17, 5, 16, 6, 15, 7, 14, 8, 13, 9, 12, 10, 11]} | 1 |
construct-mc-all-interval-l4-s4 | construct | mc_all_interval | all_interval_series | combinatorics | competition | 4 | MathConstraint/all_interval | CC-BY-4.0 | [
"agentic_trivial"
] | An all-interval series of size 26 is a permutation x[0..25] of 0..25 such that the absolute differences d[i] = |x[i+1] - x[i]| (i = 0..24) form a permutation of 1..25.
Find an all-interval series of size 26.
Answer format: {"x": [x_0, x_1, ..., x_25]}
Write your final answer as JSON to `/workdir/answer.json`. The in... | {"n": 26, "fixed": [], "family": "mc_all_interval", "subset": "construct"} | null | null | null | {"x": [0, 25, 1, 24, 2, 23, 3, 22, 4, 21, 5, 20, 6, 19, 7, 18, 8, 17, 9, 16, 10, 15, 11, 14, 12, 13]} | 1 |
construct-mc-all-interval-l4-s5 | construct | mc_all_interval | all_interval_series | combinatorics | competition | 4 | MathConstraint/all_interval | CC-BY-4.0 | [
"agentic_trivial"
] | An all-interval series of size 18 is a permutation x[0..17] of 0..17 such that the absolute differences d[i] = |x[i+1] - x[i]| (i = 0..16) form a permutation of 1..17.
Find an all-interval series of size 18.
Answer format: {"x": [x_0, x_1, ..., x_17]}
Write your final answer as JSON to `/workdir/answer.json`. The in... | {"n": 18, "fixed": [], "family": "mc_all_interval", "subset": "construct"} | null | null | null | {"x": [0, 17, 1, 16, 2, 15, 3, 14, 4, 13, 5, 12, 6, 11, 7, 10, 8, 9]} | 1 |
construct-mc-all-interval-l4-s6 | construct | mc_all_interval | all_interval_series | combinatorics | competition | 4 | MathConstraint/all_interval | CC-BY-4.0 | [
"agentic_trivial"
] | An all-interval series of size 20 is a permutation x[0..19] of 0..19 such that the absolute differences d[i] = |x[i+1] - x[i]| (i = 0..18) form a permutation of 1..19.
Find an all-interval series of size 20.
Answer format: {"x": [x_0, x_1, ..., x_19]}
Write your final answer as JSON to `/workdir/answer.json`. The in... | {"n": 20, "fixed": [], "family": "mc_all_interval", "subset": "construct"} | null | null | null | {"x": [0, 19, 1, 18, 2, 17, 3, 16, 4, 15, 5, 14, 6, 13, 7, 12, 8, 11, 9, 10]} | 1 |
construct-mc-all-interval-l4-s7 | construct | mc_all_interval | all_interval_series | combinatorics | competition | 4 | MathConstraint/all_interval | CC-BY-4.0 | [
"agentic_trivial"
] | An all-interval series of size 30 is a permutation x[0..29] of 0..29 such that the absolute differences d[i] = |x[i+1] - x[i]| (i = 0..28) form a permutation of 1..29.
Find an all-interval series of size 30.
Answer format: {"x": [x_0, x_1, ..., x_29]}
Write your final answer as JSON to `/workdir/answer.json`. The in... | {"n": 30, "fixed": [], "family": "mc_all_interval", "subset": "construct"} | null | null | null | {"x": [0, 29, 1, 28, 2, 27, 3, 26, 4, 25, 5, 24, 6, 23, 7, 22, 8, 21, 9, 20, 10, 19, 11, 18, 12, 17, 13, 16, 14, 15]} | 1 |
construct-mc-all-interval-l5-s0 | construct | mc_all_interval | all_interval_series | combinatorics | competition | 5 | MathConstraint/all_interval | CC-BY-4.0 | [
"agentic_trivial"
] | An all-interval series of size 44 is a permutation x[0..43] of 0..43 such that the absolute differences d[i] = |x[i+1] - x[i]| (i = 0..42) form a permutation of 1..43.
Find an all-interval series of size 44.
Answer format: {"x": [x_0, x_1, ..., x_43]}
Write your final answer as JSON to `/workdir/answer.json`. The in... | {"n": 44, "fixed": [], "family": "mc_all_interval", "subset": "construct"} | null | null | null | {"x": [0, 43, 1, 42, 2, 41, 3, 40, 4, 39, 5, 38, 6, 37, 7, 36, 8, 35, 9, 34, 10, 33, 11, 32, 12, 31, 13, 30, 14, 29, 15, 28, 16, 27, 17, 26, 18, 25, 19, 24, 20, 23, 21, 22]} | 1 |
construct-mc-all-interval-l5-s1 | construct | mc_all_interval | all_interval_series | combinatorics | competition | 5 | MathConstraint/all_interval | CC-BY-4.0 | [
"agentic_trivial"
] | An all-interval series of size 40 is a permutation x[0..39] of 0..39 such that the absolute differences d[i] = |x[i+1] - x[i]| (i = 0..38) form a permutation of 1..39.
Find an all-interval series of size 40.
Answer format: {"x": [x_0, x_1, ..., x_39]}
Write your final answer as JSON to `/workdir/answer.json`. The in... | {"n": 40, "fixed": [], "family": "mc_all_interval", "subset": "construct"} | null | null | null | {"x": [0, 39, 1, 38, 2, 37, 3, 36, 4, 35, 5, 34, 6, 33, 7, 32, 8, 31, 9, 30, 10, 29, 11, 28, 12, 27, 13, 26, 14, 25, 15, 24, 16, 23, 17, 22, 18, 21, 19, 20]} | 1 |
construct-mc-all-interval-l5-s2 | construct | mc_all_interval | all_interval_series | combinatorics | competition | 5 | MathConstraint/all_interval | CC-BY-4.0 | [
"agentic_trivial"
] | An all-interval series of size 36 is a permutation x[0..35] of 0..35 such that the absolute differences d[i] = |x[i+1] - x[i]| (i = 0..34) form a permutation of 1..35.
Find an all-interval series of size 36.
Answer format: {"x": [x_0, x_1, ..., x_35]}
Write your final answer as JSON to `/workdir/answer.json`. The in... | {"n": 36, "fixed": [], "family": "mc_all_interval", "subset": "construct"} | null | null | null | {"x": [0, 35, 1, 34, 2, 33, 3, 32, 4, 31, 5, 30, 6, 29, 7, 28, 8, 27, 9, 26, 10, 25, 11, 24, 12, 23, 13, 22, 14, 21, 15, 20, 16, 19, 17, 18]} | 1 |
construct-mc-all-interval-l5-s3 | construct | mc_all_interval | all_interval_series | combinatorics | competition | 5 | MathConstraint/all_interval | CC-BY-4.0 | [
"agentic_trivial"
] | An all-interval series of size 52 is a permutation x[0..51] of 0..51 such that the absolute differences d[i] = |x[i+1] - x[i]| (i = 0..50) form a permutation of 1..51.
Find an all-interval series of size 52.
