Lights Out was an electronic game released by Tiger Electronics in 1995. The game consists of a 5 by 5 grid of lights. When the game starts, a random number or a stored pattern of these lights is switched on. Pressing any of the lights will toggle it and the adjacent lights. The goal of the puzzle is to switch all the lights off, preferably with as few button presses as possible.
Here, or below, you can play a 3 x 3 version on Geogebra (courtesy of Stephen Jull and Yin Su).
One method to solve – Light Chasing
“Light chasing” is a method similar to Gaussian elimination which always solves the puzzle (if a solution exists), although with the possibility of many redundant steps. In this approach, rows are manipulated one at a time starting with the top row. All the lights are disabled in the row by toggling the adjacent lights in the row directly below. The same method is then used on the consecutive rows up to the last one. The last row is solved separately, depending on its active lights.
Here is a worksheet showing all the possibilities (effectively) for the last row. Can you solve them all, and hence solve any 3×3 grid?