Question 86
In the space, $2005$ points were marked, none four of which lie in the same plane. Planes were drawn through all the triples of marked points. Prove that all the marked points can be colored into two colors in such a way that for any two points of the same color the number of the drawn planes separating them is odd. (We say that a plane separates two points if none of those points belongs to it, and they lie in different half-spaces with respect to it.)