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IMC 2017 Problem 4

Source:

August 2, 2017
imc 2017IMCcombinatoricsapproximationProbabilistic Method

Problem Statement

There are nn people in a city, and each of them has exactly 10001000 friends (friendship is always symmetric). Prove that it is possible to select a group SS of people such that at least n2017\frac{n}{2017} persons in SS have exactly two friends in SS.
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