This electronic puzzle by Tiger Toysconsists of a 5×5 grid of buttons which also have lights in them. Bypressing a button, its light and those of the (non-diagonally) adjacentbuttons will change (switch on if it was off, and vice versa). Given apattern of lights, you have to switch them all off by pressing the correctbuttons. Not only that, but you have to do it in as few moves as possible.
This is the one of the few non-trivial puzzles I know in which the orderthat the moves are performed is unimportant (i.e. the puzzle positions forman Abelian group). This means that it is not necessary to press any buttonmore than once during the solution because we could change the order of themoves so that repetitions occur together. Since pressing a button twice willnot change anything, a button need only be pressed at most once.
Another puzzle of this kind is the Rubik's Clock puzzle,or the Orbix puzzle (type 1).
Lights Out Baseball, San Antonio, Texas. 1,031 likes 3 talking about this 129 were here. The purpose of the club is to promote the game of baseball by providing an. Find GIFs with the latest and newest hashtags! Search, discover and share your favorite Lights Out GIFs. The best GIFs are on GIPHY.
The classic version of Lights Out has recently been given a facelift, and nowhas a more curvy design. The new version has exactly the same game play, andthe same built-in puzzles as the original version.
The first electronic version of this game was called the XL-25,was produced by Vulcan Electronics Ltd. in 1983, and it was invented by LászlóMérõ. It not only could play the now standard game where eachbutton changes a cross of lights, but also played a variant where each buttonchanges its own light and those lights which are a chess knight's move away.An even older electronic game called Merlin had a similargame called Magic Square which was played on a 3x3 grid, but its moves wereslightly different. More on these variants later on.
The Tiger version of Lights Out was patented in the US on 23 May 1995 (USpatents 5,417,425, 5,573,245, 5,603,500). I have not yet been able to find any patentsfor the Merlin, but the XL-25 was patented on 21 July 1983, WO83/02399(and 27 October 1983, WO83/03691).
Amusingly the puzzle can momentarily be seen in the film 'Drive' with Mark Dacascos. Nearthe end you can see the Lights Out puzzle used as an electronic keypad to the left of abig metal door.
Lights Out is an electronic game released by Tiger Electronics in 1995.[1] 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 adjacent lights. The goal of the puzzle is to switch all the lights off, preferably in as few button presses as possible.[1][2]
Lights Out 3 2 000 Yen
Merlin, a similar electronic game, was released by Parker Brothers in the 1970s with similar rules on a 3 by 3 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 comhandheld 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.[1][2]
Inventors[edit]
Lights Out was created by a group of people including Avi Olti, Gyora Benedek, Zvi Herman, Revital Bloomberg, Avi Weiner and Michael Ganor. Dj mixer professional 3 6 10. The members of the group together and individually also invented several other games, such as Hidato, NimX, iTop and many more.
Gameplay[edit]
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.[1][3]
Mathematics[edit]
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 conclusions 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.[4] Secondly, in a minimal solution, each light needs to be pressed no more than once, because pressing a light twice is equivalent to not pressing it at all.[4] Iconkit 10 1 – icon resizer for app development.
In 1998, Marlow Anderson and Todd Feil used linear algebra to prove that not all configurations are solvable and also to prove that there are exactly four winning scenarios, not including redundant moves, for any solvable 5×5 problem.[5] The 5×5 grid of Lights Out can be represented as a 25x1 column vector with a 1 and 0 signifying a light in its on and off state respectively. Each entry is an element of Z2, the field of integers modulo 2. Anderson and Feil found that in order for a configuration to be solvable (deriving the null vector from the original configuration) it must be orthogonal to the two vectors N1 and N2 below (pictured as a 5×5 array but not to be confused with matrices).
In addition, they found that N1 and N2 can be used to find three additional solutions to a solution and that these four solutions are the only four solutions (excluding redundant moves) to the starting given configuration. These four solutions are X, X + N1, X + N2, and X + N1 + N2 where X is a solution to the starting given configuration.[5] An introduction into this method was published by Robert Eisele.[6]
Light chasing[edit]
'Light chasing' is a method similar to Gaussian elimination which always solves the puzzle (if a solution exists), although with the possibility of many redundant steps.[2][5][7] 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.[7]
| Bottom row is | Toggle on top row |
|---|---|
| ⬜⬜⬜⬛⬛ | ⬛▣⬛⬛⬛ |
| ⬜⬜⬛⬜⬜ | ⬛⬛▣⬛⬛ |
| ⬜⬛⬜⬜⬛ | ⬛⬛⬛⬛▣ |
| ⬜⬛⬛⬛⬜ | ▣▣⬛⬛⬛ |
| ⬛⬜⬜⬛⬜ | ▣⬛⬛⬛⬛ |
| ⬛⬜⬛⬜⬛ | ▣⬛⬛▣⬛ |
| ⬛⬛⬜⬜⬜ | ⬛⬛⬛▣⬛ |
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.
