MathDB
max n for which a balanced tournament with n teams exists

Source: Dutch NMO 2021 p2

December 28, 2021
combinatorics

Problem Statement

We consider sports tournaments with n4n \ge 4 participating teams and where every pair of teams plays against one another at most one time. We call such a tournament balanced if any four participating teams play exactly three matches between themselves. So, not all teams play against one another. Determine the largest value of nn for which a balanced tournament with nn teams exists.