Tiger electronics now has an entire Lights Out series. The original version, solved by means of Linear Algebra by Feil and Anderson in October 1998 is a five by five grid of lights. Pressing a button results in a change of parity of that button and a change in parity of the north, south, east, and west neighbors of that light (if such neighbors exist). The object of the game is to get all of the lights turned off. Later, Tiger released its next version of the mind puzzle, Lights Out Cube, a cube in which the sides are three by three grids of lights. The parity-changing rule still applies, except this time if a light lies on the border of a face, pressing it will change all of its neighbors, including those on adjacent faces. Thus, in Lights Out Cube, pressing any button will always result in the change of parity of five buttons, itself and its four neighbors. Again, the game presents the user with a configuration of lights, some off and some on, and the objective is to turn all the lights out. We will present a complete solution to Lights Out Cube in a style similar to that used by Feil and Anderson; however, a lack in certain mathematical conveniences of matrices present in the original Lights Out solution will complicate the process for the cube of lights.
Tawney, J. Jacob
"Turning the Lights Out in Three Dimensions,"
Rose-Hulman Undergraduate Mathematics Journal: Vol. 1
, Article 2.
Available at: https://scholar.rose-hulman.edu/rhumj/vol1/iss1/2