A very hard problem !
Source: Unrevealed source
June 12, 2006
combinatoricsExtremal combinatoricsColoringpolygondiagonalsIMO Shortlist
Problem Statement
Suppose we have a -gon. Some diagonals are coloured black and some other 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 .Proposed by Alexander Ivanov, Bulgaria