MathDB

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.
[*]select a

2\times 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

Problem Statement