The problem is like the following.
Let $n$ blue lines, no two of which are parallel and no three concurrent, be drawn on a plane.
An intersection of two blue lines is called a blue point.
Through any two blue points that have not already been joined by a blue line, a red line is drawn.
An intersection of two red lines is called a red point,
and an intersection of red line and a blue line is called a purple point.
What is the maximum possible number of purple points?
This is from Turkey National Olympiad Second Round 1994.
I have no solution and can't come up with anything.
Thank you in advance.