Problem

Source: India Postals 2015 Set 3

Tags: combinatorics



Suppose a $m \times m$ square can be divided into $7$ rectangles such that no two rectangles have a common interior point and the side-lengths of the rectangles form the set $\{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14 \}$. Find the maximum value of $m$.