Answer format: {"x": [x_0, x_1, ..., x_51]}
Write your final answer as JSON to `/workdir/answer.json`. The in... | {"n": 52, "fixed": [], "family": "mc_all_interval", "subset": "construct"} | null | null | null | {"x": [0, 51, 1, 50, 2, 49, 3, 48, 4, 47, 5, 46, 6, 45, 7, 44, 8, 43, 9, 42, 10, 41, 11, 40, 12, 39, 13, 38, 14, 37, 15, 36, 16, 35, 17, 34, 18, 33, 19, 32, 20, 31, 21, 30, 22, 29, 23, 28, 24, 27, 25, 26]} | 1 |
construct-mc-all-interval-l5-s4 | construct | mc_all_interval | all_interval_series | combinatorics | competition | 5 | MathConstraint/all_interval | CC-BY-4.0 | [
"agentic_trivial"
] | An all-interval series of size 56 is a permutation x[0..55] of 0..55 such that the absolute differences d[i] = |x[i+1] - x[i]| (i = 0..54) form a permutation of 1..55.
Find an all-interval series of size 56.
Answer format: {"x": [x_0, x_1, ..., x_55]}
Write your final answer as JSON to `/workdir/answer.json`. The in... | {"n": 56, "fixed": [], "family": "mc_all_interval", "subset": "construct"} | null | null | null | {"x": [0, 55, 1, 54, 2, 53, 3, 52, 4, 51, 5, 50, 6, 49, 7, 48, 8, 47, 9, 46, 10, 45, 11, 44, 12, 43, 13, 42, 14, 41, 15, 40, 16, 39, 17, 38, 18, 37, 19, 36, 20, 35, 21, 34, 22, 33, 23, 32, 24, 31, 25, 30, 26, 29, 27, 28]} | 1 |
construct-mc-all-interval-l5-s5 | construct | mc_all_interval | all_interval_series | combinatorics | competition | 5 | MathConstraint/all_interval | CC-BY-4.0 | [
"agentic_trivial"
] | An all-interval series of size 60 is a permutation x[0..59] of 0..59 such that the absolute differences d[i] = |x[i+1] - x[i]| (i = 0..58) form a permutation of 1..59.
Find an all-interval series of size 60.
Answer format: {"x": [x_0, x_1, ..., x_59]}
Write your final answer as JSON to `/workdir/answer.json`. The in... | {"n": 60, "fixed": [], "family": "mc_all_interval", "subset": "construct"} | null | null | null | {"x": [0, 59, 1, 58, 2, 57, 3, 56, 4, 55, 5, 54, 6, 53, 7, 52, 8, 51, 9, 50, 10, 49, 11, 48, 12, 47, 13, 46, 14, 45, 15, 44, 16, 43, 17, 42, 18, 41, 19, 40, 20, 39, 21, 38, 22, 37, 23, 36, 24, 35, 25, 34, 26, 33, 27, 32, 28, 31, 29, 30]} | 1 |
construct-mc-all-interval-l5-s6 | construct | mc_all_interval | all_interval_series | combinatorics | competition | 5 | MathConstraint/all_interval | CC-BY-4.0 | [
"agentic_trivial"
] | An all-interval series of size 32 is a permutation x[0..31] of 0..31 such that the absolute differences d[i] = |x[i+1] - x[i]| (i = 0..30) form a permutation of 1..31.
Find an all-interval series of size 32.
Answer format: {"x": [x_0, x_1, ..., x_31]}
Write your final answer as JSON to `/workdir/answer.json`. The in... | {"n": 32, "fixed": [], "family": "mc_all_interval", "subset": "construct"} | null | null | null | {"x": [0, 31, 1, 30, 2, 29, 3, 28, 4, 27, 5, 26, 6, 25, 7, 24, 8, 23, 9, 22, 10, 21, 11, 20, 12, 19, 13, 18, 14, 17, 15, 16]} | 1 |
construct-mc-all-interval-l5-s7 | construct | mc_all_interval | all_interval_series | combinatorics | competition | 5 | MathConstraint/all_interval | CC-BY-4.0 | [
"agentic_trivial"
] | An all-interval series of size 48 is a permutation x[0..47] of 0..47 such that the absolute differences d[i] = |x[i+1] - x[i]| (i = 0..46) form a permutation of 1..47.
Find an all-interval series of size 48.
Answer format: {"x": [x_0, x_1, ..., x_47]}
Write your final answer as JSON to `/workdir/answer.json`. The in... | {"n": 48, "fixed": [], "family": "mc_all_interval", "subset": "construct"} | null | null | null | {"x": [0, 47, 1, 46, 2, 45, 3, 44, 4, 43, 5, 42, 6, 41, 7, 40, 8, 39, 9, 38, 10, 37, 11, 36, 12, 35, 13, 34, 14, 33, 15, 32, 16, 31, 17, 30, 18, 29, 19, 28, 20, 27, 21, 26, 22, 25, 23, 24]} | 1 |
construct-mc-all-interval-l6-s0 | construct | mc_all_interval | all_interval_series | combinatorics | competition | 6 | MathConstraint/all_interval | CC-BY-4.0 | [
"agentic_trivial"
] | An all-interval series of size 72 is a permutation x[0..71] of 0..71 such that the absolute differences d[i] = |x[i+1] - x[i]| (i = 0..70) form a permutation of 1..71.
Find an all-interval series of size 72.
Answer format: {"x": [x_0, x_1, ..., x_71]}
Write your final answer as JSON to `/workdir/answer.json`. The in... | {"n": 72, "fixed": [], "family": "mc_all_interval", "subset": "construct"} | null | null | null | {"x": [0, 71, 1, 70, 2, 69, 3, 68, 4, 67, 5, 66, 6, 65, 7, 64, 8, 63, 9, 62, 10, 61, 11, 60, 12, 59, 13, 58, 14, 57, 15, 56, 16, 55, 17, 54, 18, 53, 19, 52, 20, 51, 21, 50, 22, 49, 23, 48, 24, 47, 25, 46, 26, 45, 27, 44, 28, 43, 29, 42, 30, 41, 31, 40, 32, 39, 33, 38, 34, 37, 35, 36]} | 1 |
construct-mc-all-interval-l6-s1 | construct | mc_all_interval | all_interval_series | combinatorics | competition | 6 | MathConstraint/all_interval | CC-BY-4.0 | [
"agentic_trivial"
] | An all-interval series of size 64 is a permutation x[0..63] of 0..63 such that the absolute differences d[i] = |x[i+1] - x[i]| (i = 0..62) form a permutation of 1..63.
Find an all-interval series of size 64.
Answer format: {"x": [x_0, x_1, ..., x_63]}
Write your final answer as JSON to `/workdir/answer.json`. The in... | {"n": 64, "fixed": [], "family": "mc_all_interval", "subset": "construct"} | null | null | null | {"x": [0, 63, 1, 62, 2, 61, 3, 60, 4, 59, 5, 58, 6, 57, 7, 56, 8, 55, 9, 54, 10, 53, 11, 52, 12, 51, 13, 50, 14, 49, 15, 48, 16, 47, 17, 46, 18, 45, 19, 44, 20, 43, 21, 42, 22, 41, 23, 40, 24, 39, 25, 38, 26, 37, 27, 36, 28, 35, 29, 34, 30, 33, 31, 32]} | 1 |
construct-mc-all-interval-l6-s2 | construct | mc_all_interval | all_interval_series | combinatorics | competition | 6 | MathConstraint/all_interval | CC-BY-4.0 | [
"agentic_trivial"
] | An all-interval series of size 104 is a permutation x[0..103] of 0..103 such that the absolute differences d[i] = |x[i+1] - x[i]| (i = 0..102) form a permutation of 1..103.
