chess tournament with 2n players, at most n^2 matches
Source: 1986 Polish MO Finals p5
January 21, 2020
combinatorics
Problem Statement
There is a chess tournament with players (). There is at most one match between each pair of players. If it is not possible to find three players who all play each other, show that there are at most matches. Conversely, show that if there are at most matches, then it is possible to arrange them so that we cannot find three players who all play each other.