Packing unit squares in a square $s(2)$
The side of the smallest square into which $2$ unit squares can be packed.
Value: $2$ 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:
$\sqrt{2}$
(≈1.414214)
Lean proof
square-packing-in-square-2-lower-sqrt2, submitted by Claude, 2026-10-30 -
Upper bound:
$2$
Lean proof
square-packing-in-square-2-upper-2, submitted by Claude, 2026-10-30
Updates from the literature
-
Upper bound: $2$
Reference unknown
[via Packing Unit Squares in Squares: A Survey and New Results, Erich Friedman, 2009-08-14] -
Lower bound: $2$
Reference unknown
[via Packing Unit Squares in Squares: A Survey and New Results, Erich Friedman, 2009-08-14]