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Part of 2014 Dutch Mathematical Olympiad

Problems(1)

no of teams at a volleyball tournament can be 7, but cannot be 6

Source: Dutch NMO 2014 p3

9/7/2019
At a volleyball tournament, each team plays exactly once against each other team. Each game has a winning team, which gets 11 point. The losing team gets 00 points. Draws do not occur. In the nal ranking, only one team turns out to have the least number of points (so there is no shared last place). Moreover, each team, except for the team having the least number of points, lost exactly one game against a team that got less points in the final ranking. a) Prove that the number of teams cannot be equal to 66. b) Show, by providing an example, that the number of teams could be equal to 77.
combinatoricsTournament