IMO Shortlist 2008 problem G5
Kvaliteta:
Avg: 0,0Težina:
Avg: 8,0 Let and be integers with . Consider a set of lines in the plane such that no two of them are parallel and no three have a common point. Denote by the set of intersections of lines in . Let be a point in the plane not lying on any line of . A point is colored red if the open line segment intersects at most lines in . Prove that contains at least red points.
Proposed by Gerhard Woeginger, Netherlands
Proposed by Gerhard Woeginger, Netherlands
Izvor: Međunarodna matematička olimpijada, shortlist 2008