Imagine a “Lights Out” board that starts with all the lights off. A plan that is not empty (it has at least one button in it) is called quiet if, after pressing all the buttons in the plan, the board ends up all off again (remember that plans can’t have buttons being pressed twice). Now take a \(3\times 2\) “Lights Out” board. Can you find two different ways to turn every light on? How can this help you to discover a quiet plan?