Hardest in ARO 2008
Source: ARO 2008, Problem 11.8
June 11, 2008
inductionsymmetrymodular arithmeticcombinatorial geometrycombinatorics unsolvedcombinatorics
Problem Statement
In a chess tournament 2n\plus{}3 players take part. Every two play exactly one match. The schedule is such that no two matches are played at the same time, and each player, after taking part in a match, is free in at least next (consecutive) matches. Prove that one of the players who play in the opening match will also play in the closing match.