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 Post subject: Re: Solving the Bandaged 3x3x3
PostPosted: Mon Jun 17, 2013 9:07 pm 
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jaap wrote:
This will have messed up the DFR corner. I hope I got this right as I don't have a cube in front of me right now.


It worked perfectly. Thank you very much jaap! Hopefully I will be able to use this strategy on future bandaged configurations. Always good to put another arrow in the quiver :lol: .


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 Post subject: Re: Solving the Bandaged 3x3x3
PostPosted: Sat Jun 29, 2013 12:49 pm 
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Recently, somebody made a puzzle that looked like a 2x2x2, but inside it was a bandaged 3x3x3.
The topic is no longer visible due to a request by the author.
The bandaged 3x3x3 was Andreas Nortmann's 2013930080085E aka "3 Quads, 3 Stripes".
I made one with the CubeTwist kit.

At first, I thought that it is hard to scramble, now I think that it is hard to solve.
I have no real strategy for it, because it is so much bandaged.

Andreas told me that it has 432 configurations, only.
Here is one of them:

Image

Has anybody tried it?

EDIT: After all the discussions below, I want to add that the term "permutations" has to be read in Andreas' enhance version
Quote:
"Permutation includes everything which makes a puzzle's state different from the other if their hexadecimal signatures are identical."
For the understanding of "hexadecimal signature", please, look at the posts below.
The 3 Quads 3 Stripes can be turned into 580 different shapes, each on represented by a different hexadecimal signature.

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 Post subject: Re: Solving the Bandaged 3x3x3
PostPosted: Sat Jun 29, 2013 6:01 pm 
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Hi Konrad,

The problem is the same as the parity on the Cross Road (the unbandaged Bicube). It will be solved with a 90* rotation of one of the unbandaged centres. I will make the cube and have a twist, thanks for the challenge.. it is a rainy day :) .

Cheers,
Burgo.

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 Post subject: Re: Solving the Bandaged 3x3x3
PostPosted: Sun Jun 30, 2013 3:25 am 
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: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:

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 Post subject: Re: Solving the Bandaged 3x3x3
PostPosted: Sun Jun 30, 2013 8:16 am 
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Burgo wrote:
Hi Konrad,

The problem is the same as the parity on the Cross Road (the unbandaged Bicube). It will be solved with a 90* rotation of one of the unbandaged centres. I will make the cube and have a twist, thanks for the challenge.. it is a rainy day :) .

Cheers,
Burgo.
Hi Burgo, it is obvious that this kind of parity needs a 90° turn of one face. On a normal 3x3, we have a double parity, one odd permutation of two corners and one of two edges. We would need a single 90° turn too.
Because the three bandaged centres (the three quads) can't do this, it must be one of the other three. So far, so good.

None of my Bicube move sequences (just two, one 5-cycle and one 3-cycle) can be done on the "3 Quads, 3 Stripes".
(BTW, we had this name discussion before the original Bicube from Dieter Gebhardt had a single 2x2 corner bandaged opposite to the single corner cubie. When we say Bicube in this thread, we mean the Cubetwist Bicube
Image which is just the Meffert's Bandaged 3x3x3 with a different colour scheme).

I had a look at your spoiler for the Cross Cube (I never tried it before) in the post from January 27th, 2013 . Just to be sure that I interpret your sequence for the parity problem correctly: When I paste your example sequence into Gelatinbrain, I get this:
Image
It is a 6-cycle of the corner-edge pieces. A 6-cycle is an odd number of permutations. After that you solve the rest with the Bicube 3-Cycles and 5-cycles.
Correct?
On the Cross Cube we have 6 stripes, on the "3 Quads, 3 Stripes" we have only three.
So, obviously we need to break the big 2x2 corner with single cubies, temporarily.

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 Post subject: Re: Solving the Bandaged 3x3x3
PostPosted: Mon Jul 01, 2013 11:37 am 
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Hi Konrad,
I am happy that you struggle with this variant as I did years ago. 8-)

Maybe you want to try the attached file.
It comes from a project of mine. I freezed this project three years ago because of the museum.
Everybody else who understands german can try it too.

Andreas


Attachments:
Solution 2013930080085E.txt [1.15 KiB]
Downloaded 69 times
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 Post subject: Re: Solving the Bandaged 3x3x3
PostPosted: Tue Jul 02, 2013 5:19 pm 
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Hi Andreas,

today I did not struggle so much with your puzzle but with my laptop. (The screen is broken and I was busy all day backing up my data (1 Terabyte) and prepare the computer that I can send it in tomorrow for repair actions. Just two months old :( )

Here is a translation of your text file with just a few small additions (e.g. I added commas that you can cut and paste the sequences into Gelatinbrain and I numbered the nine sequences):
[spoiler]3 Quads, 3 Stripes 2013930080085E

We use Singmasters Notation (normal turns clockwise)
U=Red F=Yellow L=White D=Orange B=Green R=Blue
580 signatures
432 permutations
1/12 compared with the naive count
The strategy needs 165 moves maximum.

Phase 1
Position Corner-Edge LD:
1. L=013 L, B', U', B,L2, D,F2, D', L2, B', U,B,L', (LB <->LD)
Position Corner-Edge 112:
2. L=013 D,L',F',L,D2,B,R2,B',D2,L',F,L,D', (BD <->LD)

Phase 2
Position Corner-Edge 112 BD and LB:
3. L=013 B,D',R',D,B2,L,U2,L',B2,D',R,D,B', (BD <->LB)

Phase 3
Position Edge 111 FU:
4. L=015 L,B',U',B,L',D,L',F2,D',L,D',B,R',B',D, (RU->FU -> RF -> RU)
Position Edge 111:
5. L=015 L',D,F,D',L,B',L,U2,B,L',B,D',R,D,B' (RF->FU)

Phase 4
Position Edge 111 RU and RF:
6. L=022 B',L,U,L',B,L,B',U',B',U,B2,L',D',B,R,D,B',D,L',F,L,D' (RU <->RF)

