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 Post subject: 3x3x4 Clean swap of 2 corners
PostPosted: Tue Apr 05, 2011 4:38 am 
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Hi

On my 3x3x4, does anyone have an algorithm for swapping two corners without messing up anything else?

At present, my two corners are UFL and DFR.

I've found some corner swapping algs but they always destroy other parts.

Thanks

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 Post subject: Re: 3x3x4 Clean swap of 2 corners
PostPosted: Tue Apr 05, 2011 8:37 am 
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This video appears to have a solution, though it's kind of long. The algorithm is in the video description. It is for different corners than your situation, but you could probably use some setup moves to make it work.


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 Post subject: Re: 3x3x4 Clean swap of 2 corners
PostPosted: Tue Apr 05, 2011 10:23 am 
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D R2 Z' r2 R2 B2 U2 r2 R2 U2 B2 r2 R2 Z (R2 U2)x3 Y' R2 U R2 U' R2 U' D R2 U' R2 U R2 D' B2 D'.

This was made by solving the parity, setting up the corners, T-Perming it and resolving the setup moves. Look at what happens instead of trying to memorise it.

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 Post subject: Re: 3x3x4 Clean swap of 2 corners
PostPosted: Tue Apr 05, 2011 2:32 pm 
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Maybe you should throw in a picture as well ? The solutions are usually very easy, only they consist of different alogarithms put together

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 Post subject: Re: 3x3x4 Clean swap of 2 corners
PostPosted: Tue Apr 05, 2011 4:52 pm 
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Thanks so far.

Quote:
D R2 Z' r2 R2 B2 U2 r2 R2 U2 B2 r2 R2 Z (R2 U2)x3 Y' R2 U R2 U' R2 U' D R2 U' R2 U R2 D' B2 D'

I tried this but it didn't work at all. I have no doubt it's because I don't fully understand the y and z notation. I did look it up and used what I thought was right but it obviously wasn't.

Quote:
Maybe you should throw in a picture as well ? The solutions are usually very easy, only they consist of different alogarithms put together

Here they are:
Attachment:
Picture 001.jpg
Picture 001.jpg [ 56.42 KiB | Viewed 1591 times ]

Attachment:
Picture 002.jpg
Picture 002.jpg [ 57.49 KiB | Viewed 1591 times ]

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 Post subject: Re: 3x3x4 Clean swap of 2 corners
PostPosted: Wed Apr 06, 2011 1:22 am 
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I've tried this several times and it does work. Z is where you turn the puzzle like you're doing an F move. Z' is like turning the puzzle in the same direction as an F'. Y is like turning the puzzle like a U, and Y' is the same as U'.

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 Post subject: Re: 3x3x4 Clean swap of 2 corners
PostPosted: Wed Apr 06, 2011 2:54 am 
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OK. Well thanks for explaining the Z and Y. I've done it again and it has

1) moved the ufl and dfr corner pieces (but not swapped them)
2) also done two edge pair swaps
3) also moved other corner pieces

So, my questions are:

* is it supposed to be a "clean" swap, ie no other pieces moved?
* should I have started by holding the cube upright, as in the pictures, with the two corners being at ufl and dfr?

Thanks

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 Post subject: Re: 3x3x4 Clean swap of 2 corners
PostPosted: Wed Apr 06, 2011 5:36 am 
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I would do it with T-perm and H-perm (+setup & undo).

DB2 (R2UR2U'R2U') D (R2U'R2UR2) D' B2D'
L2d2 (R2DwR2) (Dw2R2Dw2) (R2DwR2) d2L2

This will swap URF and DRB, it is easier to make series of R2 turns instead of F2. :)
Hold it in "standing" position - yellow or white up.

Peedu


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 Post subject: Re: 3x3x4 Clean swap of 2 corners
PostPosted: Wed Apr 06, 2011 10:36 am 
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The puzzle should be held like it is in the first picture, with orange being F. Remember that r2 is two layers, not just a slice turn.

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 Post subject: Re: 3x3x4 Clean swap of 2 corners
PostPosted: Wed Apr 06, 2011 11:28 am 
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I ran it through a computer, and the shortest it could find has 18 layer turns.
F u2 R U F Uu2 F R U R U2 R F U3 F Uu2
Note that u2 here is a single inner slice turn, and Uu2 is a turn of two layers, and that moves of R and F faces are half turns even though I haven't written a 2 after them. Note also that the first F turn can be skipped and done at the end instead.

