[ Symmetric Strategy ]

On an $8 \times 8$ board, two players take turns coloring cells so that no three colored cells form a corner. The player who cannot make a move loses. Who wins with correct play?
Apply a symmetric strategy.

## Solution

The second player can always move symmetrically to the first (relative to the center of the board). Then, on their turn, a corner cannot be filled - otherwise, it would have appeared on the previous turn. This means the second player will win.

## Answer

Second.