MathDB

5

Part of 1986 Polish MO Finals

Problems(1)

chess tournament with 2n players, at most n^2 matches

Source: 1986 Polish MO Finals p5

1/21/2020
There is a chess tournament with 2n2n players (n>1n > 1). 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 n2n^2 matches. Conversely, show that if there are at most n2n^2 matches, then it is possible to arrange them so that we cannot find three players who all play each other.
combinatorics