There are $2016$ 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 $2013$ participants who faced everyone else.
Problem
Source: OLCOMA Costa Rica National Olympiad, Final Round, 2016 Shortlist LR2 day1 (logical reasoning)
Tags: combinatorics