Snake-in-the-box $s(10)$

The length, in edges, of the longest induced path in the $10$-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: $379$ Checked construction
  snake-in-the-box-10-lower-379, 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: $358$
  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: $363$
  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 Snake-in-the-box records, Institute for Artificial Intelligence, University of Georgia (archived)]
• 2011-11-01 Lower bound: $367$
  D. Kinny, personal communication, recorded on the University of Georgia snake-in-the-box records page (2011).
  [via Snake-in-the-box records, Institute for Artificial Intelligence, University of Georgia (archived)]
• 2012-08 Lower bound: $370$
  D. Kinny, A new approach to the snake-in-the-box problem, Proceedings of the 20th European Conference on Artificial Intelligence (ECAI 2012) 462-467.
  [via D. Allison and D. Paulusma, New bounds for the snake-in-the-box problem, arXiv:1603.05119v2.]
• 2025-10-13 Lower bound: $373$
  T. Ace, A new lower bound for SIB in a 10-dimensional hypercube, Zenodo.
  [via Snake-in-the-box records, Tom Ace, retrieved 2026-11-04]
• 2025-12-05 Lower bound: $376$
  T. Ace, New lower bounds for snake-in-the-box in 10-, 11-, 12- and 13-dimensional hypercubes, Zenodo.
  [via Snake-in-the-box records, Tom Ace, retrieved 2026-11-04]
• 2026-07-16 Lower bound: $379$
  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]