A. 458. In space, n+1 points P1,P2,...,Pn and Q are given, n4, no four of which are in the same plane. It is known that for each triple of distinct points Pi, Pj and Pk one can find a point Pl such that Q is interior to the tetrahedron PiPjPkPl. Show that n must be even.
Bulgarian competition problem
Deadline expired on 15 October 2008.