Question 87
Alina and Bogdan play the following game. They have a heap and $330$ stones in it. They take turns. In one turn it is allowed to take from the heap exactly $1$, exactly $n$ or exactly $m$ stones. The player who takes the last stone wins. Before the beginning Alina says the number $n$, ($1 \lt n \lt 10$). After that Bogdan says the number $m$, ($m \neq n$, $1 \lt m \lt 10$). Alina goes first. Which of the two players has a winning strategy? What if initially there are $2018$ stones in the heap?
Adapted from a Belarus Olympiad problem
Adapted from a Belarus Olympiad problem