Find an all-interval series of size 104.
Answer format: {"x": [x_0, x_1, ..., x_103]}
Write your final answer as JSON to `/workdir/answer.json`.... | {"n": 104, "fixed": [], "family": "mc_all_interval", "subset": "construct"} | null | null | null | {"x": [0, 103, 1, 102, 2, 101, 3, 100, 4, 99, 5, 98, 6, 97, 7, 96, 8, 95, 9, 94, 10, 93, 11, 92, 12, 91, 13, 90, 14, 89, 15, 88, 16, 87, 17, 86, 18, 85, 19, 84, 20, 83, 21, 82, 22, 81, 23, 80, 24, 79, 25, 78, 26, 77, 27, 76, 28, 75, 29, 74, 30, 73, 31, 72, 32, 71, 33, 70, 34, 69, 35, 68, 36, 67, 37, 66, 38, 65, 39, 64,... | 1 |
construct-mc-all-interval-l6-s3 | construct | mc_all_interval | all_interval_series | combinatorics | competition | 6 | MathConstraint/all_interval | CC-BY-4.0 | [
"agentic_trivial"
] | An all-interval series of size 96 is a permutation x[0..95] of 0..95 such that the absolute differences d[i] = |x[i+1] - x[i]| (i = 0..94) form a permutation of 1..95.
Find an all-interval series of size 96.
Answer format: {"x": [x_0, x_1, ..., x_95]}
Write your final answer as JSON to `/workdir/answer.json`. The in... | {"n": 96, "fixed": [], "family": "mc_all_interval", "subset": "construct"} | null | null | null | {"x": [0, 95, 1, 94, 2, 93, 3, 92, 4, 91, 5, 90, 6, 89, 7, 88, 8, 87, 9, 86, 10, 85, 11, 84, 12, 83, 13, 82, 14, 81, 15, 80, 16, 79, 17, 78, 18, 77, 19, 76, 20, 75, 21, 74, 22, 73, 23, 72, 24, 71, 25, 70, 26, 69, 27, 68, 28, 67, 29, 66, 30, 65, 31, 64, 32, 63, 33, 62, 34, 61, 35, 60, 36, 59, 37, 58, 38, 57, 39, 56, 40,... | 1 |
construct-mc-all-interval-l6-s4 | construct | mc_all_interval | all_interval_series | combinatorics | competition | 6 | MathConstraint/all_interval | CC-BY-4.0 | [
"agentic_trivial"
] | An all-interval series of size 112 is a permutation x[0..111] of 0..111 such that the absolute differences d[i] = |x[i+1] - x[i]| (i = 0..110) form a permutation of 1..111.
Find an all-interval series of size 112.
Answer format: {"x": [x_0, x_1, ..., x_111]}
Write your final answer as JSON to `/workdir/answer.json`.... | {"n": 112, "fixed": [], "family": "mc_all_interval", "subset": "construct"} | null | null | null | {"x": [0, 111, 1, 110, 2, 109, 3, 108, 4, 107, 5, 106, 6, 105, 7, 104, 8, 103, 9, 102, 10, 101, 11, 100, 12, 99, 13, 98, 14, 97, 15, 96, 16, 95, 17, 94, 18, 93, 19, 92, 20, 91, 21, 90, 22, 89, 23, 88, 24, 87, 25, 86, 26, 85, 27, 84, 28, 83, 29, 82, 30, 81, 31, 80, 32, 79, 33, 78, 34, 77, 35, 76, 36, 75, 37, 74, 38, 73,... | 1 |
construct-mc-all-interval-l6-s5 | construct | mc_all_interval | all_interval_series | combinatorics | competition | 6 | MathConstraint/all_interval | CC-BY-4.0 | [
"agentic_trivial"
] | An all-interval series of size 128 is a permutation x[0..127] of 0..127 such that the absolute differences d[i] = |x[i+1] - x[i]| (i = 0..126) form a permutation of 1..127.
Find an all-interval series of size 128.
Answer format: {"x": [x_0, x_1, ..., x_127]}
Write your final answer as JSON to `/workdir/answer.json`.... | {"n": 128, "fixed": [], "family": "mc_all_interval", "subset": "construct"} | null | null | null | {"x": [0, 127, 1, 126, 2, 125, 3, 124, 4, 123, 5, 122, 6, 121, 7, 120, 8, 119, 9, 118, 10, 117, 11, 116, 12, 115, 13, 114, 14, 113, 15, 112, 16, 111, 17, 110, 18, 109, 19, 108, 20, 107, 21, 106, 22, 105, 23, 104, 24, 103, 25, 102, 26, 101, 27, 100, 28, 99, 29, 98, 30, 97, 31, 96, 32, 95, 33, 94, 34, 93, 35, 92, 36, 91,... | 1 |
construct-mc-all-interval-l6-s6 | construct | mc_all_interval | all_interval_series | combinatorics | competition | 6 | MathConstraint/all_interval | CC-BY-4.0 | [
"agentic_trivial"
] | An all-interval series of size 80 is a permutation x[0..79] of 0..79 such that the absolute differences d[i] = |x[i+1] - x[i]| (i = 0..78) form a permutation of 1..79.
Find an all-interval series of size 80.
Answer format: {"x": [x_0, x_1, ..., x_79]}
Write your final answer as JSON to `/workdir/answer.json`. The in... | {"n": 80, "fixed": [], "family": "mc_all_interval", "subset": "construct"} | null | null | null | {"x": [0, 79, 1, 78, 2, 77, 3, 76, 4, 75, 5, 74, 6, 73, 7, 72, 8, 71, 9, 70, 10, 69, 11, 68, 12, 67, 13, 66, 14, 65, 15, 64, 16, 63, 17, 62, 18, 61, 19, 60, 20, 59, 21, 58, 22, 57, 23, 56, 24, 55, 25, 54, 26, 53, 27, 52, 28, 51, 29, 50, 30, 49, 31, 48, 32, 47, 33, 46, 34, 45, 35, 44, 36, 43, 37, 42, 38, 41, 39, 40]} | 1 |
construct-mc-all-interval-l6-s7 | construct | mc_all_interval | all_interval_series | combinatorics | competition | 6 | MathConstraint/all_interval | CC-BY-4.0 | [
"agentic_trivial"
] | An all-interval series of size 120 is a permutation x[0..119] of 0..119 such that the absolute differences d[i] = |x[i+1] - x[i]| (i = 0..118) form a permutation of 1..119.
Find an all-interval series of size 120.
Answer format: {"x": [x_0, x_1, ..., x_119]}
Write your final answer as JSON to `/workdir/answer.json`.... | {"n": 120, "fixed": [], "family": "mc_all_interval", "subset": "construct"} | null | null | null | {"x": [0, 119, 1, 118, 2, 117, 3, 116, 4, 115, 5, 114, 6, 113, 7, 112, 8, 111, 9, 110, 10, 109, 11, 108, 12, 107, 13, 106, 14, 105, 15, 104, 16, 103, 17, 102, 18, 101, 19, 100, 20, 99, 21, 98, 22, 97, 23, 96, 24, 95, 25, 94, 26, 93, 27, 92, 28, 91, 29, 90, 30, 89, 31, 88, 32, 87, 33, 86, 34, 85, 35, 84, 36, 83, 37, 82,... | 1 |
construct-mc-all-interval-l6-s8 | construct | mc_all_interval | all_interval_series | combinatorics | competition | 6 | MathConstraint/all_interval | CC-BY-4.0 | [
"agentic_trivial"
] | An all-interval series of size 88 is a permutation x[0..87] of 0..87 such that the absolute differences d[i] = |x[i+1] - x[i]| (i = 0..86) form a permutation of 1..87.
