2008 IMO Shortlist C1

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 $i \not \equiv j \pm 1(\bmod n)$.

在平面中，我们考虑边与坐标轴平行且长度为正的矩形。这样的矩形将被称为盒子。如果两个盒子在其内部或边界上有公共点，则它们相交。找到存在$n$个框$B_{1}、\ldots、B_{n}$的最大$n$，使得$B_{i}$和$B_{j}$相交当且仅当$i \not \equiv j \pm 1(\bmod n)$。