Question 16
(USS 5) (IMO 2) Given a convex polyhedron $P_1$ with $9$ vertices $A_1,\ldots,A_9$, let us denote by $P_2,P_3,\ldots,P_9$ the images of $P_1$ under the translations mapping the vertex $A_1$ to $A_2,A_3,\ldots,A_9$, respectively. Prove that among the polyhedra $P_1,\ldots,P_9$ at least two have a common interior point.