2

Part of 2022 Turkey Junior National Olympiad

Problems(1)

School principal promotes social interactions

Source: Turkey Junior National Olympiad 2022 P2

In a school with

101

students, each student has at least one friend among the other students. Show that for every integer

1<n<101

n

students can be selected from this school in such a way that each selected student has at least one friend among the other selected students.