IMO 2014 problem 6

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Dodao/la: arhiva
Sept. 21, 2014
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 n, in any set of n lines in general position it is possible to colour at least \sqrt{n} of the lines blue in such a way that none of its finite regions has a completely blue boundary.

Note: Results with \sqrt{n} replaced by c \sqrt{n} will be awarded points depending on the value of the constant c.
Source: International Mathematical Olympiad 2014, day 2