Question 24
Arnold and Bernold play the following game in a $m \times n$ board: Arnold chooses one of its cells and places a knight on it. Then Bernold and Arnold move the knight alternately, with the condition that the knight visits a cell at most once. The player who is unable to move the knight loses. Determine, in terms of $m$ and $n$, which player has the winning strategy.
*Remark*: the knight always moves two cells in a row or a column and then one cell in the perpendicular direction.
*Remark*: the knight always moves two cells in a row or a column and then one cell in the perpendicular direction.