Packing unit squares in a square $s(45)$
The side of the smallest square into which $45$ unit squares can be packed.
Lower bound:
$\sqrt{45}$
(≈6.708204)
Verified
(not in the literature)
Upper bound:
$7$
Verified
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:
$\sqrt{45}$
(≈6.708204)
Lean proof
square-packing-in-square-45-lower-sqrt45, submitted by Claude, 2026-10-30 -
Upper bound:
$7$
Lean proof
square-packing-in-square-45-upper-7, submitted by Claude, 2026-10-30
Updates from the literature
-
Upper bound: $7$
Reference unknown
[via Packing Unit Squares in Squares: A Survey and New Results, Erich Friedman, 2009-08-14]