Phase 5
Orientate Edge 111: FU
7. L=030 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' (flip FU and RF)

Phase 6
Orientate Edge 111 RF:
8. L=032 B,D',R2,B,R,B',D',R2,D,R2,D',R2,D,B,R',B',R2,D,B',L,B',U',B,L2,D,F2,D',L2,B',U,B,L', ((flip RF and RU)

Phase 7
Orientate Corner 111: DBL
9. L=030 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' (UFR counter clockwise)
inverse of 9. : 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 (UFR clockwise)

[/spoiler]
The colour scheme used in the text is the traditional Rubik scheme and it is different from the currently common White opp. Yellow; Red opp. Orange; Green opp. Blue.
I could run Andreas' analyzer program (I'm now back on Windows 7 - it doesn't run on Win8)and produced this picture corresponding to the setup instructions in the spoiler text.
Image
Because I wanted to use Gelatinbrain corresponding to my physical cube, I used a colour scheme as on Frank's picture and I just swapped the colours Blue and Yellow.
Image

Wow, these are incredible long sequences.
So far, I have tested them on Gelatinbrain only and they seem to work fine.
You said
Quote:
It comes from a project of mine.
Did you find your sequences with the help of a program? (I thought yesterday, that I should try one in VBA. I have not done much programming in the last 20 years. :wink: )

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 Post subject: Re: Solving the Bandaged 3x3x3
PostPosted: Wed Jul 03, 2013 3:56 am 
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So my CT bandage DIY kit arrived last night I was so happy, I had compiled a list of puzzles to try out and solve.

SHOCK HORROR its missing all 9 x 1x1 orange single tiles. now that is a pain in the backside.

Im putting it down to human error as hk now store have always been good to me. I've been told they will get the factory to send over some more and they will post it but who knows how long that will take. so rather than consider the untiled side the orange side, I can can make one configuration with 0 1x1 tiles and still make is scramble-able . is this the case?

also I was thinking of the possibility of making a 3 colour bandaged puzzle 2x white sides 2 red sides and 2x blue sides, is there any way this is possible?

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 Post subject: Re: Solving the Bandaged 3x3x3
PostPosted: Thu Jul 04, 2013 4:28 am 
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I think this is more a teaser than a spoiler - as long as you do not look at Andreas' text.
I have made pictures for all nine sequences, starting with a solved cube and showing the result in the same front-view / back-view manner as in Gelatinbrain. The setup fits to the sequences, just the colour scheme is different.

This puzzle proves again that the number of the possible configurations has nothing to do with the question how hard it is to solve.
No wonder that Andreas spoke of a "project". I cannot imagine how he could find such long sequences (i.e. without the help of a computer program. (32 moves is the longest one).
Now imagine this 3x3 bandaging inside a 2x2x2. Wouldn't that be a Super Horror Nightmare Cube? :evil: :evil:

BTW, Andreas, you wrote
Quote:
580 signatures 432 permutations
How can one calculate this?
And where can I find a good (means not too complex :) ) description of the term "signature"?
Obviously it is not signature = sign of a permutation as defined here.
Sometimes you said in the past sentences like this
Quote:
Your cube has this signature of pieces
HE2[F2 C2 X10 L16][C2]
The Toru has this
HE2[F2 C2 E5 X10 L16][F2 C2]
Obviously, some puzzles have just one signature and some have many? (To be honest, I do not understand the names in the last quote, either. :roll: )

You can click onto the photo to enlarge it
Image

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 Post subject: Re: Solving the Bandaged 3x3x3
PostPosted: Fri Jul 05, 2013 12:39 am 
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Hi Konrad,

The strings of this kind
HE2[F2 C2 X10 L16][C2]
are from my attempt to classify twistypuzzles. These signatures have nothting to do with the signatures of bandaged cubes.
If you want to understand those strings you can look here:
http://www.twistypuzzles.com/forum/view ... 96#p190396

In the realm of bandaged cubes a signature is something different:
Each signature has a different hexadecimal number in my program. (Is that easy enough?) It is what makes a bandaged cube different after removing the corner and edge stickers.
Quote:
How can one calculate this?
With a program.
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 freezed that project because of the museum.
Before I freezed 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.

Thank you for illustrating the effects of the sequences.
No human solver would use #8 after seeing #7.
In this case there is even more potential for optimizing because this variant has some degree of rotational symmetry
This prooves: It is just a stupid program.

Andreas
PS: I think you made a mistake in #5 which looks identical to #3


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 Post subject: Re: Solving the Bandaged 3x3x3
PostPosted: Fri Jul 05, 2013 2:43 am 
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Thanks Andreas for the long reply! :D
I surely hope this is of interest for others as well. So, I'll post about some remaining questions later in the thread instead via PM.
(I have to leave the house in a few minutes.)
Andreas Nortmann wrote:
....PS: I think you made a mistake in #5 which looks identical to #3
:oops: I have corrected my editing error above.

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 Post subject: Re: Solving the Bandaged 3x3x3
PostPosted: Fri Jul 05, 2013 1:54 pm 
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Hi Andreas and others interested.
I think, the project you described was very interesting and ambitious.
I still wonder, how a human being can find a similar clear strategy for heavily bandaged cubes like the discussed. There may be some redundancy in the solution strategy of your program (e.g. your sequence 5. looks like the inverse of 4. The computer program has found a sequence different from the inverse of 4, though.)
I could not find a method by all my effort. The "parity" shown above was achieved by a lot of more or less accidental turning.
432 permutations in total may allow that one solves it by sheer luck. Where is a method found by human TP solvers? :wink:
Master(s) of the Bandaged 3x3x3 to the front!
Andreas Nortmann wrote:
...In the realm of bandaged cubes a signature is something different:
Each signature has a different hexadecimal number in my program. (Is that easy enough?) It is what makes a bandaged cube different after removing the corner and edge stickers....
I want to check my understanding and share it with others who might be interested.
I'll use the signature of the "3 Quads 3 Stripes" as an example (BTW, I had understood before that each bandaging of a 3x3x3 is represented by a bit-field and written in 14 hexadecimal digits between 00 00 00 00 00 00 00 and 3F FF FF FF FF FF FF. I was just not aware that this is called a "signature".)
Image
In this case altogether 15 bits are set to 1. Each binding set to 1 "glues" together two cubies of the 3x3x3.
The 8 corners can each be bound to the 3 adjacent edges = 24 bindings
The 6 centres can each be bound to 4 adjacent edges = 24 bindings
Each of the 6 centres can be bound to the core =6
24+24+6 = 54 bits represent a specific bandaged cube.
A computer program can represent this in 7 bytes (equal to 14 hex digits).

