3. There are 2021 minuses written on the board. Petya and Vasya are playing a game. A move consists of either replacing one minus with a plus, or erasing one plus and one minus, or replacing two minuses with three pluses. They take turns, with Petya going first, and the one who cannot make a move loses. Who will win with correct play?
Answer: Petya will win.

Solution. Petya's first move should be to replace two minuses with three pluses. As a result of this move, the number of minuses on the board will become divisible by 3. After any of Vasya's moves, the number of minuses will change by 1 or 2, and Petya will be able to move in such a way that the number of minuses becomes divisible by 3 again - for this, he only needs to replace 1 or 2 minuses with pluses.

By acting in this manner, Petya will ensure that after some of his moves, the number of minuses will become 0, and Vasya will not be able to make a move.