Find an all-interval series of size 88.
Answer format: {"x": [x_0, x_1, ..., x_87]}
Write your final answer as JSON to `/workdir/answer.json`. The in... | {"n": 88, "fixed": [], "family": "mc_all_interval", "subset": "construct"} | null | null | null | {"x": [0, 87, 1, 86, 2, 85, 3, 84, 4, 83, 5, 82, 6, 81, 7, 80, 8, 79, 9, 78, 10, 77, 11, 76, 12, 75, 13, 74, 14, 73, 15, 72, 16, 71, 17, 70, 18, 69, 19, 68, 20, 67, 21, 66, 22, 65, 23, 64, 24, 63, 25, 62, 26, 61, 27, 60, 28, 59, 29, 58, 30, 57, 31, 56, 32, 55, 33, 54, 34, 53, 35, 52, 36, 51, 37, 50, 38, 49, 39, 48, 40,... | 1 |
construct-mc-antimagic-square-l1-s0 | construct | mc_antimagic_square | antimagic_square | combinatorics | competition | 1 | MathConstraint/antimagic_square | CC-BY-4.0 | [
"np_search"
] | An antimagic square of order 4 is a 4x4 grid containing each of the integers 1..16 exactly once such that its 10 line sums (4 row sums, 4 column sums and the sums of the two main diagonals) are 10 consecutive integers (all distinct, max - min = 9).
Construct an antimagic square of order 4.
Answer format: {"grid": [[r... | {"n": 4, "family": "mc_antimagic_square", "subset": "construct"} | null | null | null | {"grid": [[14, 4, 2, 10], [1, 11, 16, 7], [13, 8, 6, 12], [3, 15, 9, 5]]} | 1 |
construct-mc-antimagic-square-l2-s0 | construct | mc_antimagic_square | antimagic_square | combinatorics | competition | 2 | MathConstraint/antimagic_square | CC-BY-4.0 | [
"np_search"
] | An antimagic square of order 5 is a 5x5 grid containing each of the integers 1..25 exactly once such that its 12 line sums (5 row sums, 5 column sums and the sums of the two main diagonals) are 12 consecutive integers (all distinct, max - min = 11).
Construct an antimagic square of order 5.
Answer format: {"grid": [[... | {"n": 5, "family": "mc_antimagic_square", "subset": "construct"} | null | null | null | {"grid": [[9, 21, 6, 14, 19], [24, 3, 25, 7, 5], [17, 2, 23, 16, 12], [10, 15, 8, 11, 18], [1, 22, 4, 20, 13]]} | 1 |
construct-mc-antimagic-square-l3-s0 | construct | mc_antimagic_square | antimagic_square | combinatorics | competition | 3 | MathConstraint/antimagic_square | CC-BY-4.0 | [
"np_search"
] | An antimagic square of order 6 is a 6x6 grid containing each of the integers 1..36 exactly once such that its 14 line sums (6 row sums, 6 column sums and the sums of the two main diagonals) are 14 consecutive integers (all distinct, max - min = 13).
Construct an antimagic square of order 6.
Answer format: {"grid": [[... | {"n": 6, "family": "mc_antimagic_square", "subset": "construct"} | null | null | null | {"grid": [[18, 27, 11, 32, 1, 26], [4, 19, 30, 13, 36, 12], [31, 5, 10, 3, 35, 23], [25, 22, 17, 21, 15, 16], [33, 20, 8, 28, 14, 6], [2, 24, 34, 9, 7, 29]]} | 1 |
construct-mc-antimagic-square-l4-s0 | construct | mc_antimagic_square | antimagic_square | combinatorics | competition | 4 | MathConstraint/antimagic_square | CC-BY-4.0 | [
"np_search"
] | An antimagic square of order 7 is a 7x7 grid containing each of the integers 1..49 exactly once such that its 16 line sums (7 row sums, 7 column sums and the sums of the two main diagonals) are 16 consecutive integers (all distinct, max - min = 15).
Construct an antimagic square of order 7.
Answer format: {"grid": [[... | {"n": 7, "family": "mc_antimagic_square", "subset": "construct"} | null | null | null | {"grid": [[35, 2, 48, 27, 47, 11, 1], [41, 9, 43, 30, 13, 5, 31], [28, 33, 8, 19, 16, 45, 21], [37, 12, 6, 36, 32, 15, 38], [3, 26, 49, 25, 22, 29, 23], [18, 42, 7, 40, 34, 24, 14], [20, 44, 17, 4, 10, 46, 39]]} | 1 |
construct-mc-antimagic-square-l5-s0 | construct | mc_antimagic_square | antimagic_square | combinatorics | competition | 5 | MathConstraint/antimagic_square | CC-BY-4.0 | [
"np_search"
] | An antimagic square of order 8 is a 8x8 grid containing each of the integers 1..64 exactly once such that its 18 line sums (8 row sums, 8 column sums and the sums of the two main diagonals) are 18 consecutive integers (all distinct, max - min = 17).
Construct an antimagic square of order 8.
Answer format: {"grid": [[... | {"n": 8, "family": "mc_antimagic_square", "subset": "construct"} | null | null | null | {"grid": [[6, 46, 8, 57, 23, 54, 50, 18], [13, 17, 64, 2, 32, 52, 44, 45], [34, 62, 59, 7, 21, 3, 53, 19], [51, 41, 27, 58, 43, 33, 4, 10], [48, 56, 25, 39, 36, 20, 11, 24], [42, 5, 55, 60, 15, 22, 9, 49], [28, 26, 1, 29, 37, 40, 30, 61], [38, 12, 14, 16, 47, 31, 63, 35]]} | 1 |
construct-mc-antimagic-square-l6-s0 | construct | mc_antimagic_square | antimagic_square | combinatorics | competition | 6 | MathConstraint/antimagic_square | CC-BY-4.0 | [
"np_search"
] | An antimagic square of order 9 is a 9x9 grid containing each of the integers 1..81 exactly once such that its 20 line sums (9 row sums, 9 column sums and the sums of the two main diagonals) are 20 consecutive integers (all distinct, max - min = 19).
Construct an antimagic square of order 9.
Answer format: {"grid": [[... | {"n": 9, "family": "mc_antimagic_square", "subset": "construct"} | null | null | null | {"grid": [[14, 45, 64, 49, 48, 41, 19, 67, 25], [58, 17, 69, 23, 73, 18, 77, 8, 34], [78, 24, 74, 3, 16, 52, 21, 68, 32], [50, 75, 5, 56, 65, 43, 6, 39, 27], [10, 71, 9, 61, 7, 79, 53, 29, 46], [31, 37, 1, 80, 51, 26, 76, 28, 44], [35, 30, 81, 36, 22, 11, 70, 15, 60], [59, 62, 4, 38, 63, 20, 2, 55, 66], [40, 12, 57, 13... | 1 |
construct-mc-bibd-l1-s0 | construct | mc_bibd | bibd | combinatorics | competition | 1 | MathConstraint/bibd | CC-BY-4.0 | [
"np_search"
] | A balanced incomplete block design BIBD(7, 3, 1) is a collection of b = 7 blocks, each a set of 3 distinct points from {0, 1, ..., 6}, such that every pair of distinct points is contained in exactly 1 of the blocks (consequently every point lies in exactly r = 3 blocks). The same block may appear more than once.
