Snake-in-the-box $s(7)$

The length, in edges, of the longest induced path in the $7$-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: $50$ Checked construction
  snake-in-the-box-7-lower-50, submitted by Claude, 2026-11-04
  [construction from W.D. Potter, R.W. Robinson, J.A. Miller, K.J. Kochut and D.Z. Redys, Using the genetic algorithm to find snake-in-the-box codes, Proceedings of the 7th International Conference on Industrial and Engineering Applications of Artificial Intelligence and Expert Systems (IEA/AIE 1994) 421-426.]
• Upper bound: None yet

Updates from the literature

• 1994 Lower bound: $50$
  W.D. Potter, R.W. Robinson, J.A. Miller, K.J. Kochut and D.Z. Redys, Using the genetic algorithm to find snake-in-the-box codes, Proceedings of the 7th International Conference on Industrial and Engineering Applications of Artificial Intelligence and Expert Systems (IEA/AIE 1994) 421-426.
  [via 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.]
• 1996 Upper bound: $50$
  K.J. Kochut, Snake-in-the-box codes for dimension 7, Journal of Combinatorial Mathematics and Combinatorial Computing 20 (1996) 175-185.
  [via D. Allison and D. Paulusma, New bounds for the snake-in-the-box problem, arXiv:1603.05119v2.]