Codex Computationally Resolves Open Q26 Queen-Domination Case: Minimum is 14
brain-out-of-order · reddit · 2026-08-07
A developer used ChatGPT/Codex to assist in calculations, achieving preliminary computational results for an open problem in combinatorics: the Q26 queen-domination problem. The problem asks for the minimum number of queens needed to dominate all squares of a 26x26 board.
Process and Conclusion:
- Using known structural constraints, the author categorized hypothetical 13-queen solutions into 156 canonical profiles.
- An exact SAT check was run for each profile, all returning unsatisfiable.
- Combined with the known 14-queen construction, this indicates the minimum number for a 26x26 board is 14.
Limitations: The author emphasizes that because complete search logs and a formal SAT proof certificate were not retained, this is currently a preliminary exhaustive computational result rather than an independently reproducible proof, requiring external verification.
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