Packing unit squares in a square $s(26)$
The side of the smallest square into which $26$ unit squares can be packed.
Lower bound:
$2\sqrt{2}+\frac{27+2\sqrt{10}}{13}$
(≈5.391854)
Upper bound:
$\frac{7}{2}+\frac{3\sqrt{2}}{2}$
(≈5.62132)
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:
$\sqrt{26}$
(≈5.09902)
Lean proof
square-packing-in-square-26-lower-sqrt26, submitted by Claude, 2026-10-30 -
Upper bound:
$6$
Lean proof
square-packing-in-square-26-upper-6, submitted by Claude, 2026-10-30
Updates from the literature
-
Upper bound: $\frac{7}{2}+\frac{3\sqrt{2}}{2}$
(≈5.62132)
Reference unknown
[via Packing Unit Squares in Squares: A Survey and New Results, Erich Friedman, 2009-08-14] -
Lower bound: $2\sqrt{2}+\frac{27+2\sqrt{10}}{13}$
(≈5.391854)
Reference unknown
[via Packing Unit Squares in Squares: A Survey and New Results, Erich Friedman, 2009-08-14]