KöMaL 2008 A458

In space, $n$+1 points $P_1$,$P_2$,...,$P_n$ and $Q$ are given, $n \ge$4, no four of which are in the same plane. It is known that for each triple of distinct points $P_i$, $P_j$ and $P_k$ one can find a point $P_l$ such that $Q$ is interior to the tetrahedron $P_i P_j P_k P_l$. Show that $n$ must be even.