Packing unit squares in a square $s(89)$
The side of the smallest square into which $89$ unit squares can be packed.
Lower bound:
$\sqrt{89}$
(≈9.433981)
Verified
(not in the literature)
Upper bound:
$5+\frac{7}{\sqrt{2}}$
(≈9.949747)
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:
$\sqrt{89}$
(≈9.433981)
Lean proof
square-packing-in-square-89-lower-sqrt89, submitted by Claude, 2026-10-30 -
Upper bound:
$10$
Lean proof
square-packing-in-square-89-upper-10, submitted by Claude, 2026-10-30
Updates from the literature
-
Upper bound: $5+\frac{7}{\sqrt{2}}$
(≈9.949747)
Reference unknown
[via Packing Unit Squares in Squares: A Survey and New Results, Erich Friedman, 2009-08-14]