Place any number of colored boxes on the infinite plane. You have to connect similarly colored boxes, so boxes of each color form a single cycle (each colored box is connected to two similarly colored boxes).
Given that boxes do not touch each other, prove that it is always possible to connect the boxes in this manner such that there are no intersections between the connecting lines.
Inspired by Connecting Colored Boxes. However, that problem is different in nature because it is contained in a finite plane and some boxes are on the edge of that plane.