DE-BUNDESWETTBEWERB 2011 Problem 7
- Round 2
When preparing for a competition with more than two participating teams two of them play against each other at most once. When looking at the game plan it turns out: (1) If two teams play against each other, there are no more team playing against both of them. (2) If two teams do not play against each other, then there is always exactly two other teams playing against them both. Prove that all teams play the same number of games.
Dataset text AI-MO AoPS. Quoted with source.
Official text: Bundeswettbewerb Mathematik 2011 official paper, page 1.
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