2013 IMO Problems/Problem 2

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Problem

A confi�guration of $4027$ points in the plane is called Colombian if it consists of $2013$ red points and $2014$ blue points, and no three of the points of the confi�guration are collinear. By drawing some lines, the plane is divided into several regions. An arrangement of lines is good for a Colombian con�guration if the following two conditions are satis�fied: �**no line passes through any point of the con�guration; �**no region contains points of both colours. Find the least value of $k$ such that for any Colombian con�guration of $4027$ points, there is a good arrangement of $k$ lines.

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