IMO Shortlist 2008 problem C1
Kvaliteta:
Avg: 0,0Težina:
Avg: 6,0 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
for which there exist
boxes
,
,
such that
and
intersect if and only if
.
Proposed by Gerhard Woeginger, Netherlands
![n](/media/m/a/e/5/ae594d7d1e46f4b979494cf8a815232b.png)
![n](/media/m/a/e/5/ae594d7d1e46f4b979494cf8a815232b.png)
![B_1](/media/m/5/d/9/5d9518a7c0ead344571aac61b51bb25c.png)
![\ldots](/media/m/5/8/5/58542f3cc6046ef3889f8320b7487d60.png)
![B_n](/media/m/9/4/9/949aba6eae76461763dec24a3a6fa974.png)
![B_i](/media/m/1/4/5/14587d3e0ae49b15b1042914a7f802f4.png)
![B_j](/media/m/4/e/8/4e84bacb4fc45a510492f1137862fc72.png)
![i\not\equiv j\pm 1\pmod n](/media/m/2/9/0/2902e848755e5d5521c57d59c583cfcb.png)
Proposed by Gerhard Woeginger, Netherlands
Izvor: Međunarodna matematička olimpijada, shortlist 2008