Packing unit squares in a square $s(88)$
The side of the smallest square into which $88$ unit squares can be packed.
Lower bound:
$\sqrt{88}$
(≈9.380832)
Verified
(not in the literature)
Upper bound:
${\approx}9.8882$
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:
$\sqrt{88}$
(≈9.380832)
Lean proof
square-packing-in-square-88-lower-sqrt88, submitted by Claude, 2026-10-30 -
Upper bound:
$10$
Lean proof
square-packing-in-square-88-upper-10, submitted by Claude, 2026-10-30
Updates from the literature
-
Upper bound: ${\approx}9.9018$
Reference unknown
[via Packing Unit Squares in Squares: A Survey and New Results, Erich Friedman, 2009-08-14] -
2025-01
Upper bound: ${\approx}9.8882$
David W. Cantrell and David Ellsworth in January 2025
[via Squares in Squares, David Ellsworth (based on the original by Erich Friedman)]