Question 67
Let $m$ and $n$ be positive integers greater than 1. In each 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 the bottom-right unit squares;
(3) flip the coin in **either** the top-right or the 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 the bottom-right unit squares;
(3) flip the coin in **either** the top-right or the 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.