Question 36
We consider sports tournaments with $n \ge 4$ 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 $n$ for which a balanced tournament with $n$ teams exists.
Determine the largest value of $n$ for which a balanced tournament with $n$ teams exists.