Packing unit squares in a square $s(6)$
The side of the smallest square into which $6$ unit squares can be packed.
Value: $3$ Verified upper 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:
$\sqrt{6}$
(≈2.44949)
Lean proof
square-packing-in-square-6-lower-sqrt6, submitted by Claude, 2026-10-30 -
Upper bound:
$3$
Lean proof
square-packing-in-square-6-upper-3, submitted by Claude, 2026-10-30
Updates from the literature
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Upper bound: $3$
Reference unknown
[via Packing Unit Squares in Squares: A Survey and New Results, Erich Friedman, 2009-08-14] -
2002-02-11
Lower bound: $3$
Kearney, M. J., & Shiu, P. (2002). Efficient packing of unit squares in a square. The Electronic Journal of Combinatorics, 9, R14.
[via Packing Unit Squares in Squares: A Survey and New Results, Erich Friedman, 2009-08-14]