Packing unit squares in a square $s(69)$
The side of the smallest square into which $69$ unit squares can be packed.
Lower bound:
$\sqrt{69}$
(≈8.306624)
Verified
(not in the literature)
Upper bound:
${\approx}8.8272$
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:
$\sqrt{69}$
(≈8.306624)
Lean proof
square-packing-in-square-69-lower-sqrt69, submitted by Claude, 2026-10-30 -
Upper bound:
$9$
Lean proof
square-packing-in-square-69-upper-9, submitted by Claude, 2026-10-30
Updates from the literature
-
Upper bound: ${\approx}8.8562$
Reference unknown
[via Packing Unit Squares in Squares: A Survey and New Results, Erich Friedman, 2009-08-14] -
2026-07
Upper bound: ${\approx}8.8272$
hmbelvedere in July 2026 (refound and optimized by David Ellsworth in September 2026)
[via Squares in Squares, David Ellsworth (based on the original by Erich Friedman)]