4. Along a circle, 33 points are placed at equal distances from each other. Anya and Borya take turns painting one point either blue or red (they can paint any previously unpainted point). The player loses if, after their move, two adjacent points of the same color appear. Who will win with correct play if Anya goes first?
Answer: Borya.

Solution. Let's look at how the colored points are arranged when no new moves are possible. If there are two adjacent uncolored points, one of them can be colored. Therefore, in the final position, all points are divided into groups of consecutive colored points, separated by single uncolored points. Within each group, the colors of the points alternate. If one group ends with a blue (red) point, the next group begins with a red (respectively blue) point, otherwise the point between the indicated groups can be colored. Therefore, if we remove the uncolored points, we get an alternation of red and blue points - meaning there are an equal number of red and blue points, and the total number of colored points is even. It remains to note that after any move by the first player, we have an odd number of colored points, and after any move by the second player, their number becomes even. Therefore, the final position arises after the second player's move. He wins. His strategy is very simple: not to make obviously losing moves.

Scoring. 14 points for a correct solution.