Many of you are probably familiar with the Tiger Electronics toy/puzzle called "Lights Out". If not, you can look at http://www-personal.engin.umich.edu/~kbarr/lo/ for an excellent summary of it plus links to online java simulators of Lights Out. Basically, the idea is that there is a 5x5 grid of illuminated buttons which you are supposed to extinguish by pressing the lit-up ones. Problem is, the adjacent ones flip their state, if they were on before they turn off, and if they were off before they turn on. Lights Out has various starting positions based upon difficulty. A scholarly paper on Lights Out was published by Anderson and Feil in Mathematics Magazine in October 1998, but since I don't remember anything about linear algebra from my college days, I remain un-enlightened by it.
In the mid-1980's I published a puzzle (written in Basic for the PC) called "flip". It is exactly the same as the Tiger Electronics toy, except for three variations: 1. The object is to get all the lights in the 5x5 grid to come on, not go out as in the Tiger game. 2. The program generates a starting position with 5 squares illuminated at random (which means that at least 75% of the starting positions were unsolvable, but I didn't know that at the time). 3. You can't press an illuminated square. This is a HUGE difference from the Tiger version which allows you to press any square.
My first question is, how does rule #3 affect the mathematics of the game? My second question is whether or not this puzzle idea existed before my version in the mid-1980's. I honestly have no idea what made me think of the basis of Flip, but somehow I doubt I invented a totally new puzzle concept, as I can't even solve the crossword in TV Guide magazine without professional assistance. ;-)
--
Gary Watson g...@nexsan.sex (Change dot sex to dot com to reply!!!) Nexsan Technologies Ltd. Derby DE21 7BF ENGLAND http://www.nexsan.com
Gary Watson wrote: > My first question is, how does rule #3 affect the mathematics of the game?
I have no idea. I stopped my academic study of maths when I got a multivariable calculus professor in my first year at university who knew how to suck the life out of maths and make it hell on earth -- and I always enjoyed math before meeting her.
> My second question is whether or not this puzzle idea existed before my > version in the mid-1980's. I honestly have no idea what made me think of > the basis of Flip, but somehow I doubt I invented a totally new puzzle > concept, as I can't even solve the crossword in TV Guide magazine without > professional assistance. ;-)
By any chance, you didn't have the hand-held "Merlin" game that came out back in the late '70s or so, did you? I note that you have a UK address, so you probably didn't have Merlin, which was put out by Parker Brothers (now part of Hasbro) here in the US. It was an electronic toy with several games on it, including tic-tac-toe and variations of Simon, Master Mind, and 21, if memory serves. Amongst the games on Merlin was one called "Magic Square", on which you had to get all the lights in a 3x3 grid lighted with the exception of the center square. Pressing each square "flipped" a certain set of squares, although I don't remember the exact way in which this was done. I do remember that the corners had one pattern, with each corner being a rotation of the others, with the side squares being a second pattern and the center square a third pattern, but that's about all I can remember.
Can anybody remember the rules of Magic Square better? (If you have a Merlin, save it -- it might be worth something in 20 years! Save your Timex Sinclair, too!)
> Gary Watson > g...@nexsan.sex (Change dot sex to dot com to reply!!!)
Gary Watson <g...@nexsan.sex> wrote: > Many of you are probably familiar with the Tiger Electronics toy/puzzle > called "Lights Out". If not, you can look at
[...]
Spoilers on how to solve Lights Out (don't read if you want to figure out the puzzles yourself!)
Lights Out is pretty darn easy to 'solve' very quickly once you notice something about it. That being, the only way to affect the top row is by pressing buttons on the top row or buttons on the second row. Now, after pressing some combination of buttons on the first row, -all other button pushes are fixed- because order doesn't matter. So, from then on, you just work from the top and press every button that has a light above it. Sure, you have to guess a few choices for which top buttons to press, but since each cycle only takes a few seconds, you can easily 'solve' any of the puzzles in a minute or so, if not less. Some may consider such a method not in the spirit of the game, but it certainly solves the puzzles quickly!
In article <3893BC7F.5651E...@banet.net>, Ted <fe...@banet.net> wrote: } }Can anybody remember the rules of Magic Square better? (If you have a Merlin, }save it -- it might be worth something in 20 years! Save your Timex Sinclair, }too!)
