In this GeoGebra book you can play and solve different logical problems, all based on the idea of "turning off" all the squares of a totally or partially illuminated board. The game became popular when it was marketed under the name of Lights Out.
The difficulty is that when you click on any square, in addition to its state, it changes the state of its adjacent squares.
The resolution of this problem follows the method exposed in this article of number 40 (June 2002) of Suma magazine (Spanish magazine on the teaching and learning of mathematics):
You can read a translation here:
If you want to play on greater boards, I published in 2001 the following Java applets that allow you to propose and solve problems with rectangular tables with greater dimensions (up to 50x50), number of states in each box between 2 and 7, and various surfaces besides the plane, such as the cylinder, the torus, the Moebius strip, the Klein bottle and the cross-cap (attention: today, Java applets are only visible with the IExplorer browser, and you will need to add, as a security exception in the Java console, the following address):