Changing the Rules

Many interesting puzzles can be created by altering the "rules" of Lights Out. We start with a recap of standard lights out. This puzzle is based on the Sigma+ game. You can see the graph that is used by clicking here.

The rest of this page is structured as follows:

Standard Lights Out

Changing the Graph

Making Other Changes

Standard Lights Out

Standard Lights Out is a simulation of the
sigma+ game using the graph shown here. This means that it is played on a 5x5 grid and that pressing any button affects its immediate vertical and horizontal neighbours.

Standard Lights Out has been implemented by the following games


Changing the graph

Many variants of Lights Out can be created simply by changing the underlying graph. The
Sigma+ game can be played on any directed graph so endless variations are possible. This section considers those that have been implemented in real games

Changing the size

The most obvious change to make is to vary the size of the grid. The effect that this has on the puzzle is described
here. This amounts to adding vertices (and edges) to the graph.

Standard Lights Out, but with a different size grid, has been implemented by the following games

Changing the Pattern

Another change that can be made is to alter the effect that pressing a button has. For example, Lights Out Deluxe has a mode whereby pressing a button changes the state of all the diagonal neighbours. Merlin's Magic Square uses a different pattern completely. This amounts to changing which vertices are connected by directed edges in the graph, as can be seen by examining the graph for Merlin's Magic Square (
click here).

A Lights Out type game, but with a different pattern has been implemented by the following games

Changing the Shape

Of course, the graph can also be changed much more radically. For example by taking the graph for standard lights out, but connecting the vertices at the sides to those on the opposite side, you can effectively play lights out on a Torus.

Games which play a Lights Out type game, but with a very different shape are


Making other changes

Not all the variants of Lights Out result simply from changing the underlying graph. Other rules can also be altered.

Restricting the Moves

In standard Lights Out, any button can be pressed at any time. This can be changed in several ways

Lit Only
In Lit Only games, only the buttons which are already lit can be pressed. This makes for a much more challenging puzzle. This variant was implemented as a computer program by Gary Watson called Flip. For more information
click here. Toggle
Lit Only variants of Lights Out have also been implemented in the following games

Toggle
The Toggle variant takes the Lit Only rule change a stage further. In this variant, the set of buttons that you are allowed to press changes after every move. On the first move only lit buttons can be pressed. On the second move, only unlit buttons can be pressed. On the third move you are back to pressing lit buttons again (and so on...)

The only games which has a toggle mode is

Changing the Number of States

The lights in standard Lights Out can be in one of two states: on or off. This can be altered to allow the lights to take three (or more) states. For example, in Lights Out 2000 The lights can either be off, green or red.

The only game which implements multi-state Lights Out is

Something Different