# Problem 10.2 (7 points)

Vasya, Petya, and 2020 other people stood in a circle, with Vasya and Petya not standing next to each other. Then Vasya chooses one of his two neighbors and "spots" them (taps them on the shoulder). Next, Petya does the same, followed by Vasya again, and so on. The person who is spotted leaves the circle (and the circle becomes smaller). The player who spots the other wins. Who will win with the correct play?
# Solution:

Neither player wants to create a gap of length 0 between them, as this would result in an immediate loss. Therefore, at some point, both gaps will contain only one person. By this point, $2020-2=2018$ moves will have been made (the last move was by the second player, Petya). Thus, Vasya is forced to create a gap of length 0, and Petya immediately "marks" it.

| Criteria | Points |
| :--- | :---: |
| Complete solution | 7 |
| Answer without justification or incorrect answer | 0 |

## Answer: The second player, Petya, will win.