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 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 for which a balanced tournament with teams exists.