IMO 1971 P2

Discussion on International Mathematical Olympiad (IMO)
User avatar
samiul_samin
Posts: 1004
Joined: Sat Dec 09, 2017 1:32 pm

IMO 1971 P2

Unread post by samiul_samin » 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.

Post Reply