IMO Shortlist 1971 problem 16


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April 2, 2012
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Let P_1 be a convex polyhedron with vertices A_1,A_2,\ldots,A_9. Let P_i be the polyhedron obtained from P_1 by a translation that moves A_1 to A_i. Prove that at least two of the polyhedra P_1,P_2,\ldots,P_9 have an interior point in common.
Source: Međunarodna matematička olimpijada, shortlist 1971