Question 12
Let $m, n \ge 2$. You want to completely cover an $m \times n$ board without any gaps or overlaps, using only pieces of the following two types:
Type A
Type B
Each type A piece must cover exactly 4 squares on the board, and each type B piece must cover exactly 5 squares on the board. Rotating the pieces is allowed. Determine all pairs $(m, n)$ for which this can be done.
Type A
Type B
Each type A piece must cover exactly 4 squares on the board, and each type B piece must cover exactly 5 squares on the board. Rotating the pieces is allowed. Determine all pairs $(m, n)$ for which this can be done.