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 Post subject: Hidden Cubes
PostPosted: Sat Nov 11, 2006 1:34 pm 
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Mark Longridges recent topic reminded me of the small article I wrote for CFF (the newsletter for the Dutch Cube Club) several years ago. I haven't seen the subject mentioned again so I will repeat my idea here. Forgive me if this is old hat.

Take a puzzle like a 4x4x4. Why do we call it a 4x4x4? Well it appears to be a stack of 64 little cubes in a 4x4x4 grid. We all know it isn't really but what if it was and still moved the same? That would mean there are 8 little cubes hidden in the center. If they were coloured the same as the 4x4x4 exterior then we would have a 2x2x2 puzzle waiting to be solved. Only slice moves on the 4x4x4 would affect it of cause but simply solving the 4x4x4 exterior would not be enough. Taking this idea further to a 7x7x7 for example, not only would you have an internal 5x5x5 to solve but also a central 3x3x3 as well. It is fairly obvious that the only way to play with such a puzzle is on a computer. You could have the movable 7x7x7 next to the 5x5x5 and 3x3x3 which would automatically move when appropriate. I must admit I haven't given the solution to such a puzzle much thought but I would love to see this computer simulation made by someone. Anyone up for the challenge? Below I have posted some photos of how a 5x5x5 would be with it's internal 3x3x3 pictured along side.


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hidden cubes 2.jpg
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hidden cubes 3.jpg
hidden cubes 3.jpg [ 103.49 KiB | Viewed 3824 times ]
hidden cubes 4.jpg
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 Post subject:
PostPosted: Sat Nov 11, 2006 2:24 pm 
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Hmm, that looks like it would be challenging. I'll give it a try later today.

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 Post subject: Re: Hidden Cubes
PostPosted: Sat Nov 11, 2006 9:09 pm 
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Tony Fisher wrote:
Mark Longridges recent topic reminded me of the small article I wrote for CFF (the newsletter for the Dutch Cube Club) several years ago. I haven't seen the subject mentioned again so I will repeat my idea here. Forgive me if this is old hat.

Take a puzzle like a 4x4x4. Why do we call it a 4x4x4? Well it appears to be a stack of 64 little cubes in a 4x4x4 grid. We all know it isn't really but what if it was and still moved the same? That would mean there are 8 little cubes hidden in the center. If they were coloured the same as the 4x4x4 exterior then we would have a 2x2x2 puzzle waiting to be solved. Only slice moves on the 4x4x4 would affect it of cause but simply solving the 4x4x4 exterior would not be enough. Taking this idea further to a 7x7x7 for example, not only would you have an internal 5x5x5 to solve but also a central 3x3x3 as well. It is fairly obvious that the only way to play with such a puzzle is on a computer. You could have the movable 7x7x7 next to the 5x5x5 and 3x3x3 which would automatically move when appropriate. I must admit I haven't given the solution to such a puzzle much thought but I would love to see this computer simulation made by someone. Anyone up for the challenge? Below I have posted some photos of how a 5x5x5 would be with it's internal 3x3x3 pictured along side.



This is so true. Solving the exterior nxnxn parts of a (n+2)x(n+2)x(n+2) cube, is *much* easier (intuitively or not) than solving a regular nxnxn. Sounds like a very interesting challenge and I am not sure if it can be constructed by using a partially transparent (n+2)x(n+2)x(n+2) (e.g. 5x5x5) such that the internal nxnxn cube (e.g. 3x3x3) can be seen.

Brilliant idea! :)


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 Post subject: Re: Hidden Cubes
PostPosted: Sat Nov 11, 2006 9:31 pm 
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kastellorizo wrote:
Solving the exterior nxnxn parts of a (n+2)x(n+2)x(n+2) cube, is *much* easier (intuitively or not) than solving a regular nxnxn.


You mean it is easier to solve the centerparts of a 5x5x5 that solving the entire 3x3x3?

Also I think that actually constructing this puzzle, is extremely hard, and to my oppinion might be done in one way only, and that is to use small transparent cubies and magnets, as talked about in another (or several, don't remember) topic. This has the limitation that you can only hav a small number of different n in the puzzle since the cubies can't be transparent to the extent that it is possible to view something (a sticker) throu more than a few of the cubies.

I think that this actualy present a big enough challenge when tackling it via computer, but than I am not aprogrammer, and to those of you who are, this might be a straightforward thing that is made in acouple of minutes?


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 Post subject: Re: Hidden Cubes
PostPosted: Sun Nov 12, 2006 1:20 am 
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Haara wrote:
You mean it is easier to solve the centerparts of a 5x5x5 that solving the entire 3x3x3?


Yes! This is easily seen by rotating the adjacent sides on the left, right, top and bottom of a centerpart without affect the front side (this can't be done on the 3x3x3 cube). Less common elements shared by the generators means less complexity for the 3x3x3 solve (and this is always the case for the "Smart Alex" puzzle LOL).


Haara wrote:
Also I think that actually constructing this puzzle, is extremely hard, and to my oppinion might be done in one way only, and that is to use small transparent cubies and magnets, as talked about in another (or several, don't remember) topic. This has the limitation that you can only hav a small number of different n in the puzzle since the cubies can't be transparent to the extent that it is possible to view something (a sticker) throu more than a few of the cubies.

I think that this actualy present a big enough challenge when tackling it via computer, but than I am not aprogrammer, and to those of you who are, this might be a straightforward thing that is made in acouple of minutes?


Hmmm... magnets... sounds interesting! :)



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 Post subject:
PostPosted: Sun Nov 12, 2006 5:35 am 
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http://www.gravitation3d.com/magiccube5d/
?

