Školjka

%V0 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