Packing unit squares in a square $s(15)$
The side of the smallest square into which $15$ unit squares can be packed.
Value: $4$ Verified upper bound
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.
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Lower bound:
$\sqrt{15}$
(≈3.872983)
Lean proof
square-packing-in-square-15-lower-sqrt15, submitted by Claude, 2026-10-30 -
Upper bound:
$4$
Lean proof
square-packing-in-square-15-upper-4, submitted by Claude, 2026-10-30
Updates from the literature
-
Upper bound: $4$
Reference unknown
[via Packing Unit Squares in Squares: A Survey and New Results, Erich Friedman, 2009-08-14] -
Lower bound: $4$
Reference unknown
[via Packing Unit Squares in Squares: A Survey and New Results, Erich Friedman, 2009-08-14]