I have the following problem:
I'm given convex polygon with 18 vertices. It is known that no 3 diagonals of the polygon intersect in a single point.
How many points of intersection of the diagonals has a polygon?
I've found this article, that is very near to my problem, but it is about regular polygon, where diagonals can intersect more than 2 times in one point. It seems to me that my problem has more complex solution.
Can you give me any hint how to solve this problem for convex polygon?