Lights Out 3 2 000 Yen
Merlin, a similar electronic game, was released by Parker Brothers in the 1970s with similar rules on a 3 by 3 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 comhandheld 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.[1][2]
Inventors[edit]
Lights Out was created by a group of people including Avi Olti, Gyora Benedek, Zvi Herman, Revital Bloomberg, Avi Weiner and Michael Ganor. Dj mixer professional 3 6 10. The members of the group together and individually also invented several other games, such as Hidato, NimX, iTop and many more.
Gameplay[edit]
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.[1][3]
Mathematics[edit]
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 conclusions 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.[4] Secondly, in a minimal solution, each light needs to be pressed no more than once, because pressing a light twice is equivalent to not pressing it at all.[4] Iconkit 10 1 – icon resizer for app development.
In 1998, Marlow Anderson and Todd Feil used linear algebra to prove that not all configurations are solvable and also to prove that there are exactly four winning scenarios, not including redundant moves, for any solvable 5×5 problem.[5] The 5×5 grid of Lights Out can be represented as a 25x1 column vector with a 1 and 0 signifying a light in its on and off state respectively. Each entry is an element of Z2, the field of integers modulo 2. Anderson and Feil found that in order for a configuration to be solvable (deriving the null vector from the original configuration) it must be orthogonal to the two vectors N1 and N2 below (pictured as a 5×5 array but not to be confused with matrices).
In addition, they found that N1 and N2 can be used to find three additional solutions to a solution and that these four solutions are the only four solutions (excluding redundant moves) to the starting given configuration. These four solutions are X, X + N1, X + N2, and X + N1 + N2 where X is a solution to the starting given configuration.[5] An introduction into this method was published by Robert Eisele.[6]
Light chasing[edit]
'Light chasing' is a method similar to Gaussian elimination which always solves the puzzle (if a solution exists), although with the possibility of many redundant steps.[2][5][7] 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.[7]
| Bottom row is | Toggle on top row |
|---|---|
| ⬜⬜⬜⬛⬛ | ⬛▣⬛⬛⬛ |
| ⬜⬜⬛⬜⬜ | ⬛⬛▣⬛⬛ |
| ⬜⬛⬜⬜⬛ | ⬛⬛⬛⬛▣ |
| ⬜⬛⬛⬛⬜ | ▣▣⬛⬛⬛ |
| ⬛⬜⬜⬛⬜ | ▣⬛⬛⬛⬛ |
| ⬛⬜⬛⬜⬛ | ▣⬛⬛▣⬛ |
| ⬛⬛⬜⬜⬜ | ⬛⬛⬛▣⬛ |
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[edit]
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.[5][7] If the 5×5 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,[8] while solutions to n-by-n boards for n≤200 have been explicitly constructed.[9]
There exists a solution for every N×N case. It is solvable on any undirected graph, where clicking on one vertex flips its value and its neighbours. More generally if the action matrix is symmetric then its diagonal is always solvable.[10]
Lights Out 3 2 000 Btu
See also[edit]
References[edit]
- ^ abcd'Beyond Tetris' - Lights Out, Tony Delgado, GameSetWatch, January 29, 2007. Accessed on line October 18, 2007.
- ^ abcLights Out, Jaap's Puzzle Page. Accessed on line October 18, 2007.
- ^'Archive of Interesting Code'. www.keithschwarz.com. Retrieved 2020-06-12.
- ^ abWeisstein, Eric W.'Lights Out Puzzle'. MathWorld.
- ^ abcdMarlow Anderson, Todd Feil (1998). 'Turning Lights Out with Linear Algebra'(PDF). Mathematics Magazine. 71 (4): 300–303. doi:10.1080/0025570X.1998.11996658. Archived from the original(PDF) on 15 August 2014.
- ^Eisele, Robert (2018-07-30). 'LightsOut Solution using Linear Algebra'. Retrieved 2018-07-30.Cite magazine requires
|magazine=(help) - ^ abcSolving Lights Out, Matthew Baker.
- ^unknown (20 Nov 2010). 'Lights out game on hexagonal grid'. Retrieved 30 November 2010.
- ^Jim Fowler (21 July 2008). 'Solutions to Lights Out'. Jim Fowler blog. Retrieved 30 November 2010.
- ^Igor Minevich (2012). 'Symmetric Matrices over F_2 and the Lights Out Problem'. arXiv:1206.2973 [math.RA].
External links[edit]
Lights Out 3 2 000 Euros
