Problem A. 458. (September 2008)
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 October 15, 2008.
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.