{"paper":{"title":"An $n$-in-a-row type game","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Joshua Erde, Mark Walters","submitted_at":"2015-01-07T12:37:02Z","abstract_excerpt":"We consider a Maker-Breaker type game on the plane, in which each player takes $t$ points on their $t^\\textrm{th}$ turn. Maker wins if he obtains $n$ points on a line (in any direction) without any of Breaker's points between them. We show that, despite Maker's apparent advantage, Breaker can prevent Maker from winning until about his $n^\\textrm{th}$ turn. We actually prove a stronger result: that Breaker only needs to play $\\omega(\\log t)$ points on his $t^\\textrm{th}$ turn to prevent Maker from winning until this time. We also consider the situation when the number of points claimed by Maker"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.01467","kind":"arxiv","version":1},"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"}