In a convex $2008$-gon some of the diagonals are coloured red and the rest blue, so that every vertex is an endpoint of a red diagonal and no three red diagonals concur at a point. It's known that every blue diagonal is intersected by a red diagonal in an interior point. Find the minimal number of intersections of red diagonals.
Problem
Source: 2008 Bulgarian Autumn Math Competition, Problem 11.3
Tags: combinatorics, convex polygon, Intersection diagonals