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## IMO 2014 Problem 6

A set of lines in 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 ${\sqrt{n}}$ 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 ${c}$.

IMO 2014 Problem 6 (Day 2)

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1. July 10, 2014 at 8:33 am