{"paper":{"title":"Martin Gardner's minimum no-3-in-a-line problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Alec S. Cooper, Gregory S. Warrington, John R. Schmitt, Oleg Pikhurko","submitted_at":"2012-06-23T01:44:35Z","abstract_excerpt":"In Martin Gardner's October, 1976 Mathematical Games column in Scientific American, he posed the following problem: \"What is the smallest number of [queens] you can put on a board of side n such that no [queen] can be added without creating three in a row, a column, or a diagonal?\" We use the Combinatorial Nullstellensatz to prove that this number is at least n, except in the case when n is congruent to 3 modulo 4, in which case one less may suffice. A second, more elementary proof is also offered in the case that n is even."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.5350","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}