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Dutch Mathematical Olympiad
2021 Dutch Mathematical Olympiad
2
2
Part of
2021 Dutch Mathematical Olympiad
Problems
(1)
max n for which a balanced tournament with n teams exists
Source: Dutch NMO 2021 p2
12/28/2021
We consider sports tournaments with
n
≥
4
n \ge 4
n
≥
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
n
n
for which a balanced tournament with
n
n
n
teams exists.
combinatorics