Online since 2002. Over 3300 puzzles, 2600 worldwide members, and 270,000 messages.

TwistyPuzzles.com Forum

It is currently Fri Apr 25, 2014 4:38 am

All times are UTC - 5 hours



Post new topic Reply to topic  [ 42 posts ] 
Author Message
 Post subject: How to solve Justin's Pocket (Corner) Cube?
PostPosted: Sun Nov 10, 2013 2:06 am 
Offline
User avatar

Joined: Thu Dec 15, 2011 10:04 pm
Location: Sioux Lookout, Canada
Attachment:
Pocket-Corner-Cube-Solved_sm.png
Pocket-Corner-Cube-Solved_sm.png [ 1.27 MiB | Viewed 2706 times ]

This was a lot of fun to figure out and solve, though I still have to work out an efficient method for the return to cubic step. I think a six-colour version would be cool, though not much different from solving the 4-colour version that has two logo corners.

One thing I'm curious about: can the Corner Pocket Cube be solved into other rotations of the special corner? For example, can we have yellow on the front, blue on top and green on the right? EDIT to clarify my questions: the solve would include the logo cubes in their normal solved positions.

_________________
PeteTheGeek196 on YouTube


Last edited by Pete the Geek on Sun Nov 10, 2013 11:08 am, edited 1 time in total.

Top
 Profile  
 
 Post subject: How to solve Justin's Pocket (Corner) Cube?
PostPosted: Sun Nov 10, 2013 2:34 am 
Offline
User avatar

Joined: Sun Jul 14, 2013 11:10 pm
Pete the Geek wrote:
One thing I'm curious about: can the Corner Pocket Cube be solved into other rotations of the special corner? For example, can we have yellow on the front, blue on top and green on the right?

I don't think it can. Mostly because

[Spoiler]The "corners" are all 3x3 centers, and because of the way this is bandaged, the other "cubies" wouldn't maintain cubic shape, if it even allowed the centers hidden within to be rotated in this fashion.[/spoiler]

_________________
My budding baby blog, Twisted Interests!


Top
 Profile  
 
 Post subject: Re: How to solve Justin's Pocket (Corner) Cube?
PostPosted: Sun Nov 10, 2013 4:27 am 
Offline
User avatar

Joined: Thu Sep 17, 2009 6:07 am
Location: Germany, Bavaria
I have moved the two posts above from here

This puzzle was announced first by Justin here.
cisco guessed correctly the nature of this puzzle
cisco wrote:
Justin wrote:
I used a 32mm cube as a base, 2mm styrene sheet to extend, and hand-cut the metallic stickers.
So I guess this is an offset-extended 3x3x3. The result is aweseome! I'm happy that even today there are some beautiful yet simple puzzles to create :)
I wrote in the other thread
Konrad wrote:
I have made the underlying bandaged 3x3x3 (3 quads, 3 stripes by Andreas). At first I found it hard to scramble, now I find it hard to solve. :lol:
I'm looking forward to a mass-produced version of this, hopefully it is as nice as the original.
And Andreas and I had a long conversation about it starting here

I have got the easier red and gold version, because I liked the original pictures from Justin so much.
Konrad wrote:
The bandaged 3x3x3 was Andreas Nortmann's 2013930080085E aka "3 Quads, 3 Stripes".

Image
For the two colour version the solution is: Reconstruct the cubic shape.
As Pete, I do not have a "method" for doing this. I do it just intuitively.

Andreas' method is based on the findings of his computer program. The method starts for the "3 Quads, 3 Stripes" when you have got in back into its normalized form = signature 2013930080085E.
As Andreas, the inventor of the "3 Quads, 3 Stripes", admits, he struggled with this first step too.
Pete the Geek wrote:
..., though I still have to work out an efficient method for the return to cubic step. I think a six-colour version would be cool, though not much different from solving the 4-colour version that has two logo corners.

One thing I'm curious about: can the Corner Pocket Cube be solved into other rotations of the special corner? For example, can we have yellow on the front, blue on top and green on the right?
You can do this by rotating the whole cube around the corner UFR. The big cubie at UFL, actually an extended Quad, would become DFR and Justin's signature would be on the F face. Looking at the underlying nature, it is clear that a Quad can never leave its face, because it contains a bandaged 3x3x3 centre, unless you turn the whole cube.

EDIT:
Here follow a few pictures showing how Justin's Puzzle corresponds to the "3 Quads, 3 Stripes".
Image
I have chosen a situation where the two single 3x3 corners are swapped. The three "Q" denote the Quads, the three "S" the 3 Stripes.
If you consider a form as the following as the "regular" form of the "3 Quads, 3 Stripes"
Image
then Justin's Pocket Corner in the two colour version has just two different shapes, that cannot distinguished from other permutations of the stripes and the 3x3 edges.
The one above and the cubic shape.

Here you see both swapped 3x3 corners:

Image

_________________
My collection at: http://sites.google.com/site/twistykon/home


Top
 Profile  
 
 Post subject: Re: How to solve Justin's Pocket (Corner) Cube?
PostPosted: Sun Nov 10, 2013 11:06 am 
Offline
User avatar

Joined: Thu Dec 15, 2011 10:04 pm
Location: Sioux Lookout, Canada
TheCubingKyle wrote:
Pete the Geek wrote:
One thing I'm curious about: can the Corner Pocket Cube be solved into other rotations of the special corner? For example, can we have yellow on the front, blue on top and green on the right?

I don't think it can. Mostly because

[Spoiler]The "corners" are all 3x3 centers, and because of the way this is bandaged, the other "cubies" wouldn't maintain cubic shape, if it even allowed the centers hidden within to be rotated in this fashion.[/spoiler]
I took a closer look at it this morning and I'm sure you are correct. Now if I don't care about the position of the logos, the whole puzzle can just be rotated into two alternate positions to "rotate" that corner.

_________________
PeteTheGeek196 on YouTube


Top
 Profile  
 
 Post subject: Re: How to solve Justin's Pocket (Corner) Cube?
PostPosted: Sun Nov 10, 2013 11:35 am 
Offline
User avatar

Joined: Thu Dec 15, 2011 10:04 pm
Location: Sioux Lookout, Canada
Solving the 4-Colour version (and 6-Colour if anyone ever makes one) requires a few lengthy but straightforward algorithms. Even the 2-Colour version may require a few algorithms to place the logo corners and possibly swap a small corner with a large corner. As Konrad noted earlier, this puzzle is a shape-mod of Andreas' 3 Quads, 3 Stripes. The rest is in spoiler tags.

[spoiler]
On page 4 of the thread that Konrad mentioned, are some posts from Andreas and Konrad. One is a post from Andreas with 9 algorithms (separated into phases) for solving 3 Quads, 3 Stripes and a few posts down Konrad provided an English translation. I made a 3 Quads, 3 Stripes with my CubeTwist 3x3 Bandage Kit and started to work out what each of the 9 algorithms does. After awhile, I noticed that later in the thread Konrad had also posted a beautiful diagram showing exactly what each of the algorithms does.

To solve the Corner Pocket Cube:
I returned it to cubic state (even though I had one small cube swapped with a big cube). Then I started applying the algorithms. I ignored the "phases" and just looked at the diagrams, selected one that looked useful, and applied it. Only a few are needed.

