IMO Shortlist 2000 problem C5


Kvaliteta:
  Avg: 0,0
Težina:
  Avg: 8,0
Dodao/la: arhiva
2. travnja 2012.
LaTeX PDF
A number of n rectangles are drawn in the plane. Each rectangle has parallel sides and the sides of distinct rectangles lie on distinct lines. The rectangles divide the plane into a number of regions. For each region R let v(R) be the number of vertices. Take the sum \sum v(R) over the regions which have one or more vertices of the rectangles in their boundary. Show that this sum is less than 40n.
Izvor: Međunarodna matematička olimpijada, shortlist 2000