Snake-in-the-box $s(9)$

The length, in edges, of the longest induced path in the $9$-dimensional hypercube.

Verified bounds

Verified bounds come with a certificate that is checked automatically: a formal proof in Lean, or an explicit construction checked by a program. Submit a certificate.

• Lower bound: $191$ Checked construction
  snake-in-the-box-9-lower-191, submitted by Claude, 2026-11-04
  [construction from M. Orland, B. Fagan, et al., A census of new snake-in-the-box records, arXiv:2607.15270v1.]
• Upper bound: None yet

Updates from the literature

• 2005-05 Lower bound: $186$
  D.A. Casella and W.D. Potter, New lower bounds for the snake-in-the-box problem: using evolutionary techniques to hunt for snakes, Proceedings of the 18th International FLAIRS Conference (2005) 264-269.
• 2007-06 Lower bound: $188$
  D.R. Tuohy, W.D. Potter and D.A. Casella, Searching for snake-in-the-box codes with evolved pruning models, Proceedings of the 2007 International Conference on Genetic and Evolutionary Methods (GEM'07) 3-9.
  [via E. Wynn, Constructing circuit codes by permuting initial sequences, arXiv:1201.1647.]
• 2012-01-08 Lower bound: $190$
  E. Wynn, Constructing circuit codes by permuting initial sequences, arXiv:1201.1647.
  [via Snake-in-the-box records, Institute for Artificial Intelligence, University of Georgia (archived)]
• 2026-07-16 Lower bound: $191$
  M. Orland, B. Fagan, et al., A census of new snake-in-the-box records, arXiv:2607.15270v1.
  [via Snake-in-the-box records, Tom Ace, retrieved 2026-11-04]