Question 72
A configuration of $4027$ points is called Colombian if $2013$ points are red, $2014$ points are blue, and no three points are collinear. A finite set of lines divides the plane into regions. Such a set is good for a Colombian configuration if:
- No line passes through a point of the configuration.
- No region contains points of the same colour.
Determine the smallest natural number $k$ such that every Colombian configuration of $4027$ points has a good set of $k$ lines.
- No line passes through a point of the configuration.
- No region contains points of the same colour.
Determine the smallest natural number $k$ such that every Colombian configuration of $4027$ points has a good set of $k$ lines.