I used Andreas' program to show this in the following example.
The first diagram 1. shows the fully bandaged "3 Quads 3 Stripes" with signature 2013930080085E.
The other five diagrams elaborate the right most 8 bits containing five 1 bits.
The bandaging in diagram 2. is just one bit in 02(hex) and bit by bit is switched on in 3 to 6.
Diagram 6 shows the 5 bindings represented in the five 1 bits in 5E (hex).

Image

A few more questions for Andreas (I do not want to add stress to you burden as a Museum moderator. I assume, though, that you are interested in this project, still, and that you appreciate my interest. :) Please take your time and reply whenever it seems convenient.)
Andreas Nortmann wrote:
I wanted to create a solution strategy for every of the 5844 bandaged cubes in the program.
I understand that 3563 different bandaged 3x3x3s exist.
Andreas Nortmann wrote:
....the number of permutations for each bandaged variant.
Andreas Nortmann wrote:
the restriction factor (quotient between naive and true number of permutations) for each bandaged variant.
Is the "naïve number" equivalent to the number of configurations that can be achieved by the physical rearrangement of the movable pieces? (In the example of the "3 Quads 3 Stripes": 3 stripes =corner-edges 211, 2 corners 111, 3 edges 111, 3 quads = centre-corner-edge pieces 221)
How is the term "permutation" defined in the context of bandaged cubes?
I assume that it counts different orientations of pieces as well? (like in the result of your sequence 7.)

I fail to understand why there are more signatures than permutations possible.("580 signatures / 432 permutations")
If I start counting signatures and permutations with the solved state
Image
what do we see after an L turn? (I assume: +1 for signatures and permutations.)
The 9 results of your 9 sequences above have all the same signature 2013930080085E as the solved state, right?
Andreas Nortmann wrote:
an automatic solution strategy for the ca. 3900 bandaged cubes which number of permutations (ca. 4 million if I remember right) is low enough.
How many 3x3x3's have you calculated by your program?
Andreas Nortmann wrote:
I even outlined an article for CFF in which I wanted to present all kinds of statistics about the 5844 bandaged variants.
What does CFF stand for?

EDIT: I could find an answer to my last question:
CFF is the newsletter of NKC (Nederlandse Kubus Club)
CFF= Cubism For Fun

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 Post subject: Re: Solving the Bandaged 3x3x3
PostPosted: Sat Jul 06, 2013 10:22 am 
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Konrad wrote:
(BTW, I had understood before that each bandaging of a 3x3x3 is represented by a bit-field and written in 14 hexadecimal digits between 00 00 00 00 00 00 00 and 3F FF FF FF FF FF FF. I was just not aware that this is called a "signature".)
I made up this term for myself. Maybe I should call it "hexadecimal signature" in the future to make it more clear.
I know that these hexadecimal numbers are unreadable for human beings. But all others attempts to describe bandaged 3x3x3s lack the precision a computer program needs for searching through 2^54 variants.
BTW: Why are dialogs in the image in english? It should use german captions if you use german as language in windows. Strange!
Konrad wrote:
I understand that 3563 different bandaged 3x3x3s exist.
That number came from this thread: viewtopic.php?f=1&t=24406
3563 can be implemented with the DIY kit. If you include non-implicit face-core-bonds then you get the 5844 variants of the analyzer.

All this stuff about permutations and signatures seems strange in first place but it is necessary to distinguish.
"Normal" twistypuzzles represent groups. That means (among other properties): every turn is possible in every state of the puzzle. Although there are a few exceptions, this is not true for bandaged puzzles.
The program searches for sequences which start and end at the same signature. Therefore all these sequences can be applied in arbitrary order on the puzzle. No blocking will ever occur => The puzzle is "normal" (representing a group) again.
I want to call Jaap as witness: He used the same general approach for his page about Mefferts Bandaged Cube.
Konrad wrote:
The 9 results of your 9 sequences above have all the same signature 2013930080085E as the solved state, right?
Yes. They start and end with identical hexadecimal signatures.
Konrad wrote:
I fail to understand why there are more signatures than permutations possible.("580 signatures / 432 permutations")
After understanding the difference between hexadecimal signature and permutation it should be more clear. There is an example which is easier: http://twistypuzzles.com/cgi-bin/puzzle.cgi?pkey=617 (I contact Sandy about this mistake)
Please view this hexadecimal signature: 1E8400F43FF7A1
This puzzle can be turned into 28 different hexadecimal signatures but each signatures supports only a single permutation.
Konrad wrote:
Andreas Nortmann wrote:
....the number of permutations for each bandaged variant.
How is the term "permutation" defined in the context of bandaged cubes?
I assume that it counts different orientations of pieces as well? (like in the result of your sequence 7.)
"Permutation includes everything which makes a puzzle's state different from the other if their hexadecimal signatures are identical." (I came up with this right now)
It includes orientations as well.
I just realized that I enhanced the term permutations in a misleading way. I am sorry for that.
Konrad wrote:
Andreas Nortmann wrote:
the restriction factor (quotient between naive and true number of permutations) for each bandaged variant.
Is the "naïve number" equivalent to the number of configurations that can be achieved by the physical rearrangement of the movable pieces? (In the example of the "3 Quads 3 Stripes": 3 stripes =corner-edges 211, 2 corners 111, 3 edges 111, 3 quads = centre-corner-edge pieces 221)
"naïve number" includes all permutations which can be reached by disassembling and reassembling the puzzle in the same signature.
For the naive number of the "3 Quads 3 Stripes" you have to multiply
3!(edges)
2!(corners)
3! (coner-edge-blocks)
3^2(corner orientations)
2^3(edge orientations)
Under this method the restriction factor for the unbandaged 3x3x3 is 12.
The restriction factor for the Siamese Cube is 72. (See Jaaps site for verification)
There are 1165 (out of 5844) bandaged cubes with 12 as restrictions factor.
Surprisingly there are 67 variants which restriction factor is no multiple of 12.

