points
Source: Ukraine 2005 grade 10
July 28, 2009
combinatorics proposedcombinatorics
Problem Statement
On the plane are marked points, no three of which are collinear. A line is drawn through any two of the 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 lines separating them is even. (Two points are separated by a line if they lie in different open half-planes determined by the line).