A Python solver of the Lights Out game for a square board of arbitrary size n.
The solver works by inverting the adjacency matrix of a grid graph of the size of the board. The matrix is defined over the Galois Field GF(2), and the inversion is performed in this field using Gauss-Jordan elimination.
For some board sizes n (eg., n=5) the adjacency matrix is rank deficient. This means that for those sizes some initial configurations have no solution and some other configurations have several solutions. The solver determines if a given configuration is solvable. In that case, it finds the simplest solution, ie., the solution with the minimum number of movements. To do this, it computes a base of the right null space of the adjacency matrix.
The module lightsout.py implements the solver. The class lightsout.LighsOut offers a simple interface to the module. See the function lightsout.main for an example.
You can also try the Lights Out solver with a simple GUI using the script lightsoutgui.py. Execute the script with:
$ python lightsoutgui.py 5
The first parameter indicates the board size. If omitted, it defaults to 5.
The initial setup of the board is given by red and green lights. The dark marks indicate the keys the player must press to turn the green lights red.