{"paper":{"title":"Generalized Algorithm for Wythoff's Game with Basis Vector $(2^b,2^b)$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Jared Geller, Max Yu, Shubham Aggarwal, Shuvom Sadhuka","submitted_at":"2016-12-09T15:54:57Z","abstract_excerpt":"Wythoff's Game is a variation of Nim in which players may take an equal number of stones from each pile or make valid Nim moves. W. A. Wythoff proved that the set of P-Positions (losing position), $C$, for Wythoff's Game is given by $C := \\left\\{ (\\lfloor k\\phi \\rfloor, \\lfloor k\\phi^2 \\rfloor), (\\lfloor k\\phi^2 \\rfloor, \\lfloor k\\phi \\rfloor) : k \\in \\mathbb Z_{\\geq 0} \\right\\}$. An open Wythoff problem remains where players make the valid Nim moves or remove $kb$ stones from each pile, where $b$ is a fixed integer. We denote this as the $(b,b)$ game. For example, regular Wythoff's Game is ju"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.03068","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"}