I hope this helps.
Andreas


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 Post subject: Re: Solving the Bandaged 3x3x3
PostPosted: Sun Jul 07, 2013 4:06 am 
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Thanks Andreas for all your patience! :) I wanted to improve my understanding of all the theoretical issues around Bandaged 3x3x3s for a long time. I hope that other interested people have found the discussion enlightening, too. BTW, may question (via email to Andreas) "How are the 580 hexadecimal signatures for the 3 Quads 3 Stripes calculated?", was answered by "run the program, choose the variant, press Ctrl+P".
Yesterday, I scrambled and solved the puzzle using Andreas' method and I have to say that bringing the puzzle back to a normalized form (i.e. hexadecimal signature 2013930080085E) is not trivial at all.
Andreas Nortmann wrote:
...After understanding the difference between hexadecimal signature and permutation it should be more clear. There is an example which is easier: http://twistypuzzles.com/cgi-bin/puzzle.cgi?pkey=617 (I contact Sandy about this mistake)
Please view this hexadecimal signature: 1E8400F43FF7A1
This puzzle can be turned into 28 different hexadecimal signatures but each signatures supports only a single permutation.....
The link worked for me today. Has Sandy changed anything already? Or was it just bad luck yesterday that http://twistypuzzles.com/cgi-bin/puzzle.cgi?pkey=617 did not work? I read:
Museum entry wrote:
In this cube so many cubies are glued together, that there are only 28 different permutations. You can reach any permutation from any other by at most 4 turns.
As you can see the terminology is a tricky issue in the context of bandaged cubes. If the text would say "28 hexadecimal signatures", most readers would say "Huh ???" :wink: Maybe, the term "shapes" is general enough and not in contradiction to what we have learned here.
For those who cannot run your program, here is the puzzle:
Image Image
Your program calculates 36 "Shapes" = "hexadecimal signatures". Either the Museum puzzle is different (one cannot tell from the single view) or we have a contradiction.

BTW, your Analyzer program has always talked English to me on different German Windows systems. (V 4.1.0)

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 Post subject: Re: Solving the Bandaged 3x3x3
PostPosted: Mon Jul 08, 2013 9:21 am 
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Konrad wrote:
Yesterday, I scrambled and solved the puzzle using Andreas' method and I have to say that bringing the puzzle back to a normalized form (i.e. hexadecimal signature 2013930080085E) is not trivial at all.
I discovered the same problem. The automatic solution generator can be told to generate sequences for bringing each hexadecimal signature back to the solved signature.
I omitted this in this case. 580 sequences in a textfile are anti-intuitive. The maximum would contain 92176 sequences!
Konrad wrote:
The link worked for me today. Has Sandy changed anything already? Or was it just bad luck yesterday that http://twistypuzzles.com/cgi-bin/puzzle.cgi?pkey=617 did not work?
Sandy restored it from a backup. We are working on the issue.
Konrad wrote:
Your program calculates 36 "Shapes" = "hexadecimal signatures". Either the Museum puzzle is different (one cannot tell from the single view) or we have a contradiction.
The variant in the museum is different. Its signatures is 1E8400F43FF7A1. Please enter it in the left halve of the program by pressing Shift-Ins. You can't find it in the analyzer because it contains dead ends and is therefore considered trivial.
An example on the list with more signatures than permutations is 10840080800C63. It has 628 hexadecimal signatures and 4 permutations.
In total there are 2048 (out of 5844) variants with more signatures than permutations.

Greetings


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 Post subject: Re: Solving the Bandaged 3x3x3
PostPosted: Sun Jul 14, 2013 7:22 pm 
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I just enjoyed reading about this puzzle on rline's blog. If you haven't seen it yet... why not?

Edited to fix the link

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 Post subject: Re: Solving the Bandaged 3x3x3
PostPosted: Thu Jul 18, 2013 2:03 am 
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I just scoured every post on this thread so far to see if I could find the bandaged cube below. Couldn't find it. Can anyone suggest a good name for it? It has the 3x1 white block, the 2x1 white/red/blue block and the 2x1 white/red/green block. All other cubies are single cubies.

Attachment:
993613_590985620946616_1729683436_n.jpg
993613_590985620946616_1729683436_n.jpg [ 77.51 KiB | Viewed 5461 times ]

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 Post subject: Re: Solving the Bandaged 3x3x3
PostPosted: Thu Jul 18, 2013 7:36 am 
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hmm

it reminds me of this http://img1.etsystatic.com/000/0/5400181/il_fullxfull.244960281.jpg
Japanese Geta Shoe

I think Geta Cube

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 Post subject: Re: Solving the Bandaged 3x3x3
PostPosted: Fri Jul 19, 2013 7:20 am 
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rline wrote:
I just scoured every post on this thread so far to see if I could find the bandaged cube below. Couldn't find it. Can anyone suggest a good name for it? It has the 3x1 white block, the 2x1 white/red/blue block and the 2x1 white/red/green block. All other cubies are single cubies.

Attachment:
993613_590985620946616_1729683436_n.jpg

Well I've decided to call it the bandaged bridge. I did a walkthrough solve if anyone is interested. It's a really good cube I think. It involves having to flip edges using only 2 faces and I had to invent a method to do that. It had a good feel to it: not too easy and not too hard (for me at least)!

