Grubiks team is proud to present the best online Rubik’s Cube Solver! Faster, better, and supports more devices. 'Lights Out Puzzle.Update: New and improved version. On Wolfram|Alpha Lights Out Puzzle Cite this as:īarile, Margherita.

WhitmanĬollege Department of Mathematics. 'Linear Cellular AutomataĪnd the Garden-of-Eden.' Math. 'Maximization Versions of 'Lights Out' Games in GridsĪnd Graphs.' Congr. 'Simple Proofs to Three Parity Theorems.' Ars Combin. With unique solutions (counting boards having equivalent solutions by rotation or Removing solutions that are equivalent by rotation or reflection gives the distinct solutions illustrated above, of which there are 1, 1, 1, 5, 1, 1, 1, 1, 43, 1, 10,ġ, 1, 5, 1. Theīoard sizes with unique solutions (counting boards having equivalent solutions by

The numbers of solutions (ignoring rotation and reflection) for, 2. The above illustration shows all possible solutions For example, in the pattern shown above, it is impossible to turn off allĪs shown by Sutner (1989), going from all lights on to all lights off is always possible for any size square lattice. For example, going from lights all on to all off in theĬase, there are four possible solutions to the all-lights pattern, illustrated above. Multiple solutions are sometimes possible.

Or less are solvable for every possible starting pattern. In the language of linear algebra, they are theįor instance, the solvable patterns of the -lattice are illustrated above. In general, the solvable patterns of the lattice are those which are obtained from the no-light The matrix of the above system of equations has maximal rank (it is a matrix with nonzero determinant), the game on a -lattice is always solvable. ,, and (corresponding to the red dots in the figure above). It has exactly one solution: (, , ), which means that the game is solved by pressing the

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