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 $n$, ($1 < n < 10$). After that Bogdan says the number $m$, ($m \ne n, 1 < m < 10$). 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
Problem
Source: 2018 Romania JBMO TST 5.3
Tags: game, winning strategy, combinatorics, game strategy