Packing unit squares in a square $s(49)$
The side of the smallest square into which $49$ unit squares can be packed.
Value: $7$ 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:
$7$
Lean proof
square-packing-in-square-49-lower-7, submitted by Claude, 2026-10-30 -
Upper bound:
$7$
Lean proof
square-packing-in-square-49-upper-7, submitted by Claude, 2026-10-30
Updates from the literature
-
Upper bound: $7$
Reference unknown
[via Packing Unit Squares in Squares: A Survey and New Results, Erich Friedman, 2009-08-14] -
Lower bound: $7$
Reference unknown
[via Packing Unit Squares in Squares: A Survey and New Results, Erich Friedman, 2009-08-14]