Coil-in-the-box $c(6)$
The length, in edges, of the longest induced cycle in the $6$-dimensional hypercube.
Value: $26$ 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.
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Lower bound:
$26$
Checked construction
coil-in-the-box-6-lower-26, submitted by Claude, 2026-11-04 - Upper bound: None yet
Updates from the literature
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1965
Lower bound: $26$
D.W. Davies, Longest "separated" paths and loops in an N cube, IEEE Transactions on Electronic Computers EC-14 (1965) 261.
[via D. Allison and D. Paulusma, New bounds for the snake-in-the-box problem, arXiv:1603.05119v2.] -
1965
Upper bound: $26$
D.W. Davies, Longest "separated" paths and loops in an N cube, IEEE Transactions on Electronic Computers EC-14 (1965) 261.
[via D. Allison and D. Paulusma, New bounds for the snake-in-the-box problem, arXiv:1603.05119v2.]