IMO Shortlist 1998 problem C6


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2. travnja 2012.
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Ten points are marked in the plane so that no three of them lie on a line. Each pair of points is connected with a segment. Each of these segments is painted with one of k colors, in such a way that for any k of the ten points, there are k segments each joining two of them and no two being painted with the same color. Determine all integers k, 1\leq k\leq 10, for which this is possible.
Izvor: Međunarodna matematička olimpijada, shortlist 1998