Home > Combinatorics, Geometry, IMO, Olympiad > IMO 2014 Problem 6

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

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