3n coloured lines on the plane (2015 OMCS #2)
Source:
May 16, 2015
combinatorial geometrycombinatoricsgeometry
Problem Statement
lines are drawn on the plane (), such that no two of them are parallel and no three of them are concurrent. Prove that, if of the lines are coloured red and the other 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.