Let
![P_1](/media/m/a/8/8/a886eaf7832af6b6b5f56f0ec9a97490.png)
be a convex polyhedron with vertices
![A_1,A_2,\ldots,A_9](/media/m/2/6/5/265659c9e1510b2a472d6350f22487e3.png)
. Let
![P_i](/media/m/5/2/a/52aac5a799a979529859020a68515b1b.png)
be the polyhedron obtained from
![P_1](/media/m/a/8/8/a886eaf7832af6b6b5f56f0ec9a97490.png)
by a translation that moves
![A_1](/media/m/5/a/6/5a6ce1347567551c02239ff8d4ebee67.png)
to
![A_i](/media/m/5/f/0/5f0935569a883b13bb70b83ea33eee14.png)
. Prove that at least two of the polyhedra
![P_1,P_2,\ldots,P_9](/media/m/d/f/a/dfa24b27ad99341705981283010a068f.png)
have an interior point in common.
%V0
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.