Question 85
In the plane, $2005$ points were marked, no three of which are collinear. Straight lines were drawn through all the pairs 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 lines separating them is even. (We say that a line separates two points if none of those points belongs to it, and they lie in different half-planes with respect to it.)