IMO Shortlist 2003 problem C2


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2. travnja 2012.
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Let D_1, D_2, ..., D_n be closed discs in the plane. (A closed disc is the region limited by a circle, taken jointly with this circle.) Suppose that every point in the plane is contained in at most 2003 discs D_i. Prove that there exists a disc D_k which intersects at most 7\cdot 2003 - 1 = 14020 other discs D_i.
Izvor: Međunarodna matematička olimpijada, shortlist 2003