Question 16
Consider an $a \times b$ board, with $a$ and $b$ integers greater than or equal to $2$. Initially its cells are coloured white and black like a chessboard. The allowed operation consists of choosing two cells with a common side and recolouring them as follows: a white cell becomes black; a black cell becomes green; a green cell becomes white.
Determine for which values of $a$ and $b$ it is possible, by a sequence of allowed operations, to make all the cells that were initially white end up black and all the cells that were initially black end up white.
**CLARIFICATION:** Initially there are no green cells, but they appear after the first operation.
Determine for which values of $a$ and $b$ it is possible, by a sequence of allowed operations, to make all the cells that were initially white end up black and all the cells that were initially black end up white.
**CLARIFICATION:** Initially there are no green cells, but they appear after the first operation.