MathDB

1

Part of 2023 Greece JBMO TST

Problems(1)

student that has at least 10 friends

Source: 2023 Greece JBMO TST P1

5/17/2024
A class has 2424 students. Each group consisting of three of the students meet, and choose one of the other 2121 students, A, to make him a gift. In this case, A considers each member of the group that offered him a gift as being his friend. Prove that there is a student that has at least 1010 friends.
combinatorics