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 Post subject: Re: 3x3x4 Clean swap of 2 corners
PostPosted: Thu Apr 07, 2011 2:32 am 
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Hi,

Just something I thought about on my way to work. Can't test it on a cube right now, but I'm pretty sure that the algorithm I suggested...
peedu wrote:
DB2 (R2UR2U'R2U') D (R2U'R2UR2) D' B2D'
L2d2 (R2DwR2) (Dw2R2Dw2) (R2DwR2) d2L2

... is not 100% pure or clean. It swithes the center pieces on R face. It does not matter if they are solved already (same color) or will be solved later (not important). It will matter when solving corners before centers blindfolded.

And now when I saw this one...
jaap wrote:
F u2 R U F Uu2 F R U R U2 R F U3 F Uu2

... looks like the same centers will be switched.



About the notation. Since always the meaning of small letter needs to be explained, I used the 'Dw' and leaving out just the inner slice turn for 'd'.

'U3' in jaap's algorithm must probably be 'U2', right?


Peedu


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 Post subject: Re: 3x3x4 Clean swap of 2 corners
PostPosted: Thu Apr 07, 2011 7:19 am 
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peedu wrote:
Just something I thought about on my way to work. Can't test it on a cube right now, but I'm pretty sure that the algorithm I suggested...
... is not 100% pure or clean.


A 100% clean algorithm is impossible. Every move is an even permutation:
Horizontal layer quarter turns are two 4-cycles (corners+edges, or edges+centres) and side face half turns are six transpositions.

A 'clean' corner swap will by necessity therefore also swap some identical centre pieces. It must in fact use an odd number of U/D quarter turns, and an odd number of u/d layer quarter turns and R,L,F,B side turns.

peedu wrote:
jaap wrote:
F u2 R U F Uu2 F R U R U2 R F U3 F Uu2

'U3' in jaap's algorithm must probably be 'U2', right?

No, it is U'.

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 Post subject: Re: 3x3x4 Clean swap of 2 corners
PostPosted: Thu Apr 07, 2011 11:33 am 
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jaap wrote:
peedu wrote:
Just something I thought about on my way to work. Can't test it on a cube right now, but I'm pretty sure that the algorithm I suggested...
... is not 100% pure or clean.


A 100% clean algorithm is impossible. Every move is an even permutation:
Horizontal layer quarter turns are two 4-cycles (corners+edges, or edges+centres) and side face half turns are six transpositions.

A 'clean' corner swap will by necessity therefore also swap some identical centre pieces. It must in fact use an odd number of U/D quarter turns, and an odd number of u/d layer quarter turns and R,L,F,B side turns.

peedu wrote:
jaap wrote:
F u2 R U F Uu2 F R U R U2 R F U3 F Uu2

'U3' in jaap's algorithm must probably be 'U2', right?

No, it is U'.


Hi,

I also came to the conclusion that 100% clean 2-piece swap is impossible.
Your algorithm is better.

I'm thinking about solving it blindfolded. Just have to find how to handle the 'parity' issues.


Peedu


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 Post subject: Re: 3x3x4 Clean swap of 2 corners
PostPosted: Wed Apr 20, 2011 11:12 am 
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Location: Norway
Im still wondering what you did to actually get it like that without trying?

I always solve one layer by slotting corners, then the opposite layer solving corners first, then centres/edges.

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 Post subject: Re: 3x3x4 Clean swap of 2 corners
PostPosted: Wed Apr 20, 2011 11:20 am 
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Joined: Thu Sep 24, 2009 12:21 pm
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The easiest thing to do is solve one face however you wish to do it (possibly by corners first, and then edges). Then on the top layer, solve any parity case (this is easy if you know the 21 possible OLL cases), solve corners and then do edge cycles.

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3x3x3 single: 5.73 seconds.
3x3x3 average of five: 8.92 seconds.
3x3x3 average of twelve: 9.77 seconds.

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 Post subject: Re: 3x3x4 Clean swap of 2 corners
PostPosted: Wed Apr 20, 2011 1:27 pm 
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Joined: Thu Mar 17, 2011 5:20 pm
Location: Norway
Luke wrote:
The easiest thing to do is solve one face however you wish to do it (possibly by corners first, and then edges). Then on the top layer, solve any parity case (this is easy if you know the 21 possible OLL cases), solve corners and then do edge cycles.


Honestly i have no idea what OLL cases is at all. I just solve it the same way i would solve a 3x3x2, then solve pariities :)

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