Const... | {"v": 7, "k": 3, "lambda": 1, "b": 7, "family": "mc_bibd", "subset": "construct"} | null | null | null | {"blocks": [[0, 1, 3], [1, 2, 4], [2, 3, 5], [3, 4, 6], [0, 4, 5], [1, 5, 6], [0, 2, 6]]} | 1 |
construct-mc-bibd-l1-s1 | construct | mc_bibd | bibd | combinatorics | competition | 1 | MathConstraint/bibd | CC-BY-4.0 | [
"np_search"
] | A balanced incomplete block design BIBD(7, 4, 2) is a collection of b = 7 blocks, each a set of 4 distinct points from {0, 1, ..., 6}, such that every pair of distinct points is contained in exactly 2 of the blocks (consequently every point lies in exactly r = 4 blocks). The same block may appear more than once.
Const... | {"v": 7, "k": 4, "lambda": 2, "b": 7, "family": "mc_bibd", "subset": "construct"} | null | null | null | {"blocks": [[2, 4, 5, 6], [0, 3, 5, 6], [0, 1, 4, 6], [0, 1, 2, 5], [1, 2, 3, 6], [0, 2, 3, 4], [1, 3, 4, 5]]} | 1 |
construct-mc-bibd-l1-s2 | construct | mc_bibd | bibd | combinatorics | competition | 1 | MathConstraint/bibd | CC-BY-4.0 | [
"np_search"
] | A balanced incomplete block design BIBD(9, 3, 1) is a collection of b = 12 blocks, each a set of 3 distinct points from {0, 1, ..., 8}, such that every pair of distinct points is contained in exactly 1 of the blocks (consequently every point lies in exactly r = 4 blocks). The same block may appear more than once.
Cons... | {"v": 9, "k": 3, "lambda": 1, "b": 12, "family": "mc_bibd", "subset": "construct"} | null | null | null | {"blocks": [[0, 3, 6], [1, 4, 7], [2, 5, 8], [0, 4, 8], [1, 5, 6], [2, 3, 7], [0, 5, 7], [1, 3, 8], [2, 4, 6], [0, 1, 2], [3, 4, 5], [6, 7, 8]]} | 1 |
construct-mc-bibd-l2-s0 | construct | mc_bibd | bibd | combinatorics | competition | 2 | MathConstraint/bibd | CC-BY-4.0 | [
"np_search"
] | A balanced incomplete block design BIBD(11, 5, 2) is a collection of b = 11 blocks, each a set of 5 distinct points from {0, 1, ..., 10}, such that every pair of distinct points is contained in exactly 2 of the blocks (consequently every point lies in exactly r = 5 blocks). The same block may appear more than once.
Co... | {"v": 11, "k": 5, "lambda": 2, "b": 11, "family": "mc_bibd", "subset": "construct"} | null | null | null | {"blocks": [[1, 3, 4, 5, 9], [2, 4, 5, 6, 10], [0, 3, 5, 6, 7], [1, 4, 6, 7, 8], [2, 5, 7, 8, 9], [3, 6, 8, 9, 10], [0, 4, 7, 9, 10], [0, 1, 5, 8, 10], [0, 1, 2, 6, 9], [1, 2, 3, 7, 10], [0, 2, 3, 4, 8]]} | 1 |
construct-mc-bibd-l2-s1 | construct | mc_bibd | bibd | combinatorics | competition | 2 | MathConstraint/bibd | CC-BY-4.0 | [
"np_search"
] | A balanced incomplete block design BIBD(13, 3, 1) is a collection of b = 26 blocks, each a set of 3 distinct points from {0, 1, ..., 12}, such that every pair of distinct points is contained in exactly 1 of the blocks (consequently every point lies in exactly r = 6 blocks). The same block may appear more than once.
Co... | {"v": 13, "k": 3, "lambda": 1, "b": 26, "family": "mc_bibd", "subset": "construct"} | null | null | null | {"blocks": [[0, 1, 4], [1, 2, 5], [2, 3, 6], [3, 4, 7], [4, 5, 8], [5, 6, 9], [6, 7, 10], [7, 8, 11], [8, 9, 12], [0, 9, 10], [1, 10, 11], [2, 11, 12], [0, 3, 12], [0, 2, 7], [1, 3, 8], [2, 4, 9], [3, 5, 10], [4, 6, 11], [5, 7, 12], [0, 6, 8], [1, 7, 9], [2, 8, 10], [3, 9, 11], [4, 10, 12], [0, 5, 11], [1, 6, 12]]} | 1 |
construct-mc-bibd-l2-s2 | construct | mc_bibd | bibd | combinatorics | competition | 2 | MathConstraint/bibd | CC-BY-4.0 | [
"np_search"
] | A balanced incomplete block design BIBD(9, 3, 3) is a collection of b = 36 blocks, each a set of 3 distinct points from {0, 1, ..., 8}, such that every pair of distinct points is contained in exactly 3 of the blocks (consequently every point lies in exactly r = 12 blocks). The same block may appear more than once.
Con... | {"v": 9, "k": 3, "lambda": 3, "b": 36, "family": "mc_bibd", "subset": "construct"} | null | null | null | {"blocks": [[0, 7, 8], [2, 4, 8], [3, 7, 8], [4, 7, 8], [0, 3, 7], [4, 6, 8], [0, 1, 8], [2, 6, 8], [0, 6, 8], [4, 6, 7], [1, 2, 8], [0, 2, 4], [4, 5, 7], [1, 2, 7], [1, 6, 7], [2, 6, 7], [3, 5, 8], [2, 5, 7], [0, 1, 4], [0, 2, 5], [0, 1, 7], [3, 5, 8], [4, 5, 6], [2, 3, 4], [0, 5, 6], [0, 2, 3], [1, 2, 5], [2, 3, 6], ... | 1 |
construct-mc-bibd-l2-s3 | construct | mc_bibd | bibd | combinatorics | competition | 2 | MathConstraint/bibd | CC-BY-4.0 | [
"np_search"
] | A balanced incomplete block design BIBD(13, 4, 1) is a collection of b = 13 blocks, each a set of 4 distinct points from {0, 1, ..., 12}, such that every pair of distinct points is contained in exactly 1 of the blocks (consequently every point lies in exactly r = 4 blocks). The same block may appear more than once.
Co... | {"v": 13, "k": 4, "lambda": 1, "b": 13, "family": "mc_bibd", "subset": "construct"} | null | null | null | {"blocks": [[0, 1, 3, 9], [1, 2, 4, 10], [2, 3, 5, 11], [3, 4, 6, 12], [0, 4, 5, 7], [1, 5, 6, 8], [2, 6, 7, 9], [3, 7, 8, 10], [4, 8, 9, 11], [5, 9, 10, 12], [0, 6, 10, 11], [1, 7, 11, 12], [0, 2, 8, 12]]} | 1 |
construct-mc-bibd-l2-s4 | construct | mc_bibd | bibd | combinatorics | competition | 2 | MathConstraint/bibd | CC-BY-4.0 | [
"np_search"
] | A balanced incomplete block design BIBD(11, 6, 3) is a collection of b = 11 blocks, each a set of 6 distinct points from {0, 1, ..., 10}, such that every pair of distinct points is contained in exactly 3 of the blocks (consequently every point lies in exactly r = 6 blocks). The same block may appear more than once.
