Four students stand in a large circle and four loosely tangled ropes are thrown in the center. Each student grabs 2 rope ends and the goal is to determine if the ropes can be untangled to form a planar graph, i.e. an arrangement of the students (vertices) and ropes (edges) so that no two ropes cross. A fifth student (the director) directs the movement of the other students using two operations: (1) The director may tell any student to move to any desired location on the floor. (2) The director may remove one rope end from one student, untangle that rope and return the end to that student. With 4 students and 4 ropes, they can always untangle to a planar graph.
The students then repeat the process with 5 students and 5 ropes, 6 students and 6 ropes, etc. until they begin to get non-planar graphs.