Question 32
Let $p$ be a prime. We must design a tournament of $p$-parchís under these rules:
- There are $p^2$ players.
- Each game has $p$ players.
- The tournament is divided into rounds, and rounds into games. Each player plays one game, or none, in each round.
- By the end, each player has faced each other player exactly once.
Determine whether such a tournament is possible. If so, find the minimum number of rounds.
- There are $p^2$ players.
- Each game has $p$ players.
- The tournament is divided into rounds, and rounds into games. Each player plays one game, or none, in each round.
- By the end, each player has faced each other player exactly once.
Determine whether such a tournament is possible. If so, find the minimum number of rounds.