Some Tips:
In the 3 Quads, 3 Stripes material, edges and corners are referred to by pairs and triples of the adjacent face names. Having the 3 Quads, 3 Stripes puzzle for reference helps show that edge BD is actually the BDR corner on the Pocket Corner Cube. So any algorithm that moves BD on 3 Quads, 3 Stripes will move BDR on Pocket Corner Cube. It can take some strategic application of algorithms to avoid splitting the logo corners, as the algorithms that work on LB will move the Meffert's Logo corner (good if it is not positioned yet, bad if it is). Use the 3 Quads, 3 Stripes to test things out.

[/spoiler]

_________________
PeteTheGeek196 on YouTube


Top
 Profile  
 
 Post subject: Re: How to solve Justin's Pocket (Corner) Cube?
PostPosted: Sun Nov 10, 2013 3:45 pm 
Offline
User avatar

Joined: Thu Sep 17, 2009 6:07 am
Location: Germany, Bavaria
Pete the Geek wrote:
Solving the 4-Colour version (and 6-Colour if anyone ever makes one) requires a few lengthy but straightforward algorithms. Even the 2-Colour version may require a few algorithms to place the logo corners and possibly swap a small corner with a large corner. As Konrad noted earlier, this puzzle is a shape-mod of Andreas' 3 Quads, 3 Stripes. The rest is in spoiler tags ....
Pete, why do you call these algorithms "straight-forward"? I would not say that they are easy to find, right?
If you base a method on the information pointed to in your spoiler, you can certainly state that performing them is straight forward.
When I solved the "3 Quads, 3 Stripes" for the first time, it took me a long time to create a situation with two stripes swapped. I was not able to solve it from there without Andreas' help!
And Andreas got his move sequences out of his program.

Has anybody found a different method?

For the two colour version, a single move sequence is enough to place the one distinguishable piece onto its original location, once you have achieved the "cubic" form. (The term "cubic" includes the real cubic shape and the shape above with the two swapped 3x3 corners.) The very same sequence (a [6,1]) can be used to swap the two corners.

_________________
My collection at: http://sites.google.com/site/twistykon/home


Top
 Profile  
 
 Post subject: Re: How to solve Justin's Pocket (Corner) Cube?
PostPosted: Sun Nov 10, 2013 4:47 pm 
Offline
User avatar

Joined: Thu Dec 15, 2011 10:04 pm
Location: Sioux Lookout, Canada
Konrad wrote:
Pete, why do you call these algorithms "straight-forward"? I would not say that they are easy to find, right?
If you base a method on the information pointed to in your spoiler, you can certainly state that performing them is straight forward.
Yes, I should have been much clearer! I meant that applying the algorithms is straight-forward. I find they have nice symmetric patterns that are easy for me to follow and your diagrams make them very easy to select. Generating these algorithms was definitely not a simple task and, as someone who used to write software for a living, I appreciate Andreas' effort and genius to make them and your work to illustrate them.

_________________
PeteTheGeek196 on YouTube


Top
 Profile  
 
 Post subject: Re: How to solve Justin's Pocket (Corner) Cube?
PostPosted: Mon Nov 11, 2013 1:35 am 
Offline
User avatar

Joined: Mon Aug 02, 2004 7:03 am
Location: Koblenz, Germany
Konrad wrote:
As Andreas, the inventor of the "3 Quads, 3 Stripes", admits, he struggled with this first step too.
Correct.
And therefore I enhanced the program (back in those days) with an automatic signature solver.
It creates a sequence for every signature which leads back to the solved signature.
I didn't posted it earlier because I considered such a lengthy list of no practical use. I couldn't find an easier way to guide a solver through this first step ...


Attachments:
Solution 2013930080085E - Kopie.txt [23.75 KiB]
Downloaded 68 times
Top
 Profile  
 
 Post subject: Re: How to solve Justin's Pocket (Corner) Cube?
PostPosted: Mon Nov 11, 2013 10:18 am 
Offline
User avatar

Joined: Thu Dec 15, 2011 10:04 pm
Location: Sioux Lookout, Canada
Andreas Nortmann wrote:
Konrad wrote:
As Andreas, the inventor of the "3 Quads, 3 Stripes", admits, he struggled with this first step too.
Correct.
And therefore I enhanced the program (back in those days) with an automatic signature solver.
It creates a sequence for every signature which leads back to the solved signature.
I didn't posted it earlier because I considered such a lengthy list of no practical use. I couldn't find an easier way to guide a solver through this first step ...
I'm glad you posted this idea and the file.

Yesterday, I was making making a visual guide on how to get the Corner Pocket Cube back to the cubic state. The idea is not to have every possible state (signature) shown, just enough that some twisting and turning of an unrecognized state will lead to one in the guide and then the algorithm to get back to cubic. If it turns out to be useful, I will add a few more entries to this chart.
Attachment:
Generator-Sample_w_Text_sm.jpg
Generator-Sample_w_Text_sm.jpg [ 130.67 KiB | Viewed 2524 times ]

_________________
PeteTheGeek196 on YouTube


Top
 Profile  
 
 Post subject: Re: How to solve Justin's Pocket (Corner) Cube?
PostPosted: Mon Nov 18, 2013 1:55 am 
Offline
User avatar

Joined: Wed Apr 13, 2011 8:37 am
Location: Germany
Hi friends,

I build the cube with the Cube twist set. Thanks for your work , Andreas, Konrad, Pete.

I'm unsure to order the pocket cube. I cannot solve the version with Cubetwist set.
This puzzle looks very beautifull.


Top
 Profile  
 
 Post subject: Re: How to solve Justin's Pocket (Corner) Cube?
PostPosted: Tue Nov 19, 2013 12:53 pm 
Offline
User avatar

Joined: Wed Apr 13, 2011 8:37 am
Location: Germany
I found a little technique to explore sequences without a program.

The idea is to find symetric positions. Symetric in relation to the shape.

Attachment:
pocket.jpg
pocket.jpg [ 204.86 KiB | Viewed 2282 times ]


The first 2 moves of a sequence is always equal. The symetry is the reason.
After that no much moves with sense are possible.

An example is the shape of the picture.

Put the cube that the 2x2x2 subcube with single stickers are on left/down/front position. The yellow blue red corner is on back/right/top
Then:
The sequence :A = U R' F2 U F U' R' F2 R

So it's possible to do an F2
Then undo the sequence A' = R' F2 R U F' U' F2 R U'

This causes an swap of 2 opposite corners , 2 stripes and 2 single edges.

One more technique is to get a (shape) symetric position.
Then mirror the sequence and instead of the inversion of original sequence you can do the inverse of mirror.

I still work on it. The sucess is small.


Top
 Profile  
 
 Post subject: Re: How to solve Justin's Pocket (Corner) Cube?
PostPosted: Tue Nov 19, 2013 5:31 pm 
Offline
User avatar

Joined: Wed Apr 13, 2011 8:37 am
Location: Germany
Solving the pocket cube:
I will explain the technique with mirroring sequences.
In the last posting the sequence
A = U R' F2 U F U' R' F2 R
causes a face with symetry.

after doing A you can do sequence
B = R' F' R U F' U'

Then the shape is symetric.
You can replace U with R' and vice versa. F becomes F'.

The sequence is A + B
U R' F2 U F U' R' F2 R R' F' R U F' U'

The inverse with mirror is

R' F' R U F' U' U F2 U' R' F R F2 U' R

all together

1) U R' F2 U F U' R' F2 R R' F' R U F' U' R' F' R U F' U' U F2 U' R' F R F2 U' R

This flips 2 edges and makes a 3 cycle of stripes and turns 2 opposite corners.

