# [R, U]-group blindsolving



## trying-to-speedcube... (Apr 14, 2009)

So I've been thinking about a method to solving in the [R, U]-group.

So first, theory: what is possible, what isn't?

Possible:
-5-cycles of corners
-2 2-cycles of corners*
-3-cycles of edges
-2 2-cycles of edges
-2 3-cycles of corners
-2-cycle of edges+4-cycle of corners (parity)

Impossible:
-3-cycles of corners
-Edge orientation
-2-cycle of edges+2-cycle of corners

So this is a pretty hard one.

Orientation:

Edges: -

Corners: U'RUR'URU2R'U2R'U'RU'R'U2RU' and its inverse

Permutation:

Edges: Pretty straight-forward: edge-PLL's with setups

Corners: I think this is the hardest part, with CE i found a double 2-cycle: 

R2 U2 R' U2 R2 U2 R2 U2 R' U2 R2 U2, or any RU H-perm+U2 for that matter...

5-cycle: R2 U' R2 U R2 U' R2 U R2 U' R2 U (1-3-7-4-8)
5-cycle: R U2 R2 U2 R U' R' U' R2 U R' U (1-7-8-3-4)

If you know more algs, let me know!

*Why is an H-perm possible, while an E-perm isn't?

Tell me what you think


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## AvGalen (Apr 14, 2009)

*Why is an H-perm possible, while an E-perm isn't?

Because all edges can be permuted an H-perm is possible
For switching 2 adjacent corners you need at least a L/L' couple

Corners might be easier to do with sexy-move * 3


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## trying-to-speedcube... (Apr 14, 2009)

Sexy move*3 doesn't preserve orientation though...
I could put an extra UBR+UBL corner flipping alg in it though...
But the hard thing in this is that you can't do something as simple as a single corner swap.


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## fanwuq (Apr 14, 2009)

trying-to-speedcube... said:


> Sexy move*3 doesn't preserve orientation though...



conjugate with x or x'
http://cubefreak.net/BLD/3OP_guide.html#CP2

You might need to use a different orientation definition.


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## trying-to-speedcube... (Apr 14, 2009)

fanwuq said:


> trying-to-speedcube... said:
> 
> 
> > Sexy move*3 doesn't preserve orientation though...
> ...


Hmm... That (U2RU'R'U'RU'R')*2 is pretty nice. I'll use that.

(RU'R'U'RU'R'U2)*2 is also nice, for shooting to another position.

What other definition of orientation did you have in mind, then?

EDIT: Just did a sighted solve:

Scramble: R' U R' U R' U R' U R' U' R2 U' R' U' R U R U2 R2 U' R' U R' U' R

CO: 

U R' U2 R U R' U R U2 R U2 R' U' R U' R' U
R U' U R' U2 R U R' U R U2 R U2 R' U' R U' R' U U R'
U R2 U2 U' R U R' U R U2 R' U2 R' U' R U' R' U2 R U' U2 R2 U'

EP: 

R R2 U R U R' U' R' U' R' U R' R'
U R' U R U R U R' U' R' U2

CP:

U' (U2 R' U R U R' U R)*2 U 

Sort of lucky CP, but it worked


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## cuBerBruce (Apr 16, 2009)

Technically, [R, U] is a commutator, not a group. <R, U> is a group. 

(I'll also note that the "sexy move" is very useful for solving positions in the <[R, U]> group.  )


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## SimonWestlund (Apr 16, 2009)

trying-to-speedcube... said:


> Scramble: R' U R' U R' U R' U R' U' R2 U' R' U' R U R U2 R2 U' R' U R' U' R
> 
> CO:
> 
> ...



I like the bolded move 

but nice solve though


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## cmhardw (Apr 17, 2009)

I've been doing [R,U] group BLD solving for fun on occasion for a couple years now. For some reason I've settled on this method, but I don't necessarily like it.

I solve the corner permutation by visual inspection. I then trace the location of where each piece will end up after my corner permutation solving moves. I memorize the cycles that result from this in the edges. Lastly I memorize which corners will end up flipped and orient those first at the start of solving.

I think I got down to about 2:30-ish for my pb back when I did this a lot. It seems a more traditional orient first then permute method would be much quicker, as it would greatly reduce the memorization time. I feel my memorization time is easily triple the solving time with this method, if not more.

I'm at work now, but will look into the algs you list and try out the method that way. It sounds like a good idea.

Chris


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## trying-to-speedcube... (Apr 17, 2009)

SimonWestlund said:


> trying-to-speedcube... said:
> 
> 
> > Scramble: R' U R' U R' U R' U R' U' R2 U' R' U' R U R U2 R2 U' R' U R' U' R
> ...



I know it cancels, but if I just don't do those moves, you wouldn't understand the solve


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