Co... | {"v": 11, "k": 6, "lambda": 3, "b": 11, "family": "mc_bibd", "subset": "construct"} | null | null | null | {"blocks": [[0, 2, 6, 7, 8, 10], [0, 1, 3, 7, 8, 9], [1, 2, 4, 8, 9, 10], [0, 2, 3, 5, 9, 10], [0, 1, 3, 4, 6, 10], [0, 1, 2, 4, 5, 7], [1, 2, 3, 5, 6, 8], [2, 3, 4, 6, 7, 9], [3, 4, 5, 7, 8, 10], [0, 4, 5, 6, 8, 9], [1, 5, 6, 7, 9, 10]]} | 1 |
construct-mc-bibd-l3-s0 | construct | mc_bibd | bibd | combinatorics | competition | 3 | MathConstraint/bibd | CC-BY-4.0 | [
"np_search"
] | A balanced incomplete block design BIBD(15, 7, 3) is a collection of b = 15 blocks, each a set of 7 distinct points from {0, 1, ..., 14}, such that every pair of distinct points is contained in exactly 3 of the blocks (consequently every point lies in exactly r = 7 blocks). The same block may appear more than once.
Co... | {"v": 15, "k": 7, "lambda": 3, "b": 15, "family": "mc_bibd", "subset": "construct"} | null | null | null | {"blocks": [[0, 1, 2, 4, 5, 8, 10], [1, 2, 3, 5, 6, 9, 11], [2, 3, 4, 6, 7, 10, 12], [3, 4, 5, 7, 8, 11, 13], [4, 5, 6, 8, 9, 12, 14], [0, 5, 6, 7, 9, 10, 13], [1, 6, 7, 8, 10, 11, 14], [0, 2, 7, 8, 9, 11, 12], [1, 3, 8, 9, 10, 12, 13], [2, 4, 9, 10, 11, 13, 14], [0, 3, 5, 10, 11, 12, 14], [0, 1, 4, 6, 11, 12, 13], [1,... | 1 |
construct-mc-bibd-l3-s1 | construct | mc_bibd | bibd | combinatorics | competition | 3 | MathConstraint/bibd | CC-BY-4.0 | [
"np_search"
] | A balanced incomplete block design BIBD(13, 4, 3) is a collection of b = 39 blocks, each a set of 4 distinct points from {0, 1, ..., 12}, such that every pair of distinct points is contained in exactly 3 of the blocks (consequently every point lies in exactly r = 12 blocks). The same block may appear more than once.
C... | {"v": 13, "k": 4, "lambda": 3, "b": 39, "family": "mc_bibd", "subset": "construct"} | null | null | null | {"blocks": [[0, 3, 8, 12], [0, 5, 6, 8], [0, 1, 2, 11], [1, 2, 4, 6], [4, 5, 8, 11], [0, 2, 3, 11], [1, 3, 5, 12], [2, 3, 6, 8], [3, 4, 8, 12], [0, 2, 7, 8], [0, 4, 6, 12], [1, 8, 10, 11], [4, 7, 8, 11], [0, 1, 4, 7], [3, 4, 10, 11], [0, 4, 10, 12], [2, 4, 5, 10], [0, 5, 6, 7], [2, 4, 6, 9], [3, 4, 7, 9], [3, 6, 9, 11]... | 1 |
construct-mc-bibd-l3-s2 | construct | mc_bibd | bibd | combinatorics | competition | 3 | MathConstraint/bibd | CC-BY-4.0 | [
"np_search"
] | A balanced incomplete block design BIBD(15, 3, 1) is a collection of b = 35 blocks, each a set of 3 distinct points from {0, 1, ..., 14}, such that every pair of distinct points is contained in exactly 1 of the blocks (consequently every point lies in exactly r = 7 blocks). The same block may appear more than once.
Co... | {"v": 15, "k": 3, "lambda": 1, "b": 35, "family": "mc_bibd", "subset": "construct"} | null | null | null | {"blocks": [[0, 1, 4], [1, 2, 5], [2, 3, 6], [3, 4, 7], [4, 5, 8], [5, 6, 9], [6, 7, 10], [7, 8, 11], [8, 9, 12], [9, 10, 13], [10, 11, 14], [0, 11, 12], [1, 12, 13], [2, 13, 14], [0, 3, 14], [0, 2, 8], [1, 3, 9], [2, 4, 10], [3, 5, 11], [4, 6, 12], [5, 7, 13], [6, 8, 14], [0, 7, 9], [1, 8, 10], [2, 9, 11], [3, 10, 12]... | 1 |
construct-mc-bibd-l3-s3 | construct | mc_bibd | bibd | combinatorics | competition | 3 | MathConstraint/bibd | CC-BY-4.0 | [
"np_search"
] | A balanced incomplete block design BIBD(16, 4, 1) is a collection of b = 20 blocks, each a set of 4 distinct points from {0, 1, ..., 15}, such that every pair of distinct points is contained in exactly 1 of the blocks (consequently every point lies in exactly r = 5 blocks). The same block may appear more than once.
Co... | {"v": 16, "k": 4, "lambda": 1, "b": 20, "family": "mc_bibd", "subset": "construct"} | null | null | null | {"blocks": [[0, 4, 8, 12], [1, 5, 9, 13], [2, 6, 10, 14], [3, 7, 11, 15], [0, 5, 10, 15], [1, 4, 11, 14], [2, 7, 8, 13], [3, 6, 9, 12], [0, 6, 11, 13], [1, 7, 10, 12], [2, 4, 9, 15], [3, 5, 8, 14], [0, 7, 9, 14], [1, 6, 8, 15], [2, 5, 11, 12], [3, 4, 10, 13], [0, 1, 2, 3], [4, 5, 6, 7], [8, 9, 10, 11], [12, 13, 14, 15]... | 1 |
construct-mc-bibd-l3-s4 | construct | mc_bibd | bibd | combinatorics | competition | 3 | MathConstraint/bibd | CC-BY-4.0 | [
"np_search"
] | A balanced incomplete block design BIBD(10, 3, 4) is a collection of b = 60 blocks, each a set of 3 distinct points from {0, 1, ..., 9}, such that every pair of distinct points is contained in exactly 4 of the blocks (consequently every point lies in exactly r = 18 blocks). The same block may appear more than once.
Co... | {"v": 10, "k": 3, "lambda": 4, "b": 60, "family": "mc_bibd", "subset": "construct"} | null | null | null | {"blocks": [[3, 5, 9], [2, 8, 9], [1, 5, 9], [2, 8, 9], [1, 3, 8], [7, 8, 9], [2, 8, 9], [1, 5, 9], [5, 7, 9], [0, 2, 5], [0, 2, 5], [1, 2, 8], [1, 5, 8], [3, 5, 8], [5, 7, 8], [2, 3, 7], [3, 5, 7], [0, 2, 5], [0, 3, 7], [0, 5, 7], [2, 5, 6], [1, 3, 9], [3, 5, 6], [1, 3, 6], [0, 6, 8], [4, 5, 8], [2, 4, 7], [0, 6, 8], ... | 1 |
construct-mc-bibd-l4-s0 | construct | mc_bibd | bibd | combinatorics | competition | 4 | MathConstraint/bibd | CC-BY-4.0 | [
"np_search"
] | A balanced incomplete block design BIBD(19, 3, 1) is a collection of b = 57 blocks, each a set of 3 distinct points from {0, 1, ..., 18}, such that every pair of distinct points is contained in exactly 1 of the blocks (consequently every point lies in exactly r = 9 blocks). The same block may appear more than once.
