Packing unit squares in a square $s(70)$
The side of the smallest square into which $70$ unit squares can be packed.
Lower bound:
$\sqrt{70}$
(≈8.3666)
Verified
(not in the literature)
Upper bound:
${\approx}8.8817$
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:
$\sqrt{70}$
(≈8.3666)
Lean proof
square-packing-in-square-70-lower-sqrt70, submitted by Claude, 2026-10-30 -
Upper bound:
$9$
Lean proof
square-packing-in-square-70-upper-9, submitted by Claude, 2026-10-30
Updates from the literature
-
Upper bound: ${\approx}8.9121$
Reference unknown
[via Packing Unit Squares in Squares: A Survey and New Results, Erich Friedman, 2009-08-14] -
2014-04
Upper bound: ${\approx}8.8817$
Joe DeVincentis in April 2014
[via Squares in Squares, David Ellsworth (based on the original by Erich Friedman)]