MathDB

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

Problem Statement