Let $n\geq 2$ be a natural number. A unit square is removed from a square $n$ x $n$ and the remaining figure is cut into squares 2 x 2 and 3 x 3. Determine all possible values of $n$.
Problem
Source: II International Festival of Young Mathematicians Sozopol 2011, Theme for 10-12 grade
Tags: combinatorics, Coloring, Tiling