The three squares in a rectangle problem asks for the maximum sum of the side lengths of three squares contained in a 
rectangle, where 
and the interiors of the squares
are pairwise disjoint. The squares may have different
sizes and may undergo arbitrary rotation. Yang (2026)
determined the maximum to be
 |
(1)
|
In particular, the maximum is 3/2 in a unit square and 2 in a 
rectangle. The latter
value is attained by one unit square and two squares
of side length 1/2. For 
, three unit squares attain
the maximum 3. The upper bounds allow all orientations, even though these examples
have sides parallel to the boundary.
