IMO Shortlist 1990 problem 3


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2. travnja 2012.
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Let n \geq 3 and consider a set E of 2n - 1 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 E. Find the smallest value of k so that every such coloring of k points of E is good.
Izvor: Međunarodna matematička olimpijada, shortlist 1990