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Every student is sitting next to a friend on both sides

Source: Turkey TST 2009, Problem 6

April 5, 2009
combinatorics unsolvedcombinatorics

Problem Statement

In a class of n≥4 n\geq 4 some students are friends. In this class any n \minus{} 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 n students can not be seated in that way. Prove that the minimum value of n n is 10 10.
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