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2021 points on a circle

Source: Turkey National Mathematical Olympiad 2020 P6

March 8, 2021
combinatorics

Problem Statement

20212021 points are given on a circle. Each point is colored by one of the 1,2,⋯ ,k1,2, \cdots ,k colors. For all points and colors 1≤r≤k1\leq r \leq k, there exist an arc such that at least half of the points on it are colored with rr. Find the maximum possible value of kk.
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