Packing unit squares in a square $s(67)$
The side of the smallest square into which $67$ unit squares can be packed.
Lower bound:
$2\sqrt{2}+\frac{71}{13}$
(≈8.289966)
Upper bound:
$8+\frac{1}{\sqrt{2}}$
(≈8.707107)
Updates
-
Lower bound: $2\sqrt{2}+\frac{71}{13}$
(≈8.289966)
Reference unknown
[via Packing Unit Squares in Squares: A Survey and New Results, Erich Friedman, 2009-08-14] -
1979
Upper bound: $8+\frac{1}{\sqrt{2}}$
(≈8.707107)
F. Göbel, Geometrical Packing and Covering Problems, in Packing and Covering in Combinatorics, A. Schrijver (ed.), Math Centrum Tracts 106 (1979) 179-199.
[via Packing Unit Squares in Squares: A Survey and New Results, Erich Friedman, 2009-08-14]