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Friends at a meeting

Source: 2021 Centroamerican and Caribbean Mathematical Olympiad, P4

August 12, 2021
combinatoricsgraph theorycliqueClique number

Problem Statement

There are 20212021 people at a meeting. It is known that one person at the meeting doesn't have any friends there and another person has only one friend there. In addition, it is true that, given any 44 people, at least 22 of them are friends. Show that there are 20182018 people at the meeting that are all friends with each other. Note. If AA is friend of BB then BB is a friend of AA.
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