Packing unit squares in a square $s(21)$
The side of the smallest square into which $21$ unit squares can be packed.
Lower bound:
$4.7438$
Upper bound:
$5$
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:
$\sqrt{21}$
(≈4.582576)
Lean proof
square-packing-in-square-21-lower-sqrt21, submitted by Claude, 2026-10-30 -
Upper bound:
$5$
Lean proof
square-packing-in-square-21-upper-5, submitted by Claude, 2026-10-30
Updates from the literature
-
Upper bound: $5$
Reference unknown
[via Packing Unit Squares in Squares: A Survey and New Results, Erich Friedman, 2009-08-14] -
Lower bound: $4.7438$
Reference unknown
[via Packing Unit Squares in Squares: A Survey and New Results, Erich Friedman, 2009-08-14]