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 Post subject:
PostPosted: Sun Nov 12, 2006 7:34 am 
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I think in the > 3 dimension puzzles, every cubie acts as an axis, even inner cubies.

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 Post subject:
PostPosted: Sun Nov 12, 2006 10:35 am 
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Just a question.

In case you solve a supercube...... Once super cube is solved the internal cubes you talk about would be solved, wouldn't it?

At least in 3x3x3 it will work. no?

I have to think more in that, cause I just read that threat.

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PostPosted: Sun Nov 12, 2006 11:36 am 
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Interesting idea... But I think it would be rather easy to solve. First solve 3x3 and then 5x5 using only conjugates XYX' where Y is an outer layer turn, like r U r'. The 3x3 remains solved. That idea of course works for other versions, too. There would never be parity problems.


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 Post subject:
PostPosted: Sun Nov 12, 2006 12:02 pm 
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http://games.groups.yahoo.com/group/spe ... ube/files/
=> CubixPlayer2.zip


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 Post subject:
PostPosted: Sun Nov 12, 2006 12:35 pm 
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rastarubik wrote:
Just a question.

In case you solve a supercube...... Once super cube is solved the internal cubes you talk about would be solved, wouldn't it?

At least in 3x3x3 it will work. no?

I have to think more in that, cause I just read that threat.


Excellent point David!

I believe that supercubes are harder to solve than the ones Tony mentioned, since the orientation of some of the inner parts (e.g. centres) of both inner and outer cubes (depending on the case) would not matter.



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 Post subject:
PostPosted: Sun Nov 12, 2006 1:00 pm 
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Thanks Stefan. I guess it was always likely it had already been done. I didn't even know this group existed.

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 Post subject:
PostPosted: Sun Nov 12, 2006 1:16 pm 
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rastarubik wrote:
In case you solve a supercube...... Once super cube is solved the internal cubes you talk about would be solved, wouldn't it?

At least in 3x3x3 it will work. no?
I have to think more in that, cause I just read that threat.

Don't know, to me is sounds that that will happen only if the sum of every outher layer turns on the 5x5x5 is zero*, and as far as I know that is not nesesary.

*At least that the number of turns clockwise is the same as number of turns anticlockwise. I know that if this is true there must be other additional criteria, but I think this one is hard enough...



Johannes Laire wrote:
First solve 3x3 and then 5x5 using only conjugates XYX' where Y is an outer layer turn, like r U r'. The 3x3 remains solved.

Yeah, that will work, but probably there might be a more "speedy" method that solves every part simultaneously. But I guess that would be very hard to actually implement since I think that the number of aglorithms involved would be a bit to high...

Oh, and another thing...
It would be nice to see the scrambles for such a cube, since I suspect that the cubes will have different "levels" of scrambling...


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 Post subject:
PostPosted: Sun Nov 12, 2006 1:50 pm 
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Tony Fisher wrote:
I didn't even know this group existed.

Whoa... proves the separation of builders/collectors and speeders I guess. That group is about as big as the twistypuzzles forum (in terms of members, posts, age).


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 Post subject:
PostPosted: Sun Nov 12, 2006 4:56 pm 
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Stefan Pochmann wrote:
http://games.groups.yahoo.com/group/speedsolvingrubikscube/files/
=> CubixPlayer2.zip


Well after about 15 minutes of going in circles I still can't get web access which is what the above link tells me I need to be able to download the file.

Thanks,
Carl

P.S. I finally got the file. Disregard the above... Thanks.


Last edited by wwwmwww on Sun Nov 12, 2006 6:17 pm, edited 1 time in total.

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 Post subject: Re: Hidden Cubes
PostPosted: Sun Nov 12, 2006 5:18 pm 
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Tony Fisher wrote:
It is fairly obvious that the only way to play with such a puzzle is on a computer.


I'm not so sure. I touched on this topic just a few days ago in this thread:

http://twistypuzzles.com/forum/viewtopic.php?t=5653

and I think a clear hollow 5x5x5 with a 3x3x3 inside could be made.

Carl


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 Post subject:
PostPosted: Sun Nov 12, 2006 6:09 pm 
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Here is a thought,

How do you move the 3x3 within the 5x5?

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 Post subject:
PostPosted: Mon Nov 13, 2006 5:31 pm 
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Pembo wrote:
Here is a thought,

How do you move the 3x3 within the 5x5?


I thought that this was managed like if you had the cube made of small cubies, then moving the inner layers of the 5x5x5 would simultaneously move the 3x3x3, see tonys pics...


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 Post subject:
PostPosted: Mon Nov 13, 2006 5:57 pm 
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Although it would not be so pleasing on the eye I could see a transparent 5x5x5 built around a 3x3x3 ball.

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 Post subject:
PostPosted: Mon Nov 13, 2006 8:22 pm 
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Haara wrote:
Pembo wrote:
Here is a thought,

How do you move the 3x3 within the 5x5?


I thought that this was managed like if you had the cube made of small cubies, then moving the inner layers of the 5x5x5 would simultaneously move the 3x3x3, see tonys pics...


Hi, im the creator of the cubixplayer. It was a fun codingproject, but i got too busy to complete it properly, but at least it works. I had plans to get round to recoding it in directx to make it faster. Maybe some day ...
Pembo, to turn the inner 3x3x3 of the 5x5x5 u have to turn the inner 3x3x3 pretending the outer 5x5x5 does not esist. With cubixplayer u can do this by using transparency. Then u restore the outer 5x5x5 by using solely commutators that do not affect the inner 3x3x3. Solving a 7x7x7 super-supercube as i call it u first solve the innermost 3x3x3 then the 5x5x5 and then finally the outermost 7x7x7. And yes a cube can be supersolved with all centers permuted correctly, and still the cube inside is not solved properly .... quite fun 8-)

-Per

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