Question 53
A $m \times N$ table is filled with $2 \times 2$ and $1 \times 3$ tiles. Different tiles don't have common cells. Prove that the number of ways for choosing a $1 \times 2$ rectangle (vertical or horizontal) so that one of its cells is filled with a $2 \times 2$ tile and one of them is filled with a $1 \times 3$ tile is even.