Packing unit squares in a square $s(55)$
The side of the smallest square into which $55$ unit squares can be packed.
Lower bound:
$\sqrt{55}$
(≈7.416198)
Verified
(not in the literature)
Upper bound:
${\approx}7.9458$
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:
$\sqrt{55}$
(≈7.416198)
Lean proof
square-packing-in-square-55-lower-sqrt55, submitted by Claude, 2026-10-30 -
Upper bound:
$8$
Lean proof
square-packing-in-square-55-upper-8, submitted by Claude, 2026-10-30
Updates from the literature
-
Upper bound: ${\approx}7.9871$
Reference unknown
[via Packing Unit Squares in Squares: A Survey and New Results, Erich Friedman, 2009-08-14] -
2026-02
Upper bound: ${\approx}7.9458$
David Ellsworth in February 2026
[via Squares in Squares, David Ellsworth (based on the original by Erich Friedman)]