A third sequence is : C = R U'

A + B + C
causes a new symetry. Now you can replace U with B' and F with D'.

U R' F2 U F U' R' F2 R R' F' R U F' U' R U'


The mirrored inverse is B' R B' D' B R D' R' R D2 R' B' D B D2 R' B

all together :

U R' F2 U F U' R' F2 R R' F' R U F' U' R U' B' R B' D' B R D' R' R D2 R' B' D B D2 R' B

This turns 2 opposite corners and makes a unflipped 3cycle of edges.

It's possible to solve all positions with this sequences.

Example
The sequence 1) three times makes a clean flip of two edges.

Basic for all this the three sequences:
A : U R' F2 U F U' R' F2 R
B : R' F' R U F' U'
C : R U'


Top
 Profile  
 
 Post subject: Re: How to solve Justin's Pocket (Corner) Cube?
PostPosted: Tue Nov 19, 2013 5:51 pm 
Offline
User avatar

Joined: Thu Dec 15, 2011 10:04 pm
Location: Sioux Lookout, Canada
Andrea wrote:
It's possible to solve all positions with this sequences.

Example
The sequence 1) three times makes a clean flip of two edges.

Basic for all this the three sequences:
A : U R' F2 U F U' R' F2 R
B : R' F' R U F' U'
C : R U'
Wow, that's a great analysis, Andrea. I've been looking for a solution and I never expected it to be so simple and elegant.

_________________
PeteTheGeek196 on YouTube


Top
 Profile  
 
 Post subject: Re: How to solve Justin's Pocket (Corner) Cube?
PostPosted: Wed Nov 20, 2013 3:14 pm 
Offline
User avatar

Joined: Thu Sep 17, 2009 6:07 am
Location: Germany, Bavaria
Hi Andrea,

thank you very much for sharing your ideas.
I'm afraid, I have not yet understood everything.
I shall have a detailed look at your method, but I would like to ask a question first.

My impression is that your sequences work after the "3 Quads, 3 Stripes" is put back into its regular form.
Andreas' program has found 580 "signatures", states of the puzzle.

How do I get back from one of those to the "regular form"?
Image
That was the question discussed by Andreas, Pete and me (and this is more or less the only challenge on a two colour version of the Pocket Cube).

Obviously, you assume that your sequences are performed on a "regular 3 Quads, 3 Stripes" (which is a " solved two colour Pocket (Corner)Cube" ?

E.g. U,R',F2,U,F,U',R',F2,R,R',F',R,U,F',U',R,U',B',R,B',D',B,R,D',R',R,D2,R',B',D,B,D2,R',B will not change anything recognizable on a two colour version.

Still, this is quite an achievement that you have found these three basic sequences without the help of a computer! :D

_________________
My collection at: http://sites.google.com/site/twistykon/home


Top
 Profile  
 
 Post subject: Re: How to solve Justin's Pocket (Corner) Cube?
PostPosted: Wed Nov 20, 2013 5:12 pm 
Offline
User avatar

Joined: Thu Sep 17, 2009 6:07 am
Location: Germany, Bavaria
Have you seen this in the other thread?.
leonid wrote:
I received mine! Was so excited that I accidentally pushed a block back a bit too hard.

Image

The same happened to me today.
Image
OK, I admit, it was hard work to produce this special state. :lol:

_________________
My collection at: http://sites.google.com/site/twistykon/home


Top
 Profile  
 
 Post subject: Re: How to solve Justin's Pocket (Corner) Cube?
PostPosted: Wed Nov 20, 2013 5:21 pm 
Offline
User avatar

Joined: Wed Apr 13, 2011 8:37 am
Location: Germany
Hi Konrad,

Quote:
How do I get back from one of those to the "regular form"?


I didn't discussed about it.
My analysis is only based an a regular shape. I explored sequences to permute pieces without destroing the shape.
Quote:
Andreas' program has found 580 "signatures", states of the puzzle.


Is it possible to download this program ? I don't know the functionality of this program.

Quote:
How do I get back from one of those to the "regular form"?
That was the question discussed by Andreas, Pete and me.

Ok , my posting was different to this intention.

Pete did a good work with his table from Mon Nov 11, 2013 4:18 pm.
I solve the shape with intuition. The problem are the permuted pieces in the correct shape.(4 color version or cube-twist)
I ordered the 4 color version of this cube. I hope the nice patterns you posted here are possible with this.If the 2 opposite cubes are swapped, my sequence A F2 A' is the solution.

Quote:
Do you assume that your sequences are performed on a "regular 3 Quads, 3 Stripes"?

I didn't understand this exact. I try to answer.
I checked all the sequences with a cube-twist version.
They are ok. But the single corner is on right top back and the 2x2x2 subcube on left front down. I used a different start position. A z axis 180 degrees rotation from your start - position.


Top
 Profile  
 
 Post subject: Re: How to solve Justin's Pocket (Corner) Cube?
PostPosted: Wed Nov 20, 2013 5:28 pm 
Offline
User avatar

Joined: Wed Apr 13, 2011 8:37 am
Location: Germany
Hi Konrad,

are the nice patterns possible with the 4 color version ?
That means that the colors on each faces of 2x2x2 subcube is equal.

Cheers,
Andrea


Top
 Profile  
 
 Post subject: Re: How to solve Justin's Pocket (Corner) Cube?
PostPosted: Wed Nov 20, 2013 6:33 pm 
Offline
User avatar

Joined: Thu Sep 17, 2009 6:07 am
Location: Germany, Bavaria
Andrea wrote:
Hi Konrad,

are the nice patterns possible with the 4 color version ?
That means that the colors on each faces of 2x2x2 subcube is equal.

Cheers,
Andrea
Thanks for your answers. (I have edited my post above a bit).
When I typed my reply I had not looked at all your sequences.
Nice finding!

To answer your question: I believe it is possible, but I would have to check it with the CT Cube.

EDIT: I tried to get the special pattern
Image on a "3 Quads, 3 Stripes" CT cube. I could not do it in a way that the 2x2x2 corner of 1x1x1 cubies remains solved.
I'm not sure if it is possible at all.

_________________
My collection at: http://sites.google.com/site/twistykon/home


Top
 Profile  
 
 Post subject: Re: How to solve Justin's Pocket (Corner) Cube?
PostPosted: Thu Nov 21, 2013 9:52 am 
Offline
User avatar

Joined: Wed Apr 13, 2011 8:37 am
Location: Germany
Hi Konrad,
Quote:
E.g. U,R',F2,U,F,U',R',F2,R,R',F',R,U,F',U',R,U',B',R,B',D',B,R,D',R',R,D2,R',B',D,B,D2,R',B will not change anything recognizable on a two colour version.

Yes ! On a 2 color this has no effect.

My solution. Try intuitive to build the shape.
There are some difficult cases with sequences.

1)
Two opposite corners are exchanged : A F2 A'
On a 2 color cube this makes a nice pattern.

A corner and a stripe are exchanged. (A + B + c ) '
Or the second halve of the posted sequence
B' R B' D' B R D' R' R D2 R' B' D B D2 R' B
Exchanges a stripe with a corner.
On a 2 color cube this shows a (move / push) of 2 big corners.


