1. The problem statement, all variables and given/known data Two players: A and B. Players can take 1 or 2 stones per turn. The player who takes the last stone wins. The question is: is there any winning strategy with 5 stones?, does it change with 1000 stones?. 2. Relevant equations None. 3. The attempt at a solution If there are 5 stones player A has a winning strategy if he takes 2 stones in his first turn. 3 stones left, so B can take 1 or 2 but in any case there are available stones and A wins. If there are 1000 stones I don't know.