The father of "Lights Out"
Gary Watson
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
ga...@nexsan.sex (Change dot sex to dot com to reply!!!)
Nexsan Technologies Ltd.
Derby DE21 7BF ENGLAND
http://www.nexsan.com
Ted
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
> ga...@nexsan.sex (Change dot sex to dot com to reply!!!)
One wonders what your mind's on. :-)
mark edward hardwidge
> 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!
--
Mark E. Hardwidge
hard...@uiuc.edu
Matthew T. Russotto
}
}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 russ...@pond.com
"Extremism in defense of liberty is no vice, and moderation in pursuit
of justice is no virtue."
robert a moeser
<hard...@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!
-- rob
robert a moeser
russ...@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.
-- rob
Gary Watson
news:ram-300100...@ram.tiac.net...
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
ga...@nexsan.sex (Change dot sex to dot com to reply!!!)
mark edward hardwidge
> 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
news:qzPk4.941$fF.1...@vixen.cso.uiuc.edu...
> Gary Watson <ga...@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!)
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
> 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.
mark edward hardwidge
> 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!)
Willem-Jan Monsuwe
)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
mark edward hardwidge
> )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.
You're right...I rounded far too coursely.
Wei-Hwa Huang
>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".
mark edward hardwidge
> 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?
Michael K. Neylon
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
mne...@engin.umich.edu | mind on again."
http://pinky.wtower.com/mneylon | The Brain