1989 IMO Problems/Problem 5

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Let $n\geq3$ and consider a set $E$ of $2n−1$ (Error compiling LaTeX. ! Package inputenc Error: Unicode char \u8:− not set up for use with LaTeX.) distinct points on a circle. Suppose that exactly $k$ of these points are to be colored black. Such a coloring is “good” if there is at least one pair of black points such that the interior of one of the arcs between them contains exactly $n$ points from set $E$. Find the smallest value of $k$ such that every such coloring of $k$ points of $E$ is good.

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