Problem 5. Petya and Vasya are playing a game. On the far left field of a strip consisting of 13 cells, there is a pile of 2023 stones. The players take turns, with Petya starting. Each player, on their turn, can move any stone one or two fields to the right. The player who first places any stone on the far right cell wins. Who among the boys can win regardless of the opponent's play? (20 points)

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Answer: Vasya.

Solution: After each of Petya's moves, Vasya should move the same stone by 1 if Petya moved it by 2, and vice versa. With this strategy, Vasya will always place the stone on a field numbered 4, 7, 10, or 13, while Petya will never be able to move to such a field. Since the game allows only a finite number of moves, Vasya will win.

Criteria: Only the answer with an incorrect or missing strategy - 0 points.