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(339) 1

Part of 1992 Tournament Of Towns

Problems(1)

TOT 339 1992 Autumn O J1 101 chess players in tournaments

Source:

6/10/2024
There are 101101 chess players who participated in several tournaments. There was no tournament in which all of them participated. Each pair of these 101101 players met exactly once during these tournaments. Prove that one of them participated in no less than 1111 tournaments. (Assume that each pair of participants in each tournament plays each other once in that tournament).
(A Andjans, Riga)
combinatorics