IMO Shortlist 2008 problem C1

  Avg: 0,0
  Avg: 6,0
Dodao/la: arhiva
2. travnja 2012.
In the plane we consider rectangles whose sides are parallel to the coordinate axes and have positive length. Such a rectangle will be called a box. Two boxes intersect if they have a common point in their interior or on their boundary. Find the largest n for which there exist n boxes B_1, \ldots, B_n such that B_i and B_j intersect if and only if i\not\equiv j\pm 1\pmod n.

Proposed by Gerhard Woeginger, Netherlands
Izvor: Međunarodna matematička olimpijada, shortlist 2008