colored points
Source: Ukraine 2005 grade 11
July 28, 2009
combinatorics proposedcombinatorics
Problem Statement
In space are marked points, no four of which are in the same plane. A plane is drawn through any three points. Show that the points can be painted in two colors so that for any two points of the same color the number of the drawn planes separating them is odd. (Two points are separated by a plane if they lie in different open half-spaces determined by the plane).