Co... | {"v": 19, "k": 3, "lambda": 1, "b": 57, "family": "mc_bibd", "subset": "construct"} | null | null | null | {"blocks": [[0, 1, 4], [1, 2, 5], [2, 3, 6], [3, 4, 7], [4, 5, 8], [5, 6, 9], [6, 7, 10], [7, 8, 11], [8, 9, 12], [9, 10, 13], [10, 11, 14], [11, 12, 15], [12, 13, 16], [13, 14, 17], [14, 15, 18], [0, 15, 16], [1, 16, 17], [2, 17, 18], [0, 3, 18], [0, 2, 9], [1, 3, 10], [2, 4, 11], [3, 5, 12], [4, 6, 13], [5, 7, 14], [... | 1 |
construct-mc-bibd-l4-s1 | construct | mc_bibd | bibd | combinatorics | competition | 4 | MathConstraint/bibd | CC-BY-4.0 | [
"np_search"
] | A balanced incomplete block design BIBD(13, 3, 2) is a collection of b = 52 blocks, each a set of 3 distinct points from {0, 1, ..., 12}, such that every pair of distinct points is contained in exactly 2 of the blocks (consequently every point lies in exactly r = 12 blocks). The same block may appear more than once.
C... | {"v": 13, "k": 3, "lambda": 2, "b": 52, "family": "mc_bibd", "subset": "construct"} | null | null | null | {"blocks": [[2, 5, 7], [5, 10, 11], [0, 11, 12], [0, 10, 12], [0, 1, 5], [0, 3, 10], [0, 5, 11], [0, 3, 9], [0, 1, 2], [5, 10, 12], [1, 7, 12], [1, 5, 9], [5, 8, 9], [1, 7, 11], [1, 9, 11], [1, 3, 12], [2, 9, 11], [2, 5, 12], [7, 9, 10], [2, 6, 7], [3, 7, 11], [3, 7, 9], [0, 2, 6], [1, 3, 6], [3, 6, 12], [2, 3, 10], [2... | 1 |
construct-mc-bibd-l4-s2 | construct | mc_bibd | bibd | combinatorics | competition | 4 | MathConstraint/bibd | CC-BY-4.0 | [
"np_search"
] | A balanced incomplete block design BIBD(16, 4, 3) is a collection of b = 60 blocks, each a set of 4 distinct points from {0, 1, ..., 15}, such that every pair of distinct points is contained in exactly 3 of the blocks (consequently every point lies in exactly r = 15 blocks). The same block may appear more than once.
C... | {"v": 16, "k": 4, "lambda": 3, "b": 60, "family": "mc_bibd", "subset": "construct"} | null | null | null | {"blocks": [[0, 1, 2, 7], [3, 5, 9, 14], [2, 8, 10, 11], [2, 5, 7, 14], [3, 5, 11, 13], [1, 2, 4, 9], [4, 7, 8, 12], [0, 2, 13, 15], [1, 6, 8, 9], [0, 8, 9, 11], [1, 5, 8, 11], [4, 10, 12, 14], [3, 7, 8, 12], [2, 5, 9, 12], [0, 4, 5, 14], [5, 6, 7, 8], [3, 4, 5, 13], [1, 7, 12, 14], [1, 4, 7, 11], [3, 12, 13, 15], [2, ... | 1 |
construct-mc-bibd-l4-s3 | construct | mc_bibd | bibd | combinatorics | competition | 4 | MathConstraint/bibd | CC-BY-4.0 | [
"np_search"
] | A balanced incomplete block design BIBD(21, 5, 1) is a collection of b = 21 blocks, each a set of 5 distinct points from {0, 1, ..., 20}, such that every pair of distinct points is contained in exactly 1 of the blocks (consequently every point lies in exactly r = 5 blocks). The same block may appear more than once.
Co... | {"v": 21, "k": 5, "lambda": 1, "b": 21, "family": "mc_bibd", "subset": "construct"} | null | null | null | {"blocks": [[0, 1, 4, 14, 16], [1, 2, 5, 15, 17], [2, 3, 6, 16, 18], [3, 4, 7, 17, 19], [4, 5, 8, 18, 20], [0, 5, 6, 9, 19], [1, 6, 7, 10, 20], [0, 2, 7, 8, 11], [1, 3, 8, 9, 12], [2, 4, 9, 10, 13], [3, 5, 10, 11, 14], [4, 6, 11, 12, 15], [5, 7, 12, 13, 16], [6, 8, 13, 14, 17], [7, 9, 14, 15, 18], [8, 10, 15, 16, 19], ... | 1 |
construct-mc-bibd-l4-s4 | construct | mc_bibd | bibd | combinatorics | competition | 4 | MathConstraint/bibd | CC-BY-4.0 | [
"np_search"
] | A balanced incomplete block design BIBD(15, 3, 2) is a collection of b = 70 blocks, each a set of 3 distinct points from {0, 1, ..., 14}, such that every pair of distinct points is contained in exactly 2 of the blocks (consequently every point lies in exactly r = 14 blocks). The same block may appear more than once.
C... | {"v": 15, "k": 3, "lambda": 2, "b": 70, "family": "mc_bibd", "subset": "construct"} | null | null | null | {"blocks": [[0, 10, 13], [0, 3, 4], [2, 7, 9], [10, 13, 14], [2, 8, 14], [2, 4, 5], [0, 5, 12], [1, 4, 10], [5, 10, 12], [0, 2, 6], [8, 9, 13], [9, 12, 13], [0, 1, 9], [9, 12, 14], [4, 9, 11], [0, 4, 8], [6, 9, 14], [5, 8, 13], [0, 12, 14], [3, 8, 14], [0, 10, 11], [4, 7, 10], [7, 8, 12], [2, 3, 13], [2, 10, 12], [10, ... | 1 |
construct-mc-bibd-l4-s5 | construct | mc_bibd | bibd | combinatorics | competition | 4 | MathConstraint/bibd | CC-BY-4.0 | [
"np_search"
] | A balanced incomplete block design BIBD(19, 9, 4) is a collection of b = 19 blocks, each a set of 9 distinct points from {0, 1, ..., 18}, such that every pair of distinct points is contained in exactly 4 of the blocks (consequently every point lies in exactly r = 9 blocks). The same block may appear more than once.
Co... | {"v": 19, "k": 9, "lambda": 4, "b": 19, "family": "mc_bibd", "subset": "construct"} | null | null | null | {"blocks": [[1, 4, 5, 6, 7, 9, 11, 16, 17], [2, 5, 6, 7, 8, 10, 12, 17, 18], [0, 3, 6, 7, 8, 9, 11, 13, 18], [0, 1, 4, 7, 8, 9, 10, 12, 14], [1, 2, 5, 8, 9, 10, 11, 13, 15], [2, 3, 6, 9, 10, 11, 12, 14, 16], [3, 4, 7, 10, 11, 12, 13, 15, 17], [4, 5, 8, 11, 12, 13, 14, 16, 18], [0, 5, 6, 9, 12, 13, 14, 15, 17], [1, 6, 7... | 1 |
construct-mc-bibd-l5-s0 | construct | mc_bibd | bibd | combinatorics | competition | 5 | MathConstraint/bibd | CC-BY-4.0 | [
"np_search"
] | A balanced incomplete block design BIBD(15, 3, 3) is a collection of b = 105 blocks, each a set of 3 distinct points from {0, 1, ..., 14}, such that every pair of distinct points is contained in exactly 3 of the blocks (consequently every point lies in exactly r = 21 blocks). The same block may appear more than once.
