Problem

Source: 2023 Junior Macedonian Mathematical Olympiad P1

Tags: graph theory, combinatorics



In a group of kids there are $2022$ boys and $2023$ girls. Every girl is a friend with exactly $2021$ boys. Friendship is a symmetric relation: if A is a friend of B, then B is also a friend of A. Prove that it is not possible that all boys have the same number of girl friends. Proposed by the JMMO Problem Selection Committee