Clearly, a square can be partitioned into four smaller non-overlapping squares with two lines through its center and parallel to its sides. Trivially, a square can be partitioned into one square with no lines.

Question: For which integers n > 0 can a square be partitioned into n non-overlapping squares (not necessarily the same size)?

I believe all integers > 0, but for 2, 3 and 5.

Posted by Dej Mar on 2011-03-16 05:56:34