MathNet 2010 — Part 01 Question 129

There is a heap of $360$ stones. Nick and Mary play the following game. They, in turn (Mary is the first), remove the stones from the heap. Per move it is allowed to remove exactly $1$ or exactly $m$ or exactly $n$ stones. The player wins if he/she removes the last stone. Before the start Nick fixes the value of $n$ ($2 \le n \le 9$). After that Mary fixes the value of $m$ ($m \ne n, 2 \le m \le 9$) and begins the game.
Can somebody of the players fix his/her number to win if both of them play to win?
(V. Kaskevich)