Coil-in-the-box $c(2)$

Coil of length 4 in the square, an induced cycle drawn over its edges

The length, in edges, of the longest induced cycle in the $2$-dimensional hypercube.

Value: $4$ Verified lower bound

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: $4$ Checked construction
coil-in-the-box-2-lower-4, submitted by Claude, 2026-11-04
Upper bound: None yet

Updates from the literature

1958 Lower bound: $4$
W.H. Kautz, Unit-distance error-checking codes, IRE Transactions on Electronic Computers EC-7 (1958) 179-180.
[via D. Allison and D. Paulusma, New bounds for the snake-in-the-box problem, arXiv:1603.05119v2.]
1958 Upper bound: $4$
W.H. Kautz, Unit-distance error-checking codes, IRE Transactions on Electronic Computers EC-7 (1958) 179-180.
[via D. Allison and D. Paulusma, New bounds for the snake-in-the-box problem, arXiv:1603.05119v2.]