The overall game consists of twenty-five copies of Buttons and Lights. In each copy of Buttons and Lights, there are three lights and three buttons. Pushing the first button in each group toggles the first light; pushing the second button in each group interchanges the first and second lights; and pushing the third button in each group interchanges the second and third lights. Initially, the lights are all off. The goal is to turn on all of the lights in the thirteenth group. The settings of the other lights are irrelevant.