The snaky hexomino is the hexomino represented by cells at
 |
The target is used in an unbiased Maker-Breaker game on the initially empty square point lattice.
Maker wins by occupying an allowed copy of 
, obtained by translations,
90-degree rotations, and reflections.
Halupczok and Schlage-Puchta (2007, p. 2) proved that Breaker wins on an 
board, that Maker wins on a sufficiently
large three-dimensional board, and that Maker wins on a sufficiently large planar
board if allowed one extra initial stone.
OpenAI (2026) gave a strategy that wins from the empty infinite board within 21 Maker moves against every legal Breaker continuation. Its 251-cell support fits inside
a 
board, giving the same bound
on that board. The release includes a Lean proof and an
explicit strategy certificate.
Morris (2026a) subsequently gave a winning strategy on the empty 
board, the size specified in Harary's conjecture.
The strategy and Lean formalization were produced by Claude (Anthropic) under T. Morris's
direction. Move choices from OpenAI's strategy resolved three difficult positions,
while Morris's release supplies its own certificates for them. The 8671-card certificate
can be checked independently by verifying each card's responses to all relevant Breaker
moves and requiring the card height to decrease after every continuation. The accompanying
browser game lets a human play Breaker against the certified
Maker strategy (Morris 2026b).
Sieben (2026) gave a strategy based on OpenAI's strategies that wins within 20 Maker moves on a 
board. Morris (2026c) gives a playable version of this strategy. Neither the board
sizes nor the move bounds are asserted to be minimal.
The snake of the snake-in-the-box problem is instead an induced graph path or graph cycle in a hypercube graph.
." GitHub, 2026a. 
:
Play White Against a Proof." 2026b. 
:
Play White Against Sieben's 20-Move Strategy." 2026c.