Problem

Source:

Tags: combinatorial geometry, combinatorics, geometry



3n lines are drawn on the plane (n>1), such that no two of them are parallel and no three of them are concurrent. Prove that, if 2n of the lines are coloured red and the other n lines blue, there are at least two regions of the plane such that all of their borders are red. Note: for each region, all of its borders are contained in the original set of lines, and no line passes through the region.