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11-02-05 12:59 PM
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Acmlm's Board - I2 Archive - Brain Teasers - Cursed sliding puzzle | |
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Dish

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From: Disch

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Posted on 11-13-04 09:39 AM Link | Quote
So I'm doing this sliding puzzle. It's a 4x4 grid with 15 pieces (and one blank space), each piece is numbered and you're supposed to arrange them in order. Anyone who's done one of these should know what I'm talking about (it was also the minigame in FF1 when you pressed A+B 55 times on the ship).

Anyway... in FF1 I devised a strategy which never failed. Arrange the top row (1,2,3,4), then left side (5,9,13), then second row (6,7,8) and shuffle the rest around until they fall into place. It served me well up until I tried this new game which has the same minigame... except this one must be randomized by Satan himself. Everytime I end up getting the following (or a variation of it):

01--02--03--04
05--06--07--08
09--10--11--12
13--15--14--__

(note 15 and 14 reversed). In the FF1 version, I would always be able to solve the 'left-overs' without disrupting anything but 10,11,12,14,15... but with the above setup... I've come to the conclusion that it is impossible unless you disrupt something else (and yes it is... I figured the pattern of how things move... and even wrote a quick program to try all moves possible to find the answer... and definatly, the above puzzle is impossible unless you disrupt something else in the puzzle).

So my question is... does anyone have a method of solving the above puzzle? And could you post the steps of how you do it?

Any help appreciated ^^
Drag

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From: Deogon Vally, Dragon Country

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Posted on 11-13-04 10:31 AM Link | Quote
I'm not the master at this or anything, but the way I do this is (if the blank tile goes in the upper left), I get the bottom two rows first, and then fool with the upper two. If the blank tile goes in the bottom right, you could probably just do the upper two, and then bottom two.

Point is, if you run into a situation like that, you're going to HAVE to disrupt some tiles. It takes practice to get the actual "strategy", but you should only have to disrupt the two consecutive rows the blank tile goes in.
Lenophis

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Posted on 11-13-04 01:28 PM Link | Quote
Originally posted by Disch

01--02--03--04
05--06--07--08
09--10--11--12
13--15--14--__

Any help appreciated ^^

Mr. 36 seconds is here to help.

I've been trying to get a step by step answer, but I can't remember the steps. I can't picture them in my head, and I solved the damn puzzle 4 times already trying to get it set up. (I've actually gotten it done with that set up, but couldn't reverse it afterwards. )

But, I can tell you this...

1) You want the setup to look like this:

xx--xx--xx--15
xx--xx--xx--14

2) You'll never need to touch 1-8.
3) Try to get it to look like this:

09--10--11--12
15--13--14--__

or

09--10--11--12
14--15--13--__

If it is the first, then:
move 12 down
move 11 right
move 14 up
move 15 and 13 right
move 9 down
move 10 left
move 15 up
move 13 left
move 14 down
move 10 right
move 9 up
move 13 and 14 left
move 15 down
move 11 left
move 12 up
puzzle solved

If it is the second, then:

move 12 down
move 11 right
move 13 up
move 14 and 15 right
move 9 down
move 10, 13, and 11 left
move 12 up
move 14 and 15 right
move 13 down
move 10 right
move 9 up
puzzle solved

I hope it helps
Dish

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From: Disch

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Posted on 11-13-04 10:02 PM Link | Quote
1) *shrug*.. that doesn't seem different than:
09--xx--xx--xx
13--xx--xx--xx
which is how I do it normally (which isn't working). Only difference is, you'd be shuffling the left side instead of the right side like I do.

2) This is actually a big help. I wasn't sure if I'd need to cut in the top 2 rows. It's good to know I won't have to. Thanks.

3) If I could get it to either of those, I could have it solved. Both of those examples are one "move" away from being solved (well... according to my 'strategy' anyway:

When you're just messing with:

xx--xx--xx
xx--xx--__

There's only 1 real "move" you can make. The piece you "move" has so move down the middle column (which moves it 2 pieces in either direction). All other moves are just rotating what's already in position. Like say you have:

12--15--14
11--10--__

That is already solved without any more "moves". All you have to do is rotate the whole thing clockwise (or counter clockwise) and everything goes in position.

15--14--12
11--10--__

This is solved in 1 'move' (by moving 12). You rotate in either direction until 12 is in the middle column, then you throw it down (which moves it 2 pieces in either direciton, putting it between 11 and 15), then rotate the rest into place.

The reason why the:
10--11--12
15--14--__
scenario is so tricky is because it requires a move of only 1 piece in a direction... not two. If I can get it to where the pieces are layed out so that it can be put together by moves of 2 pieces, then I can easily have it solved. So in your examples above (which all only require moves of two pieces in either direction-- the first one only needing 15 to move, and the second only needing 13 to move), I wouldnt've had any problem with them. The hard part for me is getting to how you had them.


Your post really helped me a lot though. Especially knowing that you don't have to touch 1-8. Thanks a bunch ^^

edit: are you sure you won't have to touch 1-8?

edit2: yeah... I'm still having a hard time with this. As far as I can tell... even with 9 and 13 in the mix... each 'move' can still only skip 2 pieces in either direction. To get this solved I'll need to skip an odd number (1 or 3) of pieces... which is making me think I need to step into the second row. Right now I'm looking at putting 7 and 8 in the mix and leaving 9 and 13 be.


(edited by Disch on 11-13-04 01:35 PM)
(edited by Disch on 11-13-04 02:21 PM)
Lenophis

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Posted on 11-14-04 08:57 AM Link | Quote
Ok, let's try this again. After doing a LOT of reading, I've determined that you are correct in your first post. This is gonna take a whole resuffle to solve. You might get lucky and not have to touch the top row, but I'm thinking every tile needs to be moved. Judging by your post, you know what you are doing.

I'd say, you don't have to touch the top row, and you might get away with not having to touch 5. I'm less help now.
JR11

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Posted on 11-14-04 09:04 AM Link | Quote
Is it me, or do I just get lucky everytime I do one of those puzzles. It seems like forever since I've come to a situation like that.
Dish

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From: Disch

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Posted on 11-14-04 11:56 AM Link | Quote
Originally posted by Masterofmario11
Is it me, or do I just get lucky everytime I do one of those puzzles. It seems like forever since I've come to a situation like that.


If I weren't embarrased to reveal the game which contains this particular puzzle.. I'd link you. I seem to hit this situation 80% of the time. But it never ever ever happened in FF1.

Anyway... I've decided that tomorrow I'm just going to write a program to crack it (try every move possible in sequence until it finds a result). I'll probably have to leave it running overnight (or maybe even for a day or two ), but then I'll have the answer. I'll post my results when I have them.
Heian-794

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Posted on 11-14-04 05:20 PM Link | Quote
I'm going to go out on a limb and say that this situation:

01--02--03--04
05--06--07--08
09--10--11--12
13--15--14--__


...is unsolvable. IIRC, you can see if a given situation is solvable or not by exchanging the positions of any two numbers (never mind if you can actually move them on the board; just pick them up and switch them) and if the number of switches is odd, the puzzle has the wrong "parity" and can't be done.

I read about this in a Martin Gardner column in Scientific American, where puzzlist Sam Loyd offered a big prize to anyone who could solve it, secure in the knowledge that no one could!
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