10.2. Three people are playing table tennis, with the player who loses a game giving way to the player who did not participate in it. In the end, it turned out that the first player played 21 games, and the second - 10. How many games did the third player play?
Answer: 11.

Solution: According to the problem, the first player played 21 games, so there were at least 21 games in total. Out of any two consecutive games, the second player must participate in at least one, which means there were no more than \(2 \cdot 10 + 1 = 21\) games. Therefore, a total of 21 games were played, and the first player participated in all of them. In 10 games, he played against the second player, and in the remaining 11 games, he played against the third player. An example of such a tournament: the first player plays against the second player in games with even numbers, and against the third player in games with odd numbers.

Grading Criteria: If the answer is guessed and an example of the tournament is provided: 1 point. If it is noted that out of any two consecutive games, the second player must participate in at least one: 2 points. If an example of the tournament is not provided: minus 1 point.