Question 58
A configuration of $4027$ points in the plane, of which $2013$ are red and $2014$ blue, with no three collinear, is called Colombian. Drawing some lines divides the plane into regions. A collection of lines is good for a Colombian configuration if:
- no line passes through a point of the configuration;
- no region contains points of both colors.
Find the smallest $k$ such that every Colombian configuration of $4027$ points has a good collection of $k$ lines.
- no line passes through a point of the configuration;
- no region contains points of both colors.
Find the smallest $k$ such that every Colombian configuration of $4027$ points has a good collection of $k$ lines.