MathDB

Find the largest positive integer

n

with the following property: there are rectangles

A_1, ... , A_n

and

B_1,... , B_n,

on the plane , each with sides parallel to the axis of the coordinate system, such that the rectangles

A_i

and

B_i

are disjoint for all

i \in \{1,..., n\}

, but the rectangles

A_i

and

B_j

have a common point for all

i, j \in \{1,..., n\}

i \ne j

.
Note: By points belonging to a rectangle we mean all points lying either in its interior, or on any of its sides, including its vertices

Problem Statement