This is a coloring proof problem from Arthur Engel: Consider an $m \times n$ rectangle, what is the minimum number of $1 \times 1$ tiles that are needed to be colored such that the remaining portion cannot be covered by L-Tetromino.
I tried to color rows alternatively as 'a' and 'b', but don't seem to be getting anywhere. Can anyone please help? (Please try to be explanative as I am not very good at coloring proofs.)