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2016 participants in the Olcotournament of chess

Source: OLCOMA Costa Rica National Olympiad, Final Round, 2016 Shortlist LR2 day1 (logical reasoning)

September 22, 2021
combinatorics

Problem Statement

There are 20162016 participants in the Olcotournament of chess. It is known that in any set of four participants, there is one of them who faced the other three. Prove there is at least 20132013 participants who faced everyone else.