Problem A. 458. (September 2008)

A. 458. In space, n+1 points P₁,P₂,...,P_n and Q are given, n4, 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_iP_jP_kP_l. Show that n must be even.

Bulgarian competition problem

(5 pont)

Deadline expired on October 15, 2008.

Statistics:

9 students sent a solution.
5 points:	Éles András, Nagy 235 János, Nagy 314 Dániel, Nagy 648 Donát, Tomon István, Tossenberger Anna.
2 points:	1 student.
1 point:	1 student.
0 point:	1 student.

Problems in Mathematics of KöMaL, September 2008