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 Post subject: Re: Solving the Bandaged 3x3x3
PostPosted: Fri Jul 19, 2013 8:59 am 
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Quote:
Well I've decided to call it the bandaged bridge. I did a walkthrough solve if anyone is interested. It's a really good cube I think. It involves having to flip edges using only 2 faces and I had to invent a method to do that. It had a good feel to it: not too easy and not too hard (for me at least)!
When you say 2 faces, do you mean 2 parallel faces and an inner slice? So actually 3 layers—R, L, and E. Of course, it was the middle of the night here, and I may have been somewhat in a fog as I watched the video, so set me straight if I am mistaken. :lol:

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 Post subject: Re: Solving the Bandaged 3x3x3
PostPosted: Fri Jul 19, 2013 6:34 pm 
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robertpauljr wrote:
Quote:
Well I've decided to call it the bandaged bridge. I did a walkthrough solve if anyone is interested. It's a really good cube I think. It involves having to flip edges using only 2 faces and I had to invent a method to do that. It had a good feel to it: not too easy and not too hard (for me at least)!
When you say 2 faces, do you mean 2 parallel faces and an inner slice? So actually 3 layers—R, L, and E. Of course, it was the middle of the night here, and I may have been somewhat in a fog as I watched the video, so set me straight if I am mistaken. :lol:

No, I meant that I had to achieve it with two faces, R and U, but I couldn't, so I invented something else using 2 faces, R and E (if E is the one between U and D)

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 Post subject: Re: Solving the Bandaged 3x3x3
PostPosted: Fri Jul 19, 2013 6:50 pm 
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Quote:
No, I meant that I had to achieve it with two faces, R and U, but I couldn't, so I invented something else using 2 faces, R and E (if E is the one between U and D)
Ah! Yes yes yes! I see it now. First you do it right-handed, then left-handed, but you turn the whole cube 180Ëš so that the right side becomes the left side, so really there are only 2 layers involved. Yes, you are right. I was confused. :oops: That'll teach me not to get up in the middle of the night and check the forum! :roll: :lol:

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 Post subject: Re: Solving the Bandaged 3x3x3
PostPosted: Fri Jul 19, 2013 10:37 pm 
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Interesting little puzzle rline, (I like the simpler ones with a trick :) ), we do tend to do the bandaged parts first and then find a workaround, I wonder if it's always the best way sometimes, but that's how I worked with this one too. I went edges first as well, and I used CPS and then Sunes to orientate corners. To flip 2 edges on RF & RU on my first solve I did: [Green F, Yellow U]: (L D' F D) R' (D' F D L') (do R2 to see flipped edges in place). An easier, more traditional way, though, is to use a small variant to the standard F2L edge flipping alg > [Red F, Yellow U]:F (D') UR U'R' (D) F' or F (D') RU R'U' (D) F'

Thanks,
Burgo.

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 Post subject: Re: Solving the Bandaged 3x3x3
PostPosted: Sat Jul 20, 2013 4:01 am 
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Quote:
Interesting little puzzle rline

Yes it was posed by another TP member on my FB page.

Quote:
An easier, more traditional way, though, is to use a small variant to the standard F2L edge flipping alg > [Red F, Yellow U]:F (D') UR U'R' (D) F' or F (D') RU R'U' (D) F'

I think I tried to find something along these lines, but couldn't. That's good in a way though as it allowed me to come up with something new.

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 Post subject: Re: Solving the Bandaged 3x3x3
PostPosted: Sat Jul 20, 2013 7:08 am 
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Burgo wrote:
An easier, more traditional way, though, is to use a small variant to the standard F2L edge flipping alg > [Red F, Yellow U]:F (D') UR U'R' (D) F' or F (D') RU R'U' (D) F'

Amazing!
I tried and tried to work out my own edge flipping algorithm and no matter what I tried I could not find one until Rline showed his variant on SUNE using equator turns.
I obviously have a huge amount to learn when it comes to designing my own techniques! :shock:

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 Post subject: Re: Solving the Bandaged 3x3x3
PostPosted: Sat Jul 20, 2013 8:31 am 
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Burgo, Puzzlemad, are either of you familiar with the Petrus Method for solving the Rubik's Cube? It is a block building method that starts with building a 2x2x2 clock then extending it to a 2x2x3 block, then fixing the bad edges on the remaining two faces before going on to complete the first two layers. Fixing the bad edges means flipping ones that need to flip as rline does at that stage in his walkthrough. But Petrus' method for flipping them is different.

Hold the cube with green on the left and yellow up, so the 2x2x3 block is at the back on the bottom. Turning only F and U get two edges that need to flip to UB and FL and do L' U' L. Or get two pieces that need to flip to UB and FR and do R U R'. After all the bad edges are fixed regrip the cube so you are holding the block and use only the two unsolved faces to solve all the rest of the puzzle.

Implementing this on this bandage cube is a little more challenging since the bandaged pieces need to be moved in order to do R U R' to flip the edges, but it works.

The thing I like about the algorithm Burgo reminded us of is that it is the common easy way to flip two edges on U with a D and D' thrown in to deal with the bandage. So obvious. Why didn't I think of that?

The thing I love about rline's algorithm is that it is a pure 3-cycle of edges. In this application that is not absolutely necessary, but it is something that may have interesting applications elsewhere. Plus it is something new to me—using sune only with E instead of U. I don't think I've ever run across that before. Brilliant, and fun!

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 Post subject: Re: Solving the Bandaged 3x3x3
PostPosted: Sat Jul 20, 2013 7:14 pm 
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Hi Robert,
robertpauljr wrote:
Turning only F and U get two edges that need to flip to UB and FL and do L' U' L. Or get two pieces that need to flip to UB and FR and do R U R'.
My first sequence: [Green F, Yellow U]: (L D' F D) R' (D' F D L') is like that, I have used F and R, in a nutshell the exchange happens in the critical move R', the L&D moves are setups, the second F could be F', some superfluous edges flip twice, it's all very messy (it didn't need to be pure), but the idea was turn>exchange>return. (I mean I'm critically analysing something that literally took 5 mins on my first look, so it's not really appropriate, but maybe someone will learn something).

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 Post subject: Re: Solving the Bandaged 3x3x3
PostPosted: Thu Aug 08, 2013 4:25 am 
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First of all I want to say that the Bandaged 3x3x3 Kit of CubeTwist is amazing. ;) I fixed the issue of not getting the pieces off without using a knife, by putting some thick pieces of tape in the center of each piece of the Cube. Now I can just get all the pieces of with my nails, without using a knife anymore.

I also want to say thanks to all the previous forum posters that designed some great Bandaged Cubes. I had a lot of fun (and sometimes frustration :P) trying to figure out most of them. I haven't been able to figure out all of them, some were too hard and some I haven't tried yet. But those I did so far are great.

Now some Bandaged designs of my own. They may not all be as difficult, but I think most of them are quite fun to solve. I've created two sets of Bandaged 3x3x3, one I made up myself, and the other is based on the Aurumq-1. I also have some loose bandaged 3x3x3 designs I will add here below as well.

Beginner Y-Cube, Advanced Y-Cube, Expert Y-Cube and Siamese Y-Cube:


Aurumq-1 itself (designed by Traiphum Prungtaengkit), Aurumq-1 - 2 Clock V1, Aurumq-1 - 2 Clock V2 and Aurumq-1 - 4 Clock:


Diamond Cube, PI-Cube, ILi Cube and Mirrored Edge Cube:


I also want to point out you can make every Siamese and Middle Triamese 3x3x3 bandaged with the kit. Here below are two examples, and the complete list with bandaged Siamese / Middle Triamese you can make:

Siamese 4 (1x2x2) Bandage and Middle Triamese 3 (1x1x3) Bandage:


The complete list:
  • Siamese 2 (1x1x2) Bandage
  • Siamese 3 (1x1x3) Bandage
  • Siamese 4 (1x2x2) Bandage
  • Siamese 6 (1x2x3) Bandage
  • Siamese 8 (2x2x2) Bandage (Fuse Cube)
  • Siamese 12 (2x2x3) Bandage (Big Block)
  • Middle Triamese 2 (1x1x2) Bandage
  • Middle Triamese 3 (1x1x3) Bandage
  • Middle Triamese 4 (1x2x2) Bandage
  • Middle Triamese 6 (1x2x3) Bandage

There are also some Bandaged 3x3x3 in the Twisty Puzzle Museum which aren't mentioned in this thread yet. Most of them are Bandaged Bump Cubes or different sticker designs, but they can also be made with the Bandaged 3x3x3 kit. Some examples of these are: Cabe Cube, Christians Bandaged Cube, Cab 5-5 Cube, Forest of Wander (and other "of Wander" Cubes), Most Signatures Bandaged Cube, etc. All of these can be found in the Twisty Forum Museum.

I haven't solved all of the Bandaged Puzzles yet that I posted, but I did solve most of them, and I think they are pretty good designs if I say so myself. ;) If anyone has something to add about these Bandaged 3x3x3 designs, or if someone else has any more designs of their own, I would love to give them a try.

PS: Sorry for the long post..

Have fun puzzling! :D

Greetz,
Quuador

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 Post subject: Re: Solving the Bandaged 3x3x3
PostPosted: Thu Aug 08, 2013 4:37 am 
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Thanks for adding a few easier/intermediate ones to our list of bandaged cubes! I had run out of those and can't do the really tough ones!

I love the graphics too!

Once I've finished my latest delivery from Calvin then I'll get right too it.

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 Post subject: Re: Solving the Bandaged 3x3x3
PostPosted: Thu Aug 08, 2013 4:46 am 
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Puzzlemad wrote:
Thanks for adding a few easier/intermediate ones to our list of bandaged cubes! I had run out of those and can't do the really tough ones!

I love the graphics too!

Once I've finished my latest delivery from Calvin then I'll get right too it.

No problem, namesake (my name is also Kevin ;)). Most of them aren't too hard indeed, but it's still fun to solve them in my opinion. Good luck trying to figure them out. ;)

PS: I made the "graphics" in Paint about three years ago when I printed my first 3x3x3 solution. :P Still had those 3x3x3 Paint png's lying around, so I use them for the Bandaged designs I come up with or find from other places (mostly from this thread). At the moment I have a list of 78 different Bandaged 3x3x3 in a Word-doc on my computer. ;)

Greetz,
Quuador

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Last edited by Quuador on Thu Aug 08, 2013 6:16 am, edited 1 time in total.

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 Post subject: Re: Solving the Bandaged 3x3x3
PostPosted: Thu Aug 08, 2013 5:25 am 
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Hello Quuador,

welcome to the forum and to this thread! :)

Not much criticism (Moderator's hat on), just some advice (I know, this was your third post :) ):

Can you, please, do us the favour to size down your pictures?
The horizontal scrolling on my laptop makes such posts hard to read.
If you feel that important information gets lost by the downsizing you could use
Code:
[url][img][/img][/url]
to make the smaller images clickable to get to the original size.
The easiest would be to use
Code:
[ImgPix][/ImgPix]
This is not a good solution when your originals are large, because the download time will be just the same.

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 Post subject: Re: Solving the Bandaged 3x3x3
PostPosted: Thu Aug 08, 2013 6:11 am 
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Konrad wrote:
Hello Quuador,

welcome to the forum and to this thread! :)

Not much criticism (Moderator's hat on), just some advice (I know, this was your third post :) ):

Can you, please, do us the favor to size down your pictures?

Hi and thanks.

I've changed the pictures. I hope they're in a better size now. I sometimes forget that I've got quite a wide screen. ;)

Greetz,
Quuador

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 Post subject: Re: Solving the Bandaged 3x3x3
PostPosted: Mon Aug 19, 2013 1:19 am 
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very interest cubes ;)

1) Spiral Cube-3.

Image

2) Spiral Cube-4.

Image

3) Spiral Cube-5.

Image

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 Post subject: Re: Solving the Bandaged 3x3x3
PostPosted: Thu Aug 29, 2013 5:26 pm 
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So I know the cube twist DIY bandage cube is not a hot topic right now what with the fantastic sounding crazy2/3face and b4 bandage on the horizon. But I've been playing about with my crazy earth/ Venus and my ct DIY to get myself in the mind frame for when I get one of burgo/ rlines puzzles.

A problem I continue to fall into with many of the badage variations is permuting the last 3/4 edge pieces on the last layer. I always end up just randomly turning the top layer and performing a sune / antisune and repeating until they fall into place, tonight this took me an hour!!!!!

Are there any tips out there for alternative algorithms to permute those meddlesome edge pieces???

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 Post subject: Re: Solving the Bandaged 3x3x3
PostPosted: Fri Aug 30, 2013 1:28 am 
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Hi Andy,

I made this once to share, it might be helpful for you:

https://skydrive.live.com/redir?resid=F ... Ao60JDY47g

Another U & R face LL edge 3cycle is RU' RU RU RU' R'U' R2, it also rotates the U centre by 90*CCW and the R centre by 90*CW.

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 Post subject: "EcubeR" by Andrey Yerashkevich
PostPosted: Sat Dec 14, 2013 1:57 pm 
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Hello!!! I am very glad to present my latest puzzle.This is my version bandaged 3x3x3 cube . Kind regards, Andrey Yerashkevic.


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 Post subject: Re: "EcubeR" by Andrey Yerashkevich
PostPosted: Sat Dec 14, 2013 2:35 pm 
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Ok Burgo - you're the xpert on these! What do you think?

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 Post subject: Re: Solving the Bandaged 3x3x3
PostPosted: Sun Dec 15, 2013 2:53 am 
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Puzzlemad wrote:
Ok Burgo - you're the xpert on these! What do you think?
Firstly, I think it's time for you to step in here with an opinion Kevin, make it and see what you think :) .

Secondly, it's better if all faces are photographed in the puzzle description, because, although I think I have guessed the puzzle, there are still some other possibilities.

It's not really very scrambleable.. as the examples show. M' U2 M U2 moves will suffice, unless I'm missing something. I think the total number of reachable states is very low.

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 Post subject: Re: Solving the Bandaged 3x3x3
PostPosted: Sun Dec 15, 2013 6:05 am 
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Burgo wrote:
I think the total number of reachable states is very low.
You are right.
This one is equivalent to 2DA00000C03
which has 208 shapes with 48 permutations each.

EDIT: Corrected spelling.


Last edited by Andreas Nortmann on Fri Dec 20, 2013 12:11 pm, edited 1 time in total.

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 Post subject: Re: EcubeR (bandaged mod) by Andrey Yerashkevich
PostPosted: Wed Dec 18, 2013 12:46 pm 
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ecuber wrote:
Hello!!! I am very glad to present my version bandaged 3x3x3 cube . Kind regards, Andrey Yerashkevic.
This would drive me nucking futs! I am terrible at bandaged cubes, seeing as every time I solve the bicube it is by fluke. Have you solved it yet, or is it just too hard to scramble to make a considerably hard solve?

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 Post subject: Re: EcubeR (bandaged mod) by Andrey Yerashkevich
PostPosted: Wed Dec 18, 2013 12:53 pm 
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ecuber wrote:
Hello!!! I am very glad to present my version bandaged 3x3x3 cube . Kind regards, Andrey Yerashkevic.
BelcherBoy2000 wrote:
This would drive me nucking futs! I am terrible at bandaged cubes, seeing as every time I solve the bicube it is by fluke. Have you solved it yet, or is it just too hard to scramble to make a considerably hard solve?

It's not very complicated puzzle is easily solved.


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 Post subject: Re: EcubeR (bandaged mod) by Andrey Yerashkevich
PostPosted: Wed Dec 18, 2013 1:41 pm 
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ecuber wrote:
Hello!!! I am very glad to present my version bandaged 3x3x3 cube . Kind regards, Andrey Yerashkevic.
BelcherBoy2000 wrote:
...nucking futs!...

I had a good chuckle at that. I don't solve bandaged puzzles, but I've tried the Nightmare 2x2, and never again will I touch bandaging.

But E-Cubes, you say it's easy? Is there a level of difficulty you can describe, as in what it can be compared to?

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 Post subject: Re: EcubeR (bandaged mod) by Andrey Yerashkevich
PostPosted: Wed Dec 18, 2013 3:35 pm 
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ecuber wrote:
Hello!!! I am very glad to present my version bandaged 3x3x3 cube . Kind regards, Andrey Yerashkevic.
I am E-Cubes :lol:

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 Post subject: Re: EcubeR (bandaged mod) by Andrey Yerashkevich
PostPosted: Wed Dec 18, 2013 6:09 pm 
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ecuber wrote:
Hello!!! I am very glad to present my version bandaged 3x3x3 cube . Kind regards, Andrey Yerashkevic.
E-Cubes Designer X wrote:
I am E-Cubes :lol:

I know, I just felt compelled to respond to the other post, I just forgot to quote you after :
BelcherBoy2000 wrote:
...nucking futs...


But really, can you give an example of how difficult this bandaged 3x3 is?

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 Post subject: Re: Solving the Bandaged 3x3x3
PostPosted: Fri Dec 20, 2013 5:56 am 
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Konrad, moderator's hat on:
I have merged the responses to ecuber's post in the Puzzle Building sub forum to this thread.

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 Post subject: Re: Solving the Bandaged 3x3x3
PostPosted: Fri Dec 20, 2013 10:50 am 
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I have figured out a few handy algorithms by myself that can be used in many different bandaged cubes. Some of them are very obvious and probably most of you will already know most, if not all of them. But, I'm pretty new to cubing in general and I just thought I might share my findings with y'all. I hope my notation is correct.

Triple EPS:
[ F R' F' R ] x3
Permutes corners.
Swaps FDR with FUR,
swaps FUL with UBR.

Triple Sune:
[ R U R' U | R U' R' U | R U' R' U | R U2 R' ]
Permutes corners.
Swaps UFR with UBL,
swaps UFL with UBR.

[ M U2 M U ] x6:
Permutes corners.
Does the same as Triple Sune, use in case of not being able to do Sune, but M-slice is available.

[ M2 U | S2 U] x3:
Permutes complete F2L pairs.
Does the opposite of the previous 2 algorithms:
Swaps DFR/FR pair with DBL/BL pair,
swaps DFL/FL pair with DBR/BR pair.

[ M2 U2 M2 U | M2 U2 M2 U' ]:
Permutes edges.
Swaps UF with UB,
swaps UR with UL.

Hope I can help someone :D

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 Post subject: Re: Solving the Bandaged 3x3x3
PostPosted: Sat Jan 18, 2014 5:48 pm 
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Konrad wrote:
Andreas Nortmann's 2013930080085E aka "3 Quads, 3 Stripes". I made one with the CubeTwist kit.

At first, I thought that it is hard to scramble, now I think that it is hard to solve.
I have no real strategy for it, because it is so much bandaged.

Has anybody tried it?
I really like 3 Quads, 3 Stripes. I finally ordered a CubeTwist DIY kit today, but I was keen to try out this puzzle in the meantime so I taped up a regular 3x3x3.

I start by getting the puzzle back "into shape" (so it could be solved by moving tiles around, assuming the bandaged pieces are glued together) in two stages. I call the vertex adjacent to all the stripes in the solved position the "stripe-adjacent" vertex, and the diametrically opposite corner the "regular" vertex. First I move a stripe away from the regular vertex if necessary, then I move a stripe piece away from the stripe-adjacent vertex if necessary, then the puzzle is in shape. I do the first stage intuitively, fiddling around, and the second stage with a 10-move algorithm.

From there, one can find useful algorithms by looking for sequences that do one of two things:

1) leave a face with all regular pieces apart from two stripes that are 180 degrees apart
2) leave the puzzle out of shape but with reflective symmetry across a plane that bisects opposite faces diagonally.

With 1) you can make a conjugate: [sequence] + [180 degree turn] + [inverse of sequence].
With 2) you can do [sequence] + [inverse of sequence, reflected].

Both leave the puzzle in the correct shape, with the chance that they do something useful. I use four algorithms, with the actual moves shown in invisible ink:

Algo A - [6:1], a type 1) algo - does the same as Andreas's algo 1-3 (they are rotations of each other). [U F' L' F U2 R : B2]

Algo B - [15:1], a type 1) algo - similar to algo A, but importantly the orientations of the swapped corner and edge pieces are different, with left-right symmetry to the edges but lack of left-right symmetry to the corners. The 15 moves are of the form [[3:[1,1]]+5]. [[ [R' F D : [F',R]] U F' U' F2 R'] : D2]

Algo C - [10+10], a type 2) algo - does the same as Andreas's algo 4 (or algo 5 when inverted). [R U' B' R' U F R' F D' F'] [R' D' R F' R U F' L' U' F]

These three can solve all situations except an odd permutation of stripes (just two need swapping places). For example, doing algo B followed by the left-right reflection of algo B twists two corners with no other effects, while doing algo A followed by algo B flips two edges while twisting two corners, and the corners can be fixed as above, leaving just two edges flipped.

Algo D - [17+10] - This is an irregular one, and was harder to find. It swaps two stripes while also moving the edges around the regular vertex and twisting the corners, leaving just two stripes swapped when the side effects are fixed using the other algos. The first sequence of 17 moves swaps two stripes, while pushing one into the wrong place: overlapping the stripe-adjacent vertex. The next 10 moves are the same sequence I use to finish the second stage of getting the puzzle back into shape. [F R' D2 F D F' R' D2 R D F' R F R' D' F' R] [U F' L' U' F U' R B' R' U]


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 Post subject: Re: Solving the Bandaged 3x3x3
PostPosted: Fri Jan 24, 2014 5:48 pm 
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So, I decided to solve a fairly easy bandaged cube, and found out that when solving white face first, there are 3 variations possible, that make for a completely different solve experience!

The bandaging looks like a C on this cube, so I call it C-cube.

If the 1x3 bandaged part is on the white face, it bandages the red, orange and white faces together, as if there's half the bandaging that's on a Big Block cube. This is a pretty straightforward 3x3x3 solve.

If the bandaging occurs so that the 1x3 block is on one of the side faces (blue in my example below), bandaging the red, orange and blue centers together, it solves completely different, partly like a 3x3x3 and partly like 3x3x2 (at least, that's how I solve it).

I doubt if one could solve the cube "white face first" with the bandaging on the yellow face, because the top face is unable to move in that state.

I found this a very interesting fact, and solving both versions of the cube as seen below is quite fun!

Cheers,


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File comment: 2 different orientations of the same bandaging.
Different orientations.png
Different orientations.png [ 14.55 KiB | Viewed 1878 times ]

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 Post subject: Re: Solving the Bandaged 3x3x3
PostPosted: Sat Jan 25, 2014 10:04 am 
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I already posted about this puzzle a while back :)

viewtopic.php?f=8&t=24452&start=100 a few posts down from the top

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 Post subject: Re: Solving the Bandaged 3x3x3
PostPosted: Mon Jan 27, 2014 1:22 pm 
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martywolfman wrote:
I already posted about this puzzle a while back :)

http://www.twistypuzzles.com/forum/view ... &start=100 a few posts down from the top

Great minds think alike...? :wink:

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