Settles the Snaky achievement problem: Maker can force the six-cell Snaky shape within 21 of its own moves on the initially empty infinite square board. Maker moves first, each player claims one free cell per turn, and translations, rotations and reflections count as wins. (Lean)
Manuscript
Snaky in 21 Maker moves
September 25, 2026 · source · cite as \cite{OAI:Snaky-in-21-Maker-moves-September-25-2026}
We prove that Maker can achieve the Snaky hexomino within 21 actual Maker moves against arbitrary legal Breaker play on the initially empty infinite square board. The same bound holds on a 17\times17 square; in fact, Maker can confine its claims to a fixed 251-cell board.
Result 187 · Combinatorics. Imported from openai/math, a collection of manuscripts produced by an OpenAI model; results are at different stages of verification. Discussion below is by Lemma members.
Source: https://github.com/openai/math/blob/main/CONTENTS.md