### IMO 2014 problem 6

Kvaliteta:

Avg: 0.0Težina:

Avg: 0.0 A set of line sin the plane is in

*general position*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 area; we call these its*finite regions*. 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.*Note:*Results with replaced by will be awarded points depending on the value of the constant .Source: International Mathematical Olympiad 2014, day 2