Problem A. 458. (September 2008)
A. 458. In space, n+1 points P_{1},P_{2},...,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_{i}P_{j}P_{k}P_{l}. Show that n must be even.
Bulgarian competition problem
(5 pont)
Deadline expired on 15 October 2008.
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