Lights Out (game)

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Lights Out is an electronic puzzle game, originally created by Hasbro. The game is a 5x5 grid of lights, and when the game starts, a sequence of these lights (random, or one of a set of stored puzzle patterns) are switched on. Pressing one of the lights will toggle it and the four adjacent lights between on and off. The aim of the game is to switch all the lights off.

A Lights Out game cartridge was shipped free along with many new Game.com units.

1 Strategy
- 1.1 Beyond 5x5
2 See also
3 External links

[edit] Strategy

The most common method to solve this puzzle is to start by wiping all the lights except for in the last or bottom row. This is done by pressing lights that are directly below lights that are turned on to cancel them out until only lights in the last row remain. Then the following table must be memorized:

Top row  produces  Bottom row
   A        ->       -BC-E
   B        ->       ABC--
   C        ->       AB-DE
   D        ->       --CDE
   E        ->       A-CD-

If we label the columns A through E this table tells us that if we press A in the top row then follow the steps to bring down all the lights to the bottom row that B, C, and E in the bottom row will be toggled. Some calculating must be done to figure out what combination of top row lights must be pressed in order to blank out the bottom row (The theory for this is close to basis vectors from linear algebra). A strategy that seems to work and does not require much thinking is to know the following:

If A is the first light in the bottom row that is on then press B in the top row and bring down.
If B is the first light that is on in the bottom row then press A.
If C then press D.

Repeat this as necessary until victory is achieved.

Although this method does solve the puzzle, it will not do so in the minimum number of moves.

[edit] Beyond 5x5

The same general strategy could be used for a Lights Out game with any size grid. For other square grids here are the tables:

2x2
===
A -> A-
B -> -B

3x3
===
A -> -BC
B -> ABC
C -> AB-

4x4
===
A -> ----
B -> ----
C -> ----
D -> ----

5x5
===
A -> -BC-E
B -> ABC--
C -> AB-DE
D -> --CDE
E -> A-CD-

6x6
===
A -> A---E-
B -> -B-D-F
C -> ----E-
D -> -B----
E -> A-C-E-
F -> -B---F

7x7
===
A -> A-CD-FG
B -> --CD-FG
C -> AB-----
D -> AB-D-FG
E -> -----FG
F -> AB-DE--
G -> AB-DE-G

8x8
===
A -> ----E---
B -> ---D-F--
C -> --C-E-G-
D -> -B-D-F-H
E -> A-C-E-G-
F -> -B-D-F--
G -> --C-E---
H -> ---D----

9x9
===
A -> A-C-E-G-I
B -> ---------
C -> A-C-E-G-I
D -> ---------
E -> A-C-E-G-I
F -> ---------
G -> A-C-E-G-I
H -> ---------
I -> A-C-E-G-I

These are quite easy to generate. Starting with a blank board is best, but a board that only has lights in the bottom row will do. Just press a light at the top, bring the lights down and see which ones have changed.