Then the shape is correct but edges are flipped or permuted.
For this situations I developed the sequences.

Perhaps all other cases are inuitive solveable.
Perhaps these sequences are usefull for nice shape pattern.
I cannot wait until my pocket cubes arrives.


Top
 Profile  
 
 Post subject: Re: How to solve Justin's Pocket (Corner) Cube?
PostPosted: Thu Nov 21, 2013 1:42 pm 
Offline
User avatar

Joined: Thu Sep 17, 2009 6:07 am
Location: Germany, Bavaria
Andrea, thank you for the additional clarification.
As I wrote above, looking at your sequences and your reply made it perfectly clear, how you will solve the puzzle. I hope it arrives soon.

Congratulations that you have mastered the "3 Quads, 3 Stripes" puzzle without the help of a computer program!
You seem to be the first, as far as I know :)

Just to make clear what I meant with the "regular form" of the 3 Quads 3 Stripes:
Konrad wrote:
The bandaged 3x3x3 was Andreas Nortmann's 2013930080085E aka "3 Quads, 3 Stripes".Image
For the two colour version the solution is: Reconstruct the cubic shape.
The colours of the tiles are not relevant, any permutation of the pieces that show this state are "regular" and have Andreas' signature 2013930080085E.
Image
Naturally, it has nothing to do with the location of the 2x2x2 sub-cube. Personally, I prefer diagrams where it is located at UFR. This shows the overall symmetry quite nicely.

BTW, I can now prove that the nice pattern of leonid can not be made on a 4-colour version. (I'm currently not at home, but I'll write more later or by tomorrow.)

PS Your A F2 A' is a bit similar to one of Andreas Nortmann's sequences.

_________________
My collection at: http://sites.google.com/site/twistykon/home


Top
 Profile  
 
 Post subject: Re: How to solve Justin's Pocket (Corner) Cube?
PostPosted: Thu Nov 21, 2013 3:17 pm 
Offline
User avatar

Joined: Thu Sep 17, 2009 6:07 am
Location: Germany, Bavaria
Hi Andrea and others who might be interested,

you had asked about the program of Andreas Nortmann.
Actually, there are two programs:

Andreas has made available an Analyser program in this thread
Andreas Nortmann wrote:
Hi guys,

After the presentation of the 3X3X3 DIY Bandaged Cubes I thought it a good moment to start another thread (my third during the years after 2004 and 2010) here in which I present my work about bandaged 3x3x3s and other bandaged puzzles.
Attachment:
Analyzer-Distribute.zip
This program presents English language on every Windows system except those with German settings.

What has changed?
The most important thing is this:
I succeeded in generalizing the algorithm for "dead ends" for all puzzles and therefore the number of essentially different 3x3x3 is now 5844 of which 5705 are non-trivial of which 3563 can be implemented with the 3X3X3 DIY Bandaged Cubes.
The 3 Quads, 3 Stripes is one of the 3563.

You can download this Analyser program in the other thread

Additionally, Andreas wrote in that thread:
Andreas Nortmann wrote:
The project was about programming a generator for human readable solution strategies.
I wanted to create a solution strategy for every of the 5844 bandaged cubes in the program.

I froze that project because of the museum.
Before I have frozen it I succeeded in some preliminary steps. These allowed me to calculate

the number of different signatures each bandaged variant can have by being turned.
the number of permutations for each bandaged variant.
the restriction factor (quotient between naive and true number of permutations) for each bandaged variant.
an automatic solution strategy for the ca. 3900 bandaged cubes which number of permutations (ca. 4 million if I remember right) is low enough.
Some days ago I just dug into my archives and grabbed the file for "3Quads and 3 stripes" cube.
I even outlined an article for CFF in which I wanted to present all kinds of statistics about the 5844 bandaged variants.
BTW, CFF = "Cubism For Fun" is the magazine of the NKC = Nederlandse Kubus Club.
(NKC organizes the DCD = Dutch Cube Day since 1981 without interruption.)

Probably you can get more details about this solution program directly from Andreas via PM.

_________________
My collection at: http://sites.google.com/site/twistykon/home


Top
 Profile  
 
 Post subject: Re: How to solve Justin's Pocket (Corner) Cube?
PostPosted: Thu Nov 21, 2013 4:58 pm 
Offline
User avatar

Joined: Wed Apr 13, 2011 8:37 am
Location: Germany
Hi Konrad,

Quote:
Congratulations that you have mastered the "3 Quads, 3 Stripes" puzzle without the help of a computer program!
You seem to be the first, as far as I know


Sorry, this is not correct.
:oops: :oops:

I found some configurations which are not solveable with my sequences.

One Example is a clean swap of two stripes.
This is equivalent to a swap of two edges and two opposite corners.
Perhaps it's not possible to solve this puzzle without a paper.
It's difficult to memorize many states and sequences without a paper.
My analysis was not complete. But a first step.

Cheers ,
Andrea


Top
 Profile  
 
 Post subject: Re: How to solve Justin's Pocket (Corner) Cube?
PostPosted: Thu Nov 21, 2013 7:55 pm 
Offline

Joined: Tue Jun 11, 2013 12:48 pm
Dear puzzlers :-)

the corner pocket cube is a really fascinating puzzle. I must admit that I underestimated it in the very beginning.
At the homepage of Mefferts puzzle shop the skill level for the 2 colored version is rated with 2 stars and the 4 colored version with 4 stars.
Just for comparison: the megaminx is rated with 6 stars (maximum difficulty).
If it is true what Andrea assumed that it might not be possible to solve the corner pocket cube without pen and paper then I would say that this is one of the hardest puzzles I know.

I have the 4 colored version and I was fiddling around with it for quite a while. Then I solved it accidently. But actually I have not really an idea how I did it. While solving it I realised that there are certain "key"-states which repeated very often. I also found some easy moves how to switch between certain states. I guess maybe it could be possible to subsume similar states to groups. Sort of analogue to the Friedrich method where you can decrease the 54 oll cases (not sure if this number is correct) of the Friedrich Method down to nine "2 look oll algorithms".
I wished I had the time to analyse that puzzle more deeply. It is kind of new for me :-)
I wish everyone good luck!


Top
 Profile  
 
 Post subject: Re: How to solve Justin's Pocket (Corner) Cube?
PostPosted: Fri Nov 22, 2013 1:30 am 
Offline
User avatar

Joined: Mon Aug 02, 2004 7:03 am
Location: Koblenz, Germany
Konrad wrote:
you had asked about the program of Andreas Nortmann.
Actually, there are two programs:

Andreas has made available an Analyser program in this thread
Thank you Konrad for posting this.
I was absent for some days.
Family goes first.
As hinted by Konrad I haven't made the solver public yet.
It is unprobable that I will.

Andreas


Top
 Profile  
 
 Post subject: Re: How to solve Justin's Pocket (Corner) Cube?
PostPosted: Fri Nov 22, 2013 6:25 am 
Offline
User avatar

Joined: Thu Sep 17, 2009 6:07 am
Location: Germany, Bavaria
Back to Leonid's special pattern on a 4-coloured version:
Konrad wrote:
... I tried to get the special pattern
Image on a "3 Quads, 3 Stripes" CT cube. I could not do it in a way that the 2x2x2 corner of 1x1x1 cubies remains solved.
....
The target state on a "3 Quads, 3 Stripes" would look like this:
Image
In Andreas' (please be aware of the difference between Andrea's and Andreas' :lol: ) Analyser this is:
Image
Please note, Andreas uses a different colour scheme!

