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School principal promotes social interactions

Source: Turkey Junior National Olympiad 2022 P2

December 23, 2022
combinatorics

Problem Statement

In a school with 101101 students, each student has at least one friend among the other students. Show that for every integer 1<n<1011<n<101, a group of nn 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.