A chip is placed on a chessboard. Two players take turns moving the chip to an adjacent side cell. It is forbidden to place the chip on a field it has already visited. The player who cannot make the next move loses. Who wins with correct play?

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Match the second player's move with a corresponding move of the first player.

## Solution

We will divide the board into dominoes $1 \times 2$. The strategy for the first player: if before the first player's move, the token is in one of the cells belonging to a certain domino, then by their move, the first player moves it to the other cell of the same domino. Note that after the first player's move, all allowed cells are again divided into dominoes. This means that the first player will always be able to make a move, adhering to their strategy, and therefore will not lose.

## Answer

First.