2. In a beach soccer tournament, 17 teams participate, and each team plays against each other exactly once. Teams are awarded 3 points for a win in regular time, 2 points for a win in extra time, and 1 point for a win on penalties. The losing team does not receive any points. What is the maximum number of teams that can accumulate exactly 5 points?
Answer: 11.

Sketch of the solution. Estimation. Let $n$ teams have scored exactly 5 points each. The total points include all points scored by these teams in matches against each other (at least 1) and possibly in matches against other teams: $5 n \geq(n-1) n / 2$. Hence, $n \leq 11$.

Example: Place eleven teams in a circle, and let each team win against the five teams following them in a clockwise direction by penalty. The remaining teams lost to them.

Criteria. Example without estimation: 2 points. Estimation without example: 4 points.