Performing this sequence on a solved "3Quads, 3 Stripes", (Please note, that I hold the 2x2x2 block at UFR):
L', D, F, L, D', B', L, U, B, L', B', L, U', L', B, D, L', F', D', L, B, D'2, R', D, B, R', B', R'2, D, B', L, B', U'2, L, U, L', B', U'2, B, U'2, B', U'2, B, L, U', L', U, B, L', D, L', F'
I can produce this close to target state:
Image
We see that two 3x3 edges need to be swapped, they are in an odd permutation.
As we know, 3x3 edges can be in odd permutations only if there exists an odd permutation of corners.
The two single 3x3 corners (on the Pocket Cube: one 1x1x1 cubie and one extended) are located correctly.
The remaining six 3x3 corners are bandaged with 3x3 edges to 2x1x1 corner-edges and can be permuted together, only.
The aggregated permutations of corners and edges when permuting corner-edges will always be an even number.
This means that the target pattern can never be reached by legal turns!

_________________
My collection at: http://sites.google.com/site/twistykon/home


Top
 Profile  
 
 Post subject: Re: How to solve Justin's Pocket (Corner) Cube?
PostPosted: Fri Nov 22, 2013 9:11 am 
Offline
User avatar

Joined: Wed Apr 13, 2011 8:37 am
Location: Germany
Hi Konrad
Quote:
L', D, F, L, D', B', L, U, B, L', B', L, U', L', B, D, L', F', D', L, B, D'2, R', D, B, R', B', R'2, D, B', L, B', U'2, L, U, L', B', U'2, B, U'2, B', U'2, B, L, U', L', U, B, L', D, L', F'


Great job.
Thank you for the answer.
How did you find this difficult sequence ?


Top
 Profile  
 
 Post subject: Re: How to solve Justin's Pocket (Corner) Cube?
PostPosted: Fri Nov 22, 2013 3:12 pm 
Offline
User avatar

Joined: Thu Sep 17, 2009 6:07 am
Location: Germany, Bavaria
Andrea wrote:
... How did you find this difficult sequence ?
Hi Andrea,
actually I just combined a few sequences from Andreas' input.

Here is a sequence that puts the 2-coloured version into Leonid's nice pattern state:
L, B', U', B, L'2, D, F'2, D', L, D, L', F'
doctor twist wrote:
... If it is true what Andrea assumed that it might not be possible to solve the corner pocket cube without pen and paper then I would say that this is one of the hardest puzzles I know.
....
I guess, Andrea meant that it needs a lot of work to find a solution on your own. If you use all the information contained in this thread, it is not so extremely difficult any longer.
The spoiler in Pete's post from November 10th contains all hints you need. A major part is in my diagram and in Andreas' method (based on his solution program).

Finding your own method without the help of a computer program is the big challenge.
If you want help, you can use the spoiler on this thread in my post from July 2nd and the diagrams in my post from July 4th.

As Pete has pointed out in his post on November 10th, the 4-colour version does require a smaller part of the overall solution of a "3 Quads, 3 Stripes" after you have reached the cubic form.

If you accept all the help you can get (That's what I have done. :wink: ), you can go this route

1. Try to understand the relationship between the Pocket (Corner) Cube and the "3 Quads, 3 Stripes". Just try to cut off (mentally :lol: ) the extended portions of the solved Pocket corner and recognize the underlying 3 Quads, 3 Stripes.

2. Scramble and solve it to the cubic shape (intuitively). There is the special case only where the single corners (the 1x1x1 corner and the extended single 3x3x3 corner are swapped:
Image[/quote]
In this case you can swap the two single corners by L,B',U',B,L2,D,F2,D',L2,B',U,B,L'
it is a relatively easy to memorize [6:1] conjugate. F2 is the "1" part.

3. Use some of the sequences in my diagram from July 4th (in the other thread) to permute and flip the four pieces in the 2x2x2 sub-block.

Obviously you are done with 2-colour version when it is back in cubic shape. No step 3 for this one!

BTW, I have ordered the 4-colour version today. This puzzle is really something special :)

_________________
My collection at: http://sites.google.com/site/twistykon/home


Top
 Profile  
 
 Post subject: Re: How to solve Justin's Pocket (Corner) Cube?
PostPosted: Sun Nov 24, 2013 6:15 pm 
Offline
User avatar

Joined: Wed Apr 13, 2011 8:37 am
Location: Germany
Hi puzzlers,

I wrote a little C program to analyse the 3quads3stripes / pocket cube.
The algorithm is an iterative deep first search without pruning table.
The calculation duration is only a few seconds.
Open the command window where the program pocket.exe is.
Type pocket.

Then the program calculates some sequences.
The position of subcube is L/D/F.

If you type > "pocket ruf " then the 2x2x2 subcube is on R-U-F like Konrad's position.
The most difficult sequence is exchanging only 2 stripes. ( Parity)
The last pattern is the nice pattern from Leonid.

The sourcecode is added. It's possible to compile it under linux / bsd etc.

The output from "pocket ruf" :
Code:
Pocket Cube Analyse Program by Andrea

Exchange 2 stripes :
D L' F2 D F D' L' F2 L F D' L B' L U L U' L' U' L' B D L' F' D' L B D' R' B' D

Exchange 3 stripes :
L B' U' B L' D L' F2 D' L D L' F2 L D' L' D F2 L D' L' D F2 D' L2 B' U B L'

Exchange 2 opposite corners :
L B' U' B L2 D F2 D' L2 B' U B L'

Turn 2 opposite Corners :
L B' U2 L U L' B' U B2 L' D' B R D B' L' D F D' L D L' F' D' L B D' R' B' D

3 cycle of 3 edges :
L B' U' B L2 D F2 D' L D L' F' D' L B D' R D B' D' B R2 B' D2 L' F L D'

flip 2 egdes :
L B' U' L' B D L' F' D' L B D' R' B' D L B' U' L' B D L' F' D' L B D' R' B' D

Exchange 3 stripes and turn corners :
L B' U' B L' D L' F' L D' B' L U B L' B D' R D B'

Nice Pattern (pushed blocks) :
L' D F D' L D L' F' L' F L



Download this:
Attachment:
pocket.zip [26.94 KiB]
Downloaded 17 times


Top
 Profile  
 
 Post subject: Re: How to solve Justin's Pocket (Corner) Cube?
PostPosted: Mon Nov 25, 2013 2:03 am 
Offline
User avatar

Joined: Mon Aug 02, 2004 7:03 am
Location: Koblenz, Germany
Konrad wrote:
In Andreas' (please be aware of the difference between Andrea's and Andreas' :lol: ) Analyser this is:
Image

If you look again into that lengthy text file you can find this line:
22039310000BC2 L=008 F L D' L B' U B L'
(my notation obviously)
That means you can restore the target siganture with only 8 moves.


Top
 Profile  
 
 Post subject: Re: How to solve Justin's Pocket (Corner) Cube?
PostPosted: Mon Nov 25, 2013 4:21 am 
Offline
User avatar

Joined: Thu Sep 17, 2009 6:07 am
Location: Germany, Bavaria
Andreas Nortmann wrote:
...
That means you can restore the target signature with only 8 moves.
Exactly. The shown signature is that of Leonid's nice pattern. After applying the sequence quoted by Andreas, you are back to the regular shape.
You still need to permute the 1x1x1 cubies, though.
That's why I had shown this pretty lengthy sequence (combination of Andreas' sequences) to create a pattern where the odd permutation of 1x1x1 edges is obvious.

I was answering Andrea's question, if the 4 colour Pocket Cube can be permuted to Leonid's nice pattern.
The answer is no, not exactly. The shape can be reached naturally, but the 1x1x1 edges will be swapped.

P.S. Nice to see two posts by Andrea and Andreas in a row. :lol:

@Andrea: This shows again your programming skills :)

_________________
My collection at: http://sites.google.com/site/twistykon/home


Top
 Profile  
 
 Post subject: Re: How to solve Justin's Pocket (Corner) Cube?
PostPosted: Mon Nov 25, 2013 4:05 pm 
Offline
User avatar

Joined: Thu Sep 17, 2009 6:07 am
Location: Germany, Bavaria
Andrea has found with her program a lot of good sequences. Thanks a lot for sharing it with us. :)
(Maybe, when I have more time, I'll setup a C environment and look at your program.
For now I want to show how much I appreciate your skills, by adding diagrams to your sequences)

I thought that I should make a little compendium about A&A's sequences (A&A = Andrea & Andreas).
It is interesting that there is some overlap (several found by Andreas were found by Andrea as well) and some from Andrea are new.
Here is all (or more than) you need to solve the four-colour version.
The first step (back to the cubic form) is still to be done intuitively.

First (because his solution was earlier in the "3 Quads, 3 Stripes" topic) the most important sequences found by Andreas Nortmann's program:
Image

And here the sequences found by Andrea:

Image

If you want to check something by "copy and paste" into Gelatinbrain, here follow the sequences in plain text:
Code:
3 Quads, 3 Stripes 2013930080085E
We use  David Singmaster´s Notation (normal turns clockwise)
U=Orange F=Green L=Yellow D=Red B=Blue R=White
580 signatures
432 permutations

Position Corner-Edges
a) L,  B',  U',  B, L2,  D, F2,  D',  L2,  B',  U, B, L',  (13)
inverted is identical Position 1x1x1 Edges – 3-cycle

b) L, B', U', B, L', D, L', F2, D', L, D', B, R', B', D (15)
inverted
D', B, R, B', D, L', D, F'2, L, D', L, B', U, B, L'

Position 1x1x1 Edges – swap of two edges
c) B', L, U ,L', B, L, B', U', B', U, B2, L', D', B, R, D, B', D, L', F, L, D' (22)
inverted
D, L', F', L, D', B, D', R', B', D, L, B'2, U', B, U, B, L', B', L, U', L', B

Flip 1x1x1 Edges
d) D', B, R, D, B', L', D, F, L, D', B', L, U, B, L', D', B, R, D, B', L', D, F, L, D', B', L, U, B, L' (30)
inverted
L, B', U', L', B, D, L', F', D', L, B, D', R', B', D, L, B', U', L', B, D, L', F', D', L, B, D', R', B', D

Orientate 1x1x1 corners
e) L', D, F, L, D', B', L, U, B, L', B', L, U', L', B, D, L', F', D', L, B, D2, R', D, B, R', B', R2, D, B' (30)
inverted
B, D', R'2, B, R, B', D', R, D'2, B', L', D, F, L, D', B', L, U, L', B, L, B', U', L', B, D, L', F', D', L

Andrea's Sequences Exchange 2 stripes
D,L',F2,D,F,D',L',F2,L,F,D',L,B',L,U,L,U',L',U',L',B,D,L',F',D',L,B,D',R',B',D (31)
inverted
D', B, R, D, B', L', D, F, L, D', B', L, U, L, U, L', U', L', B, L', D, F', L', F'2, L, D, F', D', F'2, L, D'

3-cycle of Stripes
L,B',U',B,L',D,L',F2,D',L,D,L',F2,L,D',L',D,F2,L,D',L',D,F2,D',L2,B',U,B,L'  (29)
inverted
L, B', U', B, L'2, D, F'2, D', L, D, L', F'2, D', L, D, L', F'2, L, D', L', D, F'2, L, D', L, B', U, B, L'

Exchange 2 opposite corners
L,B',U',B,L2,D,F2,D',L2,B',U,B,L',
identical to "a)" above

Turn 2 opposite Corners :
L,B',U2,L,U,L',B',U,B2,L',D',B,R,D,B',L',D,F,D',L,D,L',F',D',L,B,D',R',B',D
identical to "e) inverted " above

Pure 3 cycle of 3 edges  (the impure version in b) above is just 15 turns):
L,B',U',B,L2,D,F2,D',L,D,L',F',D',L,B,D',R,D,B',D',B,R2,B',D2,L',F,L,D' (28)
inverted
D, L', F', L, D'2, B, R'2, B', D, B, D', R', D, B', L', D, F, L, D', L', D, F'2, D', L'2, B', U, B, L'

flip 2 egdes :
L,B',U',L',B,D,L',F',D',L,B,D',R',B',D,L,B',U',L',B,D,L',F',D',L,B,D',R',B',D,(30)
identical to "d) inverted" above

Exchange 3 stripes and turn corners :
L,B',U',B,L',D,L',F',L,D',B',L,U,B,L',B,D',R,D,B', (20)
inverted
B, D', R', D, B', L, B', U', L', B, D, L', F, L, D', L, B', U, B, L'

Nice Pattern (pushed blocks) :
L',D,F,D',L,D,L',F',L',F,L
From solved to pattern
inverted
L', F', L, F, L, D', L', D, F', D', L



We can still offer the position of the "first solver without the help of a program". :wink:
Andrea has achieved a good part, but the rest was done by programming (which is something by itself).

Do not underestimate the first step: Back to the cubic form of the Pocket Corner just using your intuition.
The text file generated by Andreas can be a help if you are completely lost.
If you want to use it, the problem remains to generate the hexadecimal signature.
Yesterday I reduced the 580 cases shown in Andreas' table to 200.
(Please, note that you can turn the cubic form around the corner RUF generating three out of one sequence. I'm not sure why Andreas has in his text file 579 cases, but only 279 were duplicates when turning the whole cube in space.)
I started with a document in which I included pictures of the "3 Quads, 3 Stripes" for half of the 200 cases.
I gave up this idea, because it is definitely not so easy to map mentally a shape shifted Pocket Corner Cube to a 2D picture of a "3 Quads, 3 Stripes")

_________________
My collection at: http://sites.google.com/site/twistykon/home


Top
 Profile  
 
 Post subject: Re: How to solve Justin's Pocket (Corner) Cube?
PostPosted: Mon Nov 25, 2013 5:31 pm 
Offline
User avatar

Joined: Wed Apr 13, 2011 8:37 am
Location: Germany
Hi Konrad,

great job. You put it together very visual.

One more sequence is L' D F D' L B' L U2 B L' B D' R D B'
This is equivalent to b. Turn corners and a 3cycle of edges.
A good idea is to use short sequences. e.g. Use a to exchange stripes.
Use b to make an edge 3cycle, and turn the corners later.

The worst case is the swap of 2 stripes. Perhaps it's easier to solve this case with intuition/try and error than memorize 31 moves.


Top
 Profile  
 
 Post subject: Re: How to solve Justin's Pocket (Corner) Cube?
PostPosted: Tue Nov 26, 2013 2:04 am 
Offline
User avatar

Joined: Mon Aug 02, 2004 7:03 am
Location: Koblenz, Germany
Konrad wrote:
We can still offer the position of the "first solver without the help of a program". :wink:
Back in the days when I was a solver I solved it by pen and paper after I created it by hand. Sadly my original sketches got lost. I have no proof.
Konrad wrote:
I'm not sure why Andreas has in his text file 579 cases, but only 279 were duplicates when turning the whole cube in space.
A dumb computer program created the list I posted.
Only 1777 of the 5844 variants in the analyzer have symmetries, most of them are mirrorings.
Only 191 variants have a higher degree of symmetry.
Only 28 varaints have a degree of symmetry comparable to the "3 Quads and 3 Stripes" or higher.
I focused on the solution generator itself. Making use of the rare symmetries was on the TODO-list but with low priority.

BTW: The numbers presented here are already optimal. For each variant the filtering program picks always the most symmetric shape out of all the possible ones. It didn't help much as you can see by the numbers.


Top
 Profile  
 
 Post subject: Re: How to solve Justin's Pocket (Corner) Cube?
PostPosted: Tue Nov 26, 2013 2:57 am 
Offline
User avatar

Joined: Mon Feb 27, 2012 10:57 am
Location: In my study drooling over my puzzle hoard - Precioussssss!
I am disappointed!
I bought this puzzle because I thought it looked good an would be a fun solve but now realise that effectively I'll never solve it! I like to take a new puzzle and apply what I know in new ways and maybe work out a commutator and solve without resorting to ultra complex algorithms.
It would appear that this approach is completely impossible for this cube and everyone has had to resort to computer analysis! Even Rline has posted on Facebook that he doesn't think he will manage it!

I guess this will just stay on my shelves as an oddity! Had I known this then I would never have bought it! :cry:

_________________
Kevin
Hopelessly addicted to puzzles!! :oops:
Visit my blog: Puzzlemad


Top
 Profile  
 
 Post subject: Re: How to solve Justin's Pocket (Corner) Cube?
PostPosted: Tue Nov 26, 2013 6:40 am 
Offline
User avatar

Joined: Thu Sep 17, 2009 6:07 am
Location: Germany, Bavaria
Puzzlemad wrote:
...I guess this will just stay on my shelves as an oddity! Had I known this then I would never have bought it! :cry:
Justin has revealed in his very first post here that it is a variant of the "3 Quads, 3 Stripes".
Justin wrote:
This a shape transformation of 2013930080085E aka '3 Quads, 3 stripes' first made by Andreas Nortmann.
Maybe you have missed the discussion in this thread? No, I just see that you even responded this
Puzzlemad wrote:
:shock: :shock: :shock:
This puzzle (not the parity) enticed me back to the bandaged kit again. OMG! Absolutely no chance of a solve on this one. Way beyond my skills. It is so bandaged up that I can't use any intuitive moves, none of my algorithms work and I can't even start to make any myself.

I surrender! :oops:
Anyway, the difficulty of the two colour and the four colour version is quite different. For the two colour version it is sufficient to go back to the cubic form:
Konrad wrote:
....If you consider a form as the following as the "regular" form of the "3 Quads, 3 Stripes"
Image
then Justin's Pocket Corner in the two colour version has just two different shapes, that cannot distinguished from other permutations of the stripes and the 3x3 edges.
The one above and the cubic shape.

Here you see both swapped 3x3 corners:

Image
This "bringing it back to cubic shape" was done by everybody intuitively, so far. Just a single [6:1] conjugate L, B', U', B, L2, D, F2, D', L2, B', U, B, L', (13)
may be needed in addition to the intuitive part. It is not very easy but doable.

If you have got the four colour version the story is a bit different. It is still easier than the original "3 Quads, 3 Stripes" solved by Andreas Nortmann by pen and paper, but is really hard, in my opinion. The Meffert's skill level of **** is underestimating it.

If you use the sequences by A&A and my diagrams (please see my post above), it is not hard any longer. If you want to memorize those long sequences, it is a different story again :)
And if you want to start from scratch, it is really, really hard (ask Andreas) :lol:

I still consider it a wonderful puzzle and like its beauty.
I even like its deceiving nature, that it looks so innocent at the first glance :wink:

_________________
My collection at: http://sites.google.com/site/twistykon/home


Top
 Profile  
 
 Post subject: Re: How to solve Justin's Pocket (Corner) Cube?
PostPosted: Tue Nov 26, 2013 6:50 am 
Offline

Joined: Tue Jun 11, 2013 12:48 pm
Hello Konrad,

thank you very much for your detailed answer and your helpful hints.
Usually I am not a friend of long algorithms as long as I dont exactly understand what I am doing with these sequences.
I hope I get a little bit time soon. Then I plan to mod my 3x3x3 cube into that "3 Quads, 3 Stripes"-puzzle.
I guess it will be easier to experiment with that one and to understand what is going on.

I am really curious if it is possible to find an intuitive and understandable method for solving that small beast ;-).
Actually it remembers me a little bit on my solving experiences with the Bermuda cube. All these blockings were so annoying until I found a system how to deal with it. From that point it was enough to know f2l and some oll cases - the rest are just set up moves, which are always intuitive. Maybe it will be the same for the corner pocket cube. But I´m not sure.. :-)

Good Luck!! :lol:


Top
 Profile  
 
 Post subject: Re: How to solve Justin's Pocket (Corner) Cube?
PostPosted: Tue Nov 26, 2013 7:23 am 
Offline
User avatar

Joined: Wed Apr 13, 2011 8:37 am
Location: Germany
Hi friends,

A shorter sequence to exchange 2 stripes (partiy);

do z2 ( turn cube that the subcube is left front down.

R' B' D' B R2 U F' R' F2 R U F' U' F2 R U'

16 turns instead of 31 !

Because this sequence changes other pieces this should be the first solving step.

I work on a solution for pocket-cube 3Quad 2Stripes with easy sequences. Easier to memorize.
So it's possible to solve it watching tv etc. without looking to paper. Only 2 short sequence and two tiny sequences.


Top
 Profile  
 
 Post subject: Re: How to solve Justin's Pocket (Corner) Cube?
PostPosted: Tue Nov 26, 2013 10:58 am 
Offline
User avatar

Joined: Wed Apr 13, 2011 8:37 am
Location: Germany
Solving the Pocket-Cube 3Quad/3Stripes with only TWO relative easy sequences.

(in my last posting the first move R' was an mistake, it must be R)

The idea was the folowing from last sequence.

The first sequence is known ( exchanging 2 corners)
A = R B’ D’ B R2 U F2 U’ R2 B’ D B R’

The next sequence
B ( C ) = R B’ D’ B R2 U F’ (F) R’ F2 R U F’ U’ F2 R U’
that means the letter in the brace replaces the letter before
so:
B = R B’ D’ B R2 U F’ R’ F2 R U F’ U’ F2 R U’
C = R B’ D’ B R2 U F R’ F2 R U F’ U’ F2 R U’

The first part is similar to A.

This sequences makes very usefull permutations.
All is solveable with this.
(Perhaps B ( C ) = R B’ D’ B R2 U F’ (F) R’ F2 R U F’ U’ F2 R U’ is a god's sequence)

I wrote a PDF file, this contains pictures an explains the solution.
It's possible to solve the cube after you solved the shape.

