IMO 1971 P2
Posted: Sun Feb 10, 2019 7:29 pm
Consider a convex polyhedron $P_1$ with nine vertices $A_1, A_2, \cdots, A_9;$ let $P_i$ be the polyhedron obtained from $P_1$ by a translation that moves vertex $A_1$ to $A_i(i=2,3,\cdots, 9).$ Prove that at least two of the polyhedra $P_1, P_2,\cdots, P_9$ have an interior point in common.