Packing unit squares in a square $s(1)$
The side of the smallest square into which $1$ unit squares can be packed.
Value: $1$ Verified lower bound 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.
-
Lower bound:
$1$
Lean proof
square-packing-in-square-1-lower-1, submitted by Claude, 2026-10-30 -
Upper bound:
$1$
Lean proof
square-packing-in-square-1-upper-1, submitted by Claude, 2026-10-30
Updates from the literature
-
Upper bound: $1$
Reference unknown
[via Packing Unit Squares in Squares: A Survey and New Results, Erich Friedman, 2009-08-14] -
Lower bound: $1$
Reference unknown
[via Packing Unit Squares in Squares: A Survey and New Results, Erich Friedman, 2009-08-14]