3. Kolya and Olya place bishops on a $5 \times 5$ board so that they do not attack each other. The player who cannot make a move loses. Kolya moves first, but he is not allowed to place a bishop in the center of the board on his first move. Who will win with the best play from both sides?
Answer: Kolya will win.

Solution. We will use a chessboard coloring (center - black). Kolya can make the first move, for example, to the cell c1. Thereafter, when Olya moves to a white cell, Kolya responds symmetrically (such a move will be valid; the position of the bishops on the white cells will remain symmetrical, allowing Kolya to continue using the "white-symmetric" strategy). As for the "black" moves, there will be only 2 in total: in response to a move to c3, Kolya will move to c5 (and vice versa), and for a move to a corner cell, Kolya will respond with a move to a non-corner cell on the other "black" diagonal (and vice versa).

Evaluation. Full solution - 7 points. Deduct 1-2 points for gaps in the justification of the winning strategy. Correct answer without justification - 0 points.

Note. Other winning strategies are possible. However, the first move to a corner loses.