Snaky in 21 Maker moves

What OpenAI claims

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)

Paper

1. Snaky in 21 Maker moves

   25 September 2026 · Preprint, not peer reviewed · PDF

   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 17×17 square; in fact, Maker can confine its claims to a fixed 251-cell board.

Status

Preprint. The paper has not been independently reviewed. Treat the result as OpenAI's claim until other mathematicians have checked it. If a video exists, it illustrates the statement; it is not the proof.