IIRC, the corners flipped the corner and the three around it, the middle of the side flipped the whole side, and the center flipped all but the corners. -- Matthew T. Russotto russo...@pond.com "Extremism in defense of liberty is no vice, and moderation in pursuit of justice is no virtue."
In article <_%Uk4.2753$e56.136...@monger.newsread.com>, russo...@wanda.vf.pond.com (Matthew T. Russotto) wrote:
> IIRC, the corners flipped the corner and the three around it, the > middle of the side flipped the whole side, and the center flipped all > but the corners.
YDRC. i saw this first as a computer game called "Star Shooter" and later i made one out of flip-flops and gates, still works great and takes me a few pleasant minutes each time i come across it to figure it out again.
there was an interesting consequence of having to press a lamp that was ON, in that you could fall into a "black hole" where no buttons worked and all lamps were off. a modern electronic version would take this opportunity to give a raspberry and reset itself somehow, perhaps to the last goal state seen.
the two goal states were a) all the peripheral lamps on or b) just the one in the middle.
> In article <qzPk4.941$fF.15...@vixen.cso.uiuc.edu>, mark edward hardwidge > <hardw...@ux8.cso.uiuc.edu> wrote:
> > Lights Out is pretty darn easy to 'solve' very quickly once > > you notice something about it.... <snip spolier>
> bzzzt! not quite! lights out (tm) *counts* your moves and if you take more > than eight above the minimum required you do not get credit!
The paper in Mathematics Magazine appears to be saying that you can generate a table of "hints" by doing a matrix multiply (in binary) of the board position with the "hint matrix", which is a constant [0,0,1,1,0,0,0,0,0,1,0,0,0,0,1,0,1,0, 0,0,1,0,0,0,0]. You can press the hint squares in any order (!!!).
Once you know the "trick" described in the previous messages, it's certain you'll solve the puzzle but they are trying to encourage you to do it in the least number of moves (there are at most 4 optimum strategies according to this paper).
I think it would make it much more challenging if Lights Out prevented you from pressing a button where the light was already off. As it is, the game simply flips the polarity of the button you press, plus the neighbors. This is reversible, so you can "experimentally" make moves to see the effect, then un-do them (of course, these button presses are counted).
--
Gary Watson g...@nexsan.sex (Change dot sex to dot com to reply!!!) Nexsan Technologies Ltd. Derby DE21 7BF ENGLAND http://www.nexsan.com
> bzzzt! not quite! lights out (tm) *counts* your moves and if you take more > than eight above the minimum required you do not get credit!
My method, after you find the right initial condition, uses the minimum number of 'moves', almost by definition. The only way to get extra moves is to turn a light on and later off, because you've changed your mind / made a mistake. My solution doesn't involve pressing the same button twice. Sure, you might not win the first time you try each puzzle, but if that was a requirement, you'd have to throw away the game if you ever made a mistake!
> Gary Watson <g...@nexsan.sex> wrote: > > Many of you are probably familiar with the Tiger Electronics toy/puzzle > > called "Lights Out". If not, you can look at > [...]
> Spoilers on how to solve Lights Out > (don't read if you want to figure out the puzzles yourself!)
> Lights Out is pretty darn easy to 'solve' very quickly once > you notice something about it. That being, the only way to affect the > top row is by pressing buttons on the top row or buttons on the second > row. Now, after pressing some combination of buttons on the first > row, -all other button pushes are fixed- because order doesn't matter. > So, from then on, you just work from the top and press every > button that has a light above it. > Sure, you have to guess a few choices for which top buttons to > press, but since each cycle only takes a few seconds, you can easily > 'solve' any of the puzzles in a minute or so, if not less. > Some may consider such a method not in the spirit of the game, > but it certainly solves the puzzles quickly!
Did you skip a step? Once you chase the buttons to the bottom, you have to press certain top row lights based on the buttons left over from the first "pass", then repeat the process. At least, that's the cheat I've been using to annoy the kid who I bought the game for. Note that there are a few starting positions which can be solved in a single pass. There's an excellent java simulator at http://www.whitman.edu/offices_departments/mathematics/lights_out/ which includes source code.
