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p players, n games, out of 3, 2 haven't played => n<=p²/4

Source: Bundeswettbewerb Mathematik 1972, round 2, problem 4

May 1, 2007
combinatorics proposedcombinatorics

Problem Statement

p>2p>2 persons participate at a chess tournament, two players play at most one game against each other. After nn games were made, no more game is running and in every subset of three players, we can find at least two that havem't played against each other. Show that n≤p24n \leq \frac{p^{2}}4.
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