Let m and n be positive integers greater than 1. In each unit square of an m×n grid lies a coin with its tail side up. A move consists of the following steps.[*]select a 2×2 square in the grid;
[*]flip the coins in the top-left and bottom-right unit squares;
[*]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.Thanasin Nampaisarn, Thailand IMO ShortlistcombinatoricsAZE IMO TST