--
Gary Watson g...@nexsan.sex (Change dot sex to dot com to reply!!!) Nexsan Technologies Ltd. Derby DE21 7BF ENGLAND http://www.nexsan.com
Gary Watson <g...@nexsan.sex> wrote: > Did you skip a step? Once you chase the buttons to the bottom, you have to > press certain top row lights based on the buttons left over from the first
[...]
No, I just start over with a different combination of top buttons. Most solutions only require a couple of tries, so it's very quick. (although I do remember one that I had to press, I think, four of the top bottons to get...that took me about 50 tries!)
) No, I just start over with a different combination of top )buttons. Most solutions only require a couple of tries, so it's very )quick. (although I do remember one that I had to press, I think, four )of the top bottons to get...that took me about 50 tries!)
Huh? 2^5=32, so that's the maximum amount of tries you would need. And anyhow, I think you can deduce the top buttons to press from the bottom lights that are still burning somehow, which would make it two tries. After a little experimenting, it turns out there are three bottom-row patterns which form a base, for 8 possible bottom-row solutions: Base: XXX.. ..XXX X...X XORed: ..... XX.XX .XX.X X.XX. .X.X.
Since there are 32 combinations to try, and only 8 possible outcomes, you would need 5 tries in total to solve the puzzle this way, if you want to find the minimum.
SaSW, -- Willem (at stack dot nl) Disclaimer: I am in no way responsible for any of the statements made in the above text. For all I know I might be drugged or something.. No I'm not paranoid. You all think I'm paranoid, don't you ! #EOT
Willem-Jan Monsuwe <wil...@snail.stack.nl> wrote: > )of the top bottons to get...that took me about 50 tries!) > Huh? 2^5=32, so that's the maximum amount of tries you would need.
Ted <fe...@banet.net> writes: >the late '70s or so, did you? I note that you have a UK address, so you >probably didn't have Merlin, which was put out by Parker Brothers (now part of >Hasbro) here in the US. It was an electronic toy with several games on it, >including tic-tac-toe and variations of Simon, Master Mind, and 21, if memory >serves. Amongst the games on Merlin was one called "Magic Square", on which you >had to get all the lights in a 3x3 grid lighted with the exception of the center >square. Pressing each square "flipped" a certain set of squares, although I >don't remember the exact way in which this was done. I do remember that the >corners had one pattern, with each corner being a rotation of the others, with >the side squares being a second pattern and the center square a third pattern, >but that's about all I can remember. >Can anybody remember the rules of Magic Square better? (If you have a Merlin, >save it -- it might be worth something in 20 years! Save your Timex Sinclair, >too!)
I still have my Merlin, and it works fine. Each corner flipped itself and the three squares adjacent to it, each edge flipped itself and the two corners next to it, and the center flipped itself and all edges.
A professor at college said that the game started out as "Enigma" back in the 60s on some mainframe computer, but I forget which one.
The game is also the coffin puzzle in the computer game "The 7th Guest".
-- Wei-Hwa Huang, whu...@ugcs.caltech.edu, http://www.ugcs.caltech.edu/~whuang/ --------------------------------------------------------------------------- There is no word in Chinese for "quest".
Wei-Hwa Huang <whu...@ugcs.caltech.edu> wrote: > The game is also the coffin puzzle in the computer game > "The 7th Guest".
How about that! I never made the connection until now.
Speaking of games using classic puzzles, did anyone ever play "BC: The Quest for Fire" (I think that was the title) on the Colecovision? There were parts where you could enter in a code to jump to the next level, and only recently did I think it was probably the 1,11,21,1211,... puzzle. I was only about ten when I last played that game, so I don't feel too bad about not solving the puzzle... Can anyone confirm that it was, indeed, the puzzle I think it was?
Preivously, on 'rec.puzzles', Wei-Hwa Huang (whu...@ugcs.caltech.edu) wrote: [...]
>The game is also the coffin puzzle in the computer game >"The 7th Guest".
There's also a three state varient in the 7th Guest as well (with the picture frame puzzle).
-- Dr. Michael K. Neylon, PhD ChE | University of Michigan | "Pinky, you've left the lens cap of your mney...@engin.umich.edu | mind on again." http://pinky.wtower.com/mneylon | The Brain
