BG-MO 1984 Problem 3

Points $P_1,P_2,\ldots,P_n,Q$ are given in space $(n\ge4)$ , no four of which are in a plane. Prove that if for any three distinct points $P_\alpha,P_\beta,P_\gamma$ there is a point $P_\delta$ such that the tetrahedron $P_\alpha P_\beta P_\gamma P_\delta$ contains the point $Q$ , then $n$ is an even number.