My friend discovered this when we were in college, using the original lights out game. For any starting configuration, make a note of all the lights that are on. Press all of these lights (some of them will turn off as you press others, but be sure to press all the squares that were initially on). Repeat the above process from this new configuration (using the lights that are on now, not the ones that were on initially). All the lights are now off. (Okay, maybe not guaranteed as I haven't tried it on all possible configurations or proven it rigorously, but we never found one where it didn't work). Edit for clarity: obviously this doesn't work for ALL configurations (for example, one light on only). But it worked for all the original Lights Out game's configurations.