MathNet 2010 — Part 01 Question 121

There is a heap of $25201$ stones. Nick and Mary play the following game. They, in turn, remove the stones from the heap. Per move it is allowed to remove either exactly $m$ or exactly $n$ stones. The player wins if he removes the last stone. If the last stone can not be removed by any of the players, then the result of the game is a draw. Before the start Nick fixes the value of $n$ ($1 \le n \le 10$) and defines the player to start the game. After that Mary fixes the value of $m$ ($m \ne n, 1 \le m \le 10$), then the game starts.
Can somebody of the players fix his/her number to win if both of them play to win?
(V. Kaskevich)