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JBMO TST Bosnia and Herzegovina 2022 P4

Source: JBMO TST Bosnia and Herzegovina 2022

May 21, 2022
JBMO TSTcombinatoricsnational olympiad

Problem Statement

Some people know each other in a group of people, where "knowing" is a symmetric relation. For a person, we say that it is socialsocial if it knows at least 2020 other persons and at least 22 of those 2020 know each other. For a person, we say that it is shyshy if it doesn't know at least 2020 other persons and at least 22 of those 2020 don't know each other. Find the maximal number of people in that group, if we know that group doesn't have any socialsocial nor shyshy persons.