Packing unit squares in a square $s(31)$
The side of the smallest square into which $31$ unit squares can be packed.
Lower bound:
$5.6415$
Upper bound:
$6$
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:
$\sqrt{31}$
(≈5.567764)
Lean proof
square-packing-in-square-31-lower-sqrt31, submitted by Claude, 2026-10-30 -
Upper bound:
$6$
Lean proof
square-packing-in-square-31-upper-6, submitted by Claude, 2026-10-30
Updates from the literature
-
Upper bound: $6$
Reference unknown
[via Packing Unit Squares in Squares: A Survey and New Results, Erich Friedman, 2009-08-14] -
Lower bound: $5.6415$
Reference unknown
[via Packing Unit Squares in Squares: A Survey and New Results, Erich Friedman, 2009-08-14]