Mini Lights Out

There are several variants of Merlin's Magic Square puzzle. It is called "Mini Lights Out" to distinguish it from the 5×5 puzzle, which we'll present elsewhere. The one below is played on a 4×4 board wrapped on a torus. That is, the uppermost and lowermost rows are considered neighbors and likewise the leftmost and rightmost columns are considered neighbors. The task is to switch all the buttons off. Each button is embedded into a neighborhood of five buttons according to the 4-connectedness rules. A button's neighborhood includes the button itself and its vertical and horizontal neighbors. All neighborhoods on the torus consist of five buttons. When a button is pressed, all the buttons in its neighborhood are affected and change their states.

The Theory

Copyright © 1996-2008 Alexander Bogomolny