2014 IMO Problems
Problem
A set of lines in the plane is in 
if no two are parallel and no three pass through the same point. A set of lines in general position cuts the plane into regions, some of which have finite are; we call these its 
. Prove that for all sufficiently large 
, in any set of lines in general position it is possible to colour at least 
of the lines blue in such a way that none of its finite regions has a completely blue boundary.
