Kovalzhi V.K.

On an $8 \times 8$ board, two identical chips are placed in cells a1 and c3. Pete and Vasya take turns, with Pete starting first. On their turn, a player selects any chip and moves it either vertically upwards or horizontally to the right by any number of cells. The player who moves a chip to cell h8 wins. Who among the players can always win, regardless of how the opponent plays? Only one chip can occupy a cell at a time, and jumping over a chip is not allowed.

![](https://cdn.mathpix.com/cropped/2024_05_06_61f459f9e45cb4d6ceb6g-27.jpg?height=420&width=412&top_left_y=1299&top_left_x=823)
Vasya will make sure that Petya is the first to jump to the top or right line. As soon as this happens, Vasya will move this piece to h8 and win. Before this, Vasya adheres to the following strategy.

Initially, the pieces are on the diagonal a1 - h8, not adjacent. Petya escapes from it, and Vasya, if possible, returns this piece to the diagonal, maintaining the specified situation. Vasya will not be able to do this only when the pieces end up in the same or adjacent lines. Then Vasya will make a move so that the pieces form a domino. It is clear that this is possible. After this, Vasya will maintain the domino, that is, repeat Petya's move with the other piece. Eventually, Petya will be the first to jump to the top or right line.

## Answer

Vasya.