... | {"v": 15, "k": 3, "lambda": 3, "b": 105, "family": "mc_bibd", "subset": "construct"} | null | null | null | {"blocks": [[2, 6, 12], [3, 6, 11], [0, 6, 10], [3, 13, 14], [3, 6, 13], [3, 6, 11], [0, 13, 14], [1, 7, 12], [6, 12, 13], [8, 11, 13], [8, 10, 11], [2, 11, 14], [0, 7, 12], [0, 7, 8], [3, 7, 12], [3, 10, 12], [7, 11, 14], [2, 7, 11], [7, 10, 13], [9, 11, 12], [2, 4, 12], [5, 7, 13], [4, 5, 13], [2, 6, 14], [2, 6, 10],... | 1 |
construct-mc-bibd-l5-s1 | construct | mc_bibd | bibd | combinatorics | competition | 5 | MathConstraint/bibd | CC-BY-4.0 | [
"np_search"
] | A balanced incomplete block design BIBD(25, 5, 1) is a collection of b = 30 blocks, each a set of 5 distinct points from {0, 1, ..., 24}, such that every pair of distinct points is contained in exactly 1 of the blocks (consequently every point lies in exactly r = 6 blocks). The same block may appear more than once.
Co... | {"v": 25, "k": 5, "lambda": 1, "b": 30, "family": "mc_bibd", "subset": "construct"} | null | null | null | {"blocks": [[0, 5, 10, 15, 20], [1, 6, 11, 16, 21], [2, 7, 12, 17, 22], [3, 8, 13, 18, 23], [4, 9, 14, 19, 24], [0, 6, 12, 18, 24], [1, 7, 13, 19, 20], [2, 8, 14, 15, 21], [3, 9, 10, 16, 22], [4, 5, 11, 17, 23], [0, 7, 14, 16, 23], [1, 8, 10, 17, 24], [2, 9, 11, 18, 20], [3, 5, 12, 19, 21], [4, 6, 13, 15, 22], [0, 8, 1... | 1 |
construct-mc-bibd-l5-s2 | construct | mc_bibd | bibd | combinatorics | competition | 5 | MathConstraint/bibd | CC-BY-4.0 | [
"np_search"
] | A balanced incomplete block design BIBD(13, 3, 4) is a collection of b = 104 blocks, each a set of 3 distinct points from {0, 1, ..., 12}, such that every pair of distinct points is contained in exactly 4 of the blocks (consequently every point lies in exactly r = 24 blocks). The same block may appear more than once.
... | {"v": 13, "k": 3, "lambda": 4, "b": 104, "family": "mc_bibd", "subset": "construct"} | null | null | null | {"blocks": [[3, 4, 12], [3, 11, 12], [4, 6, 12], [4, 11, 12], [3, 4, 7], [4, 6, 11], [4, 7, 11], [4, 7, 12], [4, 6, 11], [4, 9, 10], [4, 9, 10], [4, 9, 10], [4, 9, 10], [1, 4, 8], [1, 4, 8], [1, 4, 5], [1, 4, 5], [4, 5, 8], [0, 3, 4], [3, 4, 8], [0, 3, 7], [3, 7, 12], [2, 5, 7], [0, 3, 11], [1, 3, 11], [1, 5, 6], [1, 6... | 1 |
construct-mc-bibd-l5-s3 | construct | mc_bibd | bibd | combinatorics | competition | 5 | MathConstraint/bibd | CC-BY-4.0 | [
"np_search"
] | A balanced incomplete block design BIBD(18, 3, 2) is a collection of b = 102 blocks, each a set of 3 distinct points from {0, 1, ..., 17}, such that every pair of distinct points is contained in exactly 2 of the blocks (consequently every point lies in exactly r = 17 blocks). The same block may appear more than once.
... | {"v": 18, "k": 3, "lambda": 2, "b": 102, "family": "mc_bibd", "subset": "construct"} | null | null | null | {"blocks": [[4, 15, 16], [3, 13, 14], [0, 3, 7], [4, 5, 13], [5, 10, 17], [4, 7, 10], [6, 16, 17], [3, 4, 17], [0, 4, 10], [1, 10, 16], [1, 13, 17], [2, 7, 10], [10, 12, 16], [11, 13, 15], [8, 13, 17], [1, 4, 9], [0, 4, 16], [6, 7, 11], [4, 8, 12], [5, 11, 16], [4, 8, 15], [1, 2, 11], [2, 4, 13], [2, 6, 17], [1, 2, 16]... | 1 |
construct-mc-bibd-l5-s4 | construct | mc_bibd | bibd | combinatorics | competition | 5 | MathConstraint/bibd | CC-BY-4.0 | [
"np_search"
] | A balanced incomplete block design BIBD(23, 11, 5) is a collection of b = 23 blocks, each a set of 11 distinct points from {0, 1, ..., 22}, such that every pair of distinct points is contained in exactly 5 of the blocks (consequently every point lies in exactly r = 11 blocks). The same block may appear more than once.
... | {"v": 23, "k": 11, "lambda": 5, "b": 23, "family": "mc_bibd", "subset": "construct"} | null | null | null | {"blocks": [[1, 2, 3, 4, 6, 8, 9, 12, 13, 16, 18], [2, 3, 4, 5, 7, 9, 10, 13, 14, 17, 19], [3, 4, 5, 6, 8, 10, 11, 14, 15, 18, 20], [4, 5, 6, 7, 9, 11, 12, 15, 16, 19, 21], [5, 6, 7, 8, 10, 12, 13, 16, 17, 20, 22], [0, 6, 7, 8, 9, 11, 13, 14, 17, 18, 21], [1, 7, 8, 9, 10, 12, 14, 15, 18, 19, 22], [0, 2, 8, 9, 10, 11, 1... | 1 |
construct-mc-bibd-l6-s0 | construct | mc_bibd | bibd | combinatorics | competition | 6 | MathConstraint/bibd | CC-BY-4.0 | [
"np_search"
] | A balanced incomplete block design BIBD(31, 6, 1) is a collection of b = 31 blocks, each a set of 6 distinct points from {0, 1, ..., 30}, such that every pair of distinct points is contained in exactly 1 of the blocks (consequently every point lies in exactly r = 6 blocks). The same block may appear more than once.
Co... | {"v": 31, "k": 6, "lambda": 1, "b": 31, "family": "mc_bibd", "subset": "construct"} | null | null | null | {"blocks": [[0, 1, 3, 8, 12, 18], [1, 2, 4, 9, 13, 19], [2, 3, 5, 10, 14, 20], [3, 4, 6, 11, 15, 21], [4, 5, 7, 12, 16, 22], [5, 6, 8, 13, 17, 23], [6, 7, 9, 14, 18, 24], [7, 8, 10, 15, 19, 25], [8, 9, 11, 16, 20, 26], [9, 10, 12, 17, 21, 27], [10, 11, 13, 18, 22, 28], [11, 12, 14, 19, 23, 29], [12, 13, 15, 20, 24, 30]... | 1 |
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