2005 IMO Shortlist S20

Suppose we have a $n$ -gon. Some $n-3$ diagonals are coloured black and some other $n-3$ diagonals are coloured red (a side is not a diagonal), so that no two diagonals of the same colour can intersect strictly inside the polygon, although they can share a vertex. Find the maximum number of intersection points between diagonals coloured differently strictly inside the polygon, in terms of $n$ .

*Proposed by Alexander Ivanov, Bulgaria*

假设我们有一个 $n$ 边形。一些$n-3$对角线被涂成黑色，一些其他$n-3$对角线被涂成红色(边不是对角线)，因此相同颜色的两条对角线不能在多边形内部严格相交，尽管它们可以共享一个顶点。求多边形内部严格不同颜色的对角线之间交点的最大数量，以 $n$ 为单位。

*由保加利亚亚历山大·伊万诺夫提议*