Question 127
A board with $2 m$ rows and $2 n$ columns is given, where $m$ and $n$ are positive integers. You may place one pawn on a square of this board, but not on the bottom-left square or the top-right square. Then a snail starts a walk over the board. The snail starts in the bottom-left square and may move horizontally and vertically. The snail does not enter the square with the pawn, but otherwise wants to visit every square exactly once, with the top-right square as its end point. On which squares can you place the pawn so that the snail can succeed in its plan?