Question 111
Let $m, n \geq 2$ be natural numbers. We have four colours and want to colour every cell of an $m \times n$ rectangle with one of them, so that all four colours occur in every $2 \times 2$ square. How many different ways are there to do this?
Remark: We count two ways as different if there is at least one cell that received different colours.
Remark: We count two ways as different if there is at least one cell that received different colours.