International Mathematical Olympiad 2013 Problem 2
A configuration 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 configuration are collinear. By drawing some lines, the plane is divided into several regions. An arrangement of lines is good for a Colombian configuration if the following two conditions are satisfied:
- no line passes through any point of the configuration;
- no region contains points of both colours.
Find the least value of such that for any Colombian configuration of 4027 points, there is a good arrangement of lines.