5. Given a grid board $3 \times 2021$ (3 cells vertically and 2021 cells horizontally) and an unlimited supply of cardboard strips $1 \times 3$. Petya and Vasya play the following game. They take turns placing the strips on the board (cell by cell) without overlapping, one strip per turn. Petya places his strips horizontally, while Vasya places his strips vertically. The player who cannot make a move loses, and Petya starts. Who of the players can ensure their victory regardless of the opponent's actions?
# Answer: Petya

Solution. Since there are a total of $3 \cdot 2021$ cells on the board, both players together will make no more than 2021 moves. We will show how Petya should act to win. He will mentally divide the board into 673 squares of $3 \times 3$ and one rectangle of $2 \times 3$. With his first moves, Petya will place the strips in the squares where nothing has been placed yet. He will follow this strategy until it is no longer possible. Since Vasya can occupy no more than one square with his move, Petya will make no fewer than 337 moves. In the rectangles occupied by Petya's strips, Vasya will not be able to move. Therefore, Petya can make at least $2 \cdot 337$ more moves. Thus, in total, he will be able to make no fewer than $337 + 2 \cdot 337 = 1011$ moves. But this is more than half of the total number of possible moves. Therefore, for each move Vasya makes, Petya will have the opportunity to respond, and if Vasya does not lose earlier, after Petya's 1011th move, the board will be completely covered and Vasya will not be able to move.