(a) In Example 2.36, suppose that all of the lights are initially off. Show that it is possible to push the switches in some order so that the lights are off, dark blue, and light blue, in that order.
(b) Show that it is possible to push the switches in some order so that the lights are light blue, off, and light blue, in that order.
(c) Prove that any configuration of the three lights can be achieved.