MathDB

A finite set

M

of unit squares on the plane is considered. The sides of the squares are parallel to the coordinate axes and the squares are allowed to intersect. It is known that the distance between the centres of any pair of squares is no greater than

2

. Prove that there exists a unit square (not necessarily belonging to

M

) with sides parallel to the coordinate axes and which has at least one common point with each of the squares in

M

.
(A Andjans, Riga)

Problem Statement