Problem

Source: Turkey TST 2009, Problem 6

Tags: combinatorics unsolved, combinatorics



In a class of $ n\geq 4$ some students are friends. In this class any $ n - 1$ students can be seated in a round table such that every student is sitting next to a friend of him in both sides, but $ n$ students can not be seated in that way. Prove that the minimum value of $ n$ is $ 10$.