Lights Out (game)
Encyclopedia
Lights Out is an electronic game
, released by Tiger Toys in 1995. The game consists of a 5 by 5 grid of lights. When the game starts, a random number or a stored pattern of these lights is switched on. Pressing any of the lights will toggle it and the four adjacent lights. The goal of the puzzle is to switch all the lights off, preferably in as few button presses as possible.
A similar electronic game Merlin
was released by Parker Brothers
in the 1970s with similar rules on a 3x3 grid. Another similar game was produced by Vulcan Electronics in 1983 under the name XL-25. Tiger Toys also produced a cartridge version of Lights Out for its Game.com
handheld game console
in 1997, shipped free with the console. A number of new puzzles similar to Lights Out have been released, such as Lights Out 2000, Lights Out Cube, and Lights Out Deluxe.
, NimX, iTop and many more.
If a light is on, it must be toggled an odd number of times to be turned off. If a light is off, it must be toggled an even number of times (including none at all) for it to remain off. Several conclusion are used for the game's strategy. Firstly, the order in which the lights are pressed does not matter, as the result will be the same. Secondly, each light needs to be pressed no more than once, because pressing a light twice is equivalent to not pressing it at all.
which always solves the puzzle, although with the possibility of many redundant steps. In this approach rows are manipulated one at a time starting with the top row. All the lights are disabled in the row by toggling the adjacent lights in the row directly below. The same method is then used on the consecutive rows up to the last one. The last row is solved separately, depending on its active lights. Corresponding lights (see table below) in the top row are toggled and the initial algorithm is run again, resulting in a solution.
Bottom row Top row
OxxxO OOxxx
xOxOx OxxOx
OOOxx xOxxx
xxOOO xxxOx
OxOOx xxxxO
xOOxO Oxxxx
OOxOO xxOxx
Tables and strategies for other board sizes are generated by playing Lights Out with a blank board and observing the result of bringing a particular light from the top row down to the bottom row.
Existence of solutions has been proved for a wide variety of board configurations, such as hexagonal, while solutions to n-by-n boards for n≤200 have been explicitly constructed.
Electronic game
An electronic game is a game that employs electronics to create an interactive system with which a player can play. The most common form of electronic game today is the video game, and for this reason the terms are often mistakenly used synonymously. Other common forms of electronic game include...
, released by Tiger Toys in 1995. The game consists of a 5 by 5 grid of lights. When the game starts, a random number or a stored pattern of these lights is switched on. Pressing any of the lights will toggle it and the four adjacent lights. The goal of the puzzle is to switch all the lights off, preferably in as few button presses as possible.
A similar electronic game Merlin
Merlin (game)
----Merlin was a handheld electronic game first made by Parker Brothers in 1978. Merlin is notable as one of the earliest and most popular handheld games, selling over 5 million units during its initial run, as well as one of the most long-lived, remaining popular throughout the 1980s...
was released by Parker Brothers
Parker Brothers
Parker Brothers is a toy and game manufacturer and brand. Since 1883, the company has published more than 1,800 games; among their best known products are Monopoly, Cluedo , Sorry, Risk, Trivial Pursuit, Ouija, Aggravation, and Probe...
in the 1970s with similar rules on a 3x3 grid. Another similar game was produced by Vulcan Electronics in 1983 under the name XL-25. Tiger Toys also produced a cartridge version of Lights Out for its Game.com
Game.com
The Game.com is a handheld game console released by Tiger Electronics in September 1997. It featured many new ideas for handheld consoles and was aimed at an older target audience, sporting PDA-style features and functions such as a touch screen and stylus...
handheld game console
Handheld game console
A handheld game console is a lightweight, portable electronic device with a built-in screen, game controls and speakers. Handheld game consoles are run on machines of small size allowing people to carry them and play them at any time or place...
in 1997, shipped free with the console. A number of new puzzles similar to Lights Out have been released, such as Lights Out 2000, Lights Out Cube, and Lights Out Deluxe.
Inventors
Lights Out was created by a group of people including Avi Olti, Gyora Benedek, Zvi Herman, Revital Bloomberg, Avi Weiner and Michael Ganor. The members of the group together and individually also invented several other games, such as HidatoHidato
Hidato is a logic puzzle game invented by Dr. Gyora Benedek, an Israeli mathematician. The goal of Hidato is to fill the grid with consecutive numbers that connect horizontally, vertically, or diagonally.-About the puzzle:...
, NimX, iTop and many more.
Gameplay
The game consists of a 5 by 5 grid of lights. When the game starts, a random number or a stored pattern of these lights is switched on. Pressing any of the lights will toggle it and the four adjacent lights. The goal of the puzzle is to switch all the lights off, preferably in as few button presses as possible.If a light is on, it must be toggled an odd number of times to be turned off. If a light is off, it must be toggled an even number of times (including none at all) for it to remain off. Several conclusion are used for the game's strategy. Firstly, the order in which the lights are pressed does not matter, as the result will be the same. Secondly, each light needs to be pressed no more than once, because pressing a light twice is equivalent to not pressing it at all.
Light chasing
"Light chasing" is a method similar to Gaussian eliminationGaussian elimination
In linear algebra, Gaussian elimination is an algorithm for solving systems of linear equations. It can also be used to find the rank of a matrix, to calculate the determinant of a matrix, and to calculate the inverse of an invertible square matrix...
which always solves the puzzle, although with the possibility of many redundant steps. In this approach rows are manipulated one at a time starting with the top row. All the lights are disabled in the row by toggling the adjacent lights in the row directly below. The same method is then used on the consecutive rows up to the last one. The last row is solved separately, depending on its active lights. Corresponding lights (see table below) in the top row are toggled and the initial algorithm is run again, resulting in a solution.
Bottom row Top row
OxxxO OOxxx
xOxOx OxxOx
OOOxx xOxxx
xxOOO xxxOx
OxOOx xxxxO
xOOxO Oxxxx
OOxOO xxOxx
Tables and strategies for other board sizes are generated by playing Lights Out with a blank board and observing the result of bringing a particular light from the top row down to the bottom row.
Further results
Once a single solution is found, a solution with the minimum number of moves can be determined through elimination of redundant sets of button presses that have no cumulative effect. If the 5x5 puzzle is unsolvable under legal game creation, two leftmost lights on the bottom row will remain on when all other lights have been turned off.Existence of solutions has been proved for a wide variety of board configurations, such as hexagonal, while solutions to n-by-n boards for n≤200 have been explicitly constructed.
External links
- Official Lights Out site at genuine-lights-out.com.