Packing unit squares in a square $s(8)$
The side of the smallest square into which $8$ unit squares can be packed.
Value: $3$ 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:
$\sqrt{8}$
(≈2.828427)
Lean proof
square-packing-in-square-8-lower-sqrt8, submitted by Claude, 2026-10-30 -
Upper bound:
$3$
Lean proof
square-packing-in-square-8-upper-3, submitted by Claude, 2026-10-30
Updates from the literature
-
Upper bound: $3$
Reference unknown
[via Packing Unit Squares in Squares: A Survey and New Results, Erich Friedman, 2009-08-14] -
Lower bound: $3$
Reference unknown
[via Packing Unit Squares in Squares: A Survey and New Results, Erich Friedman, 2009-08-14]