# M2 Corner/Edge Parity



## Tyson (Aug 3, 2008)

I am a blindfolding noob... if you guys can't tell. In my old age, I am only recently beginning to catch up on this new thing that you young kids call "M2".

Anyway, my old blindfold system is probably pretty well known. I can still do about 90 seconds (100 seconds is a more realistic average) with the following system:

orient edges (allowing R/L, but restricting to F2/B2), orient corners, permute edges, permute corners

I use 3-cycles, and start from certain places. The product of this is that in the end, if I have parity, usually it's parity with one piece (corner or edge) with another one... but the FIRST corner (or edge) has a much higher probability of being a certain corner given the nature of how I do these things. This corner turns out to be UFR. So generally, when I have 2 corners and 2 edges that need to be swapped, one of those corners is UFR.

Now, we move onto this Tyson who's a bit bored, and working on M2 just to see what "all these kids are all about." So, I come to the situation where you have 2 corners and 2 edges.

Currently, I am now experimenting with solving the cube like this:
orient corners, permute corners, M2 for edges

If I come to the edge/corner parity situations, it's always the UB and DF edges that need to be swapped. Big deal... right? WRONG! Unfortunately, for me, the UFR corner is generally the other incorrect wrong. This makes life slightly difficult, as the easiest way to bring DF to the top layer is with an F2 turn... which, now I have a stupid UFR corner in the way!

Before I switch my initial starting corner for edge permutation, I'm wonder if there are good quick algorithms out there that allow me to swap UFR with another corner (probably in the top layer) along with UB and DF edges?

To be quick, I would like to be able to set this up into a PLL, without much thinking. But with the UFR corner in the way, I more commonly have to reduce this to T-perms and H-perms, and it's really a waste of time.

Am I making sense? This complication is only arising because I'm old... and developed a method of blindfold solving when separating orientation and permutation was cool. And lead to world records. But in my advanced age, (though the nurses at this retirement home seem to think I'm rather lucid) I might as well try to understand the cube a bit more.

Any ideas? Anyone need clarification? It's 11:45 AM, so I guess it's about bed time for me.


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## Stefan (Aug 3, 2008)

One thing you could try is the variant of M2 where you use DB/UF instead of DF/UB. Someone I think actually does this, but I don't remember who and why and how he likes it.

Or try this alg after you're done with M2, this will restore the M-slice and leave you with the UB and UR edges swapped:
D R2 D' M2 D R2 D'


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## Stefan (Aug 3, 2008)

Or try this after M2, should restore the M-slice and leave you with UF and UR swapped, which I think is ideal for you:
F2 U' M' U2 M' U' F2


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## Tyson (Aug 3, 2008)

My dearest Stefan, the idea of DB/UF vs. DF/UB is interesting. Does it make the setup moves easier? More difficult?

The problem with the algorithm you provided me is that it costs time. And look at these little kids these days. They're FAST! There's no reason to waste time in setting up something into another thing if there's an algorithm similar to the T-permutation that allows you to solve it in one step with a setup move as minimal as "L2" right?


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## Gprano (Aug 3, 2008)

I use the same system : M2 and 3cycles corners.

For the parity, there is not so many cases considering a R2/L2 setup.
I solve them using a quick setup and a PLL.
For example, with the UFR corner :
and DFR : D'L2 [pll Y] L2D
and DBR : RU'F2 [pll Jsym] F2UR'
and UFL : M'y'L2[pll T]L2yM
You can easily figure out each case.

If you use always the same setup, it becomes not so slow 

I think it's faster than first swapping UB and UR and then a pll.


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## Stefan (Aug 3, 2008)

Just mirror the whole method front<->back. So you have F turns instead of B turns, don't know what you like better. And the finger tricks become slightly different, for example:

Target FR: (U R U' M2 U R' U') becomes (U' R U M2 U' R' U)
Target BR: (U R' U' M2 U R U') becomes (U' R' U M2 U' R U)


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## Stefan (Aug 3, 2008)

Wait, I totally ignored that you have the corners "oriented" already. That makes things easier (or at least reduces the number of cases).


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## Tyson (Aug 3, 2008)

Yeah, it does. How would you go about figuring this out? Cube Explorer?


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## Gprano (Aug 3, 2008)

With an only L & R setup, there is 10 cases
-3 with the corners in the R slice : diagonal, horizontally adjacents and vertically adjacents
-the same for the L slice
-4 cases with one L slice corner and one R slice. We can see it by putting the corners in the U layer, keeping their orientation correct.

All the cases are here a blind page in french (by deadalnix)
The algs are setup and PLL too.


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## Tyson (Aug 3, 2008)

Gprano said:


> I use the same system : M2 and 3cycles corners.
> 
> For the parity, there is not so many cases considering a R2/L2 setup.
> I solve them using a quick setup and a PLL.
> ...



Great, thank you. This isn't a pressing issue for me now, as I'm just struggling to solve cubes at this point, but it will be of great help when I get there.


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## Stefan (Aug 3, 2008)

Figure what out? That having oriented makes things easier? If you mean finding algs... I like using ACube and Herbert's qtm-optimal solver. The M-slice being off complicates things, though, it drives me mad all the time.


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## joey (Aug 3, 2008)

It was Chris Hardwick who uses DB/UF.
You *could* use a 3-cycle corners to solve UFR, and change the corner parity? But that involves another alg too.


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## Pedro (Aug 4, 2008)

Cube explorer gave this:
F2 U2 F R2 F2 U2 F R2 F2 L2 D2 B R2 D2 (14f) for UFR - UBL

U F2 U' R2 L2 B2 U B2 U' L2 D L2 B2 (13f) for UFR - UBR

U L2 B2 R D R' B2 L U R' L F2 R' L2 (14f) for UFR - UFL

I like M2 U2 M' U2 M for parity fixing. Swaps UB and UF, and you can use them for a PLL with the other corner and UFR


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## blah (Aug 4, 2008)

Tyson, I use M2 + 3OP too, and I once faced the exact same problem. Only mine was worse - I didn't have a "fixed" corner that was "usually" wrong. So I used Cube Explorer to generate algorithms for _all_ possible cases of UB and DF swapped, and 2 random (oriented) corners swapped, but unfortunately they were all _very_ unfinger-friendly, so I didn't use them, but I have the file somewhere in my computer, I'll look for it later, upload it, and post you the link.

What I'm currently doing is M2 F2 + T-perm (choose the "more advantageous" direction to do it) + F2, then solve the remaining corners in one algorithm. Not very move-efficient, but not much thinking required either, 'cause I plan what I'm gonna do while executing the T-perm, which is relatively long and gives me time to think how to setup my last cycle (usually 1 setup move only), so I don't usually have a lag time between the T-perm and the final cycle alg.

I recently had a new idea for this parity fix thingy too, but it's still a bