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A regular polygon obtained on a circle from blue & red pts

Source: INMO 2016 Problem 4

January 17, 2016
combinatoricscombinatorics proposed

Problem Statement

Suppose 20162016 points of the circumference of a circle are colored red and the remaining points are colored blue . Given any natural number n≥3n\ge 3, prove that there is a regular nn-sided polygon all of whose vertices are blue.
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