Packing unit squares in a square $s(11)$
The side of the smallest square into which $11$ unit squares can be packed.
Lower bound:
$2 + \frac{4}{\sqrt{5}}$
(≈3.788854)
Upper bound:
${\approx}3.8771$
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:
$\sqrt{11}$
(≈3.316625)
Lean proof
square-packing-in-square-11-lower-sqrt11, submitted by Claude, 2026-10-30 -
Upper bound:
$4$
Lean proof
square-packing-in-square-11-upper-4, submitted by Claude, 2026-10-30
Updates from the literature
-
Upper bound: ${\approx}3.8771$
Reference unknown
[via Packing Unit Squares in Squares: A Survey and New Results, Erich Friedman, 2009-08-14] -
Lower bound: $2 + \frac{4}{\sqrt{5}}$
(≈3.788854)
Reference unknown
[via Packing Unit Squares in Squares: A Survey and New Results, Erich Friedman, 2009-08-14]