MathDB

Let

n \geq 5

be an integer. Consider

n

squares with side lengths

1, 2, \dots , n

, respectively. The squares are arranged in the plane with their sides parallel to the

x

and

y

axes. Suppose that no two squares touch, except possibly at their vertices. Show that it is possible to arrange these squares in a way such that every square touches exactly two other squares.

Problem Statement