Question 16
Let $n$ be a positive integer. Given an $n \times n$ board, the unit cell in the top left corner is initially coloured black, and the other cells are coloured white. We then apply a series of colouring operations to the board. In each operation, we choose a $2 \times 2$ square with exactly one cell coloured black and we colour the remaining three cells of that $2 \times 2$ square black.
Determine all values of n such that we can colour the whole board black.
Determine all values of n such that we can colour the whole board black.