Mathematical and Physical Journal
for High Schools
Issued by the MATFUND Foundation
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Problem A. 458. (September 2008)

A. 458. In space, n+1 points P1,P2,...,Pn and Q are given, n\ge4, 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

(5 pont)

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.

Problems in Mathematics of KöMaL, September 2008