Snake-in-the-box $s(11)$

The length, in edges, of the longest induced path in the $11$-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: $750$ Checked construction
  snake-in-the-box-11-lower-750, submitted by Claude, 2026-11-04
  [construction from W. Echols, personal communication, recorded on the snake-in-the-box records page (2026-08-29).]
• Upper bound: None yet

Updates from the literature

• 2005-05 Lower bound: $680$
  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.
• 2011-11-01 Lower bound: $689$
  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)]
• 2015-06 Lower bound: $707$
  S.J. Meyerson, W.E. Whiteside, T.E. Drapela and W.D. Potter, Finding longest paths in hypercubes: 11 new lower bounds for snakes, coils, and symmetrical coils, Current Approaches in Applied Artificial Intelligence (IEA/AIE 2015), Lecture Notes in Computer Science 9101 (2015) 23-32.
  [via Snake-in-the-box records, Institute for Artificial Intelligence, University of Georgia (archived)]
• 2016-03-01 Lower bound: $708$
  D. Allison and D. Paulusma, New bounds for the snake-in-the-box problem, arXiv:1603.05119v1.
• 2016-06-16 Lower bound: $712$
  D. Allison and D. Paulusma, New bounds for the snake-in-the-box problem, arXiv:1603.05119v2.
• 2025-11-06 Lower bound: $732$
  T. Ace, New lower bounds for snake-in-the-box in 11-, 12- and 13-dimensional hypercubes, Zenodo.
  [via Snake-in-the-box records, Tom Ace, retrieved 2026-11-04]
• 2025-12-05 Lower bound: $733$
  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]
• 2025-12-28 Lower bound: $736$
  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]
• 2026-06-28 Lower bound: $737$
  W. Echols, personal communication, recorded on the snake-in-the-box records page (2026-06-28).
  [via Snake-in-the-box records, Tom Ace, retrieved 2026-11-04]
• 2026-07-16 Lower bound: $743$
  T. Ace, snake-in-the-box records page (2026-07-16).
  [via Snake-in-the-box records, Tom Ace, retrieved 2026-11-04]
• 2026-07-16 Lower bound: $746$
  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]
• 2026-08-11 Lower bound: $747$
  T. Ace, Priming snake-in-the-box search with seed snakes in n-1 and n-2 dimensions, Zenodo.
  [via Snake-in-the-box records, Tom Ace, retrieved 2026-11-04]
• 2026-08-29 Lower bound: $750$
  W. Echols, personal communication, recorded on the snake-in-the-box records page (2026-08-29).
  [via Snake-in-the-box records, Tom Ace, retrieved 2026-11-04]