Question 8
Let $m$ and $n$ be positive integers greater than 1 . In each unit square of an $m \times n$ grid lies a coin with its tail-side up. A move consists of the following steps:
1. select a $2 \times 2$ square in the grid;
2. flip the coins in the top-left and bottom-right unit squares;
3. flip the coin in either the top-right or bottom-left unit square.
Determine all pairs $(m, n)$ for which it is possible that every coin shows head-side up after a finite number of moves.
1. select a $2 \times 2$ square in the grid;
2. flip the coins in the top-left and bottom-right unit squares;
3. flip the coin in either the top-right or bottom-left unit square.
Determine all pairs $(m, n)$ for which it is possible that every coin shows head-side up after a finite number of moves.