Have a look to the description :


Top
 Profile  
 
 Post subject: Re: How to solve Justin's Pocket (Corner) Cube?
PostPosted: Tue Nov 26, 2013 4:08 pm 
Offline
User avatar

Joined: Wed Apr 13, 2011 8:37 am
Location: Germany
There is one more position and one more sequence:

I added this to the PDF file:

With this sequences I solved the Pocket-Cube / 3Quads3Stripes without watching the paper.
I solved it while watching tv.

Please donwload the updatet instructions.
Attachment:
Pocket-Cube.pdf [553.91 KiB]
Downloaded 34 times


Cheers,
Andrea


Top
 Profile  
 
 Post subject: Re: How to solve Justin's Pocket (Corner) Cube?
PostPosted: Thu Nov 28, 2013 4:20 am 
Offline
User avatar

Joined: Thu Sep 17, 2009 6:07 am
Location: Germany, Bavaria
Andrea, this is a big step forward to an easier solution. :D
Finding the sequences "B" and almost identical "C" is a wonderful achievement!
Thank you very much for all your effort!


Probably I can add a bit to make things even more straight forward.
The following is based completely on your sequences A, B and C (where B and C are almost identical!).
We should no longer need the last addition (which could be named "D", if we still find it necessary).

I rewrite the sequences to a setup where the 2x2x2 subcube is at URF.

I shall use mainly Gelatinbrain diagrams starting with a solved "3 Quads, 3 Stripes".
The Gelatinbrain diagrams do not show the bandaging, but it should be obvious. (You may want to practise on a normal 3x3x3 first, anyway.) I'll use different back views. Usually I use the Gelatinbrain fashion, but because Andreas' program shows it with D on top, this back view may be more appropriate in this case.

The mentally to be added bandaging is the same as on my physical Cube:

Image

A= L,B',U',B,L'2,D,F'2,D',L'2,B',U,B,L'
result:
Image

The symmetry of this cube in its regular form allows you to rotate the whole cube freely around corner URF.

B= L,B',U',B,L2,D,F',L',F2,L,D,F',D',F2,L,D'
result:
Image

C= L,B',U',B,L'2,D,F,L',F'2,L,D,F',D',F'2,L,D'
result:
Image

So far, this was just a repetition of Andrea' sequences, using a different setup.

Now I use the symmetry of the regular form to combine the sequences with their mirrored counterparts.
(If you have memorized A,B and C once, the mirrored versions should be quite easy, too.)
M(A) is the mirrored sequence A, where the mirroring plane goes diagonally through the cube containing edges RF and BL.
M(A) = B', L, U, L', B2, D', R2, D, B2, L, U', L', B
We combine A and M(A).
Code:
A + M(A) = L,B',U',B,L'2,D,F'2,D',L'2,B',U,B,L',
           B', L, U, L', B2, D', R2, D, B2, L, U', L', B (26)

result:
Image
This is a different 3-cycle for edges. (The 3-cycle of stripes is not recognizable on a 4-colour Corner Pocket)
We have now two edges 3-cycles in our repertoire.
Code:
B+M(B)= L,B',U',B,L2,D, F',L',F'2,L,D,F',D',F'2,L,D',
        B', L, U, L', B2, D', R, B, R2, B', D', R, D, R2, B', D (32)

Image
We have now a pure flipping of edges. (The term "flip" is dependent on the definition somebody is using. In a case where the cubies are located at their correct locations, the "flipping" should be unambiguous.)
This whole sequence is just two moves longer than the sequence d) in my diagram above (found by Andreas' program)

Now the last
Code:
C + M(C)=  L, B', U', B, L'2, D, F, L', F'2, L, D, F', D', F'2, L, D',
           B', L, U, L', B2, D', R', B, R2, B', D', R, D, R2, B', D (32)

Image
This re-orientates purely the 1x1x1 corners.
Again, this whole sequence is just two moves longer than Andreas' (30) above.

So, with these simple re-combination of Andrea's two to be memorized sequences (C being almost identical to B), we should have everything we need.
I do not see a case where we need the sequence D (the addition in Andrea's second pdf file; name "D" wasn't used there).

If you accept a bit of help (OK, some is based on computer programming) solving this innocently looking beast should be feasible.

_________________
My collection at: http://sites.google.com/site/twistykon/home


Top
 Profile  
 
 Post subject: Re: How to solve Justin's Pocket (Corner) Cube?
PostPosted: Thu Nov 28, 2013 4:24 am 
Offline
User avatar

Joined: Wed Apr 13, 2011 8:37 am
Location: Germany
Hi puzzlers,

solving the 3quad3stripes:

I used the subcube in left down front position, because the movements are more visual. I tried more positions, but this was the best in my opinion. Ok, thats bad for a descrition. For a description right up front is better. Do a z2 turn before and after then the you can do the sequences with right up front.

The description is to learn the sequences. I wrote about flipping. But definition of flipping may be confusing.

I try to explain it better.

Perhaps the sequence A is not necessary. You need only sequence B C and D.
B and C are similar , only ONE turn is different.
So, you must memorize only 2 sequences.


First step: Solve the shape. To do that you need only this sequences,too. I don't explain it. other authors did it.

Second step:

Solve the 3 edges of subcube.
You need only this one sequence:
left = orange
front = white
C: R B’ D’ B R2 U F R’ F2 R U F’ U’ F2 R U’
Attachment:
sequencec.jpg
sequencec.jpg [ 532.76 KiB | Viewed 1487 times ]

This swaps down / front and down/left edge.
It's possible to solve all edges with this. If pieces are visual flipped you can swap it over a third place.

After this the corners are on the right place automatically !! (edges / corner parity)


Third step:

If 2 stripes are swaped do sequence B three time. This is a clean stripes swap.

B = R B’ D’ B R2 U F’ R’ F2 R U F’ U’ F2 R U’

Turn (R B’ D’ B R2 U F’ R’ F2 R U F’ U’ F2 R U’) 3 times.

4th step:
Turn corners !
Now turn sequence C until the cube is solved or this case:
Attachment:
sequenced.jpg
sequenced.jpg [ 227.98 KiB | Viewed 1487 times ]


Now you can turn sequence D
D= R B’ D’ B R2 U U’ R U R ‘ F’ R U ‘
Z x’ R B’ R’ B
U R’ F R U’ R’ U U’ R2 B’ D B R’

If the symmery case happens you must repeat this sequence.
I can't explain it better. I hope every understand this.

Cheers,
Andrea


Top
 Profile  
 
 Post subject: Re: How to solve Justin's Pocket (Corner) Cube?
PostPosted: Thu Nov 28, 2013 4:26 am 
Offline
User avatar

Joined: Wed Apr 13, 2011 8:37 am
Location: Germany
Hi Konrad,

while I worked on my posting you posted a new.
I hope my last description is better understandable.


Top
 Profile  
 
Display posts from previous:  Sort by  
Post new topic Reply to topic  [ 42 posts ] 

All times are UTC - 5 hours


Who is online

Users browsing this forum: Elias Acrich and 5 guests


You cannot post new topics in this forum
You cannot reply to topics in this forum
You cannot edit your posts in this forum
You cannot delete your posts in this forum
You cannot post attachments in this forum

Search for:
Jump to:  

Forum powered by phpBB © 2000, 2002, 2005, 2007 phpBB Group