IMO 2008 Shortlist C1
In the plane we consider rectangles whose sides are parallel to the coordinate axes and have positive length. Such a rec...
Category: Combinatorics
Problem
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 B1,...,Bn such that Bi and Bj intersect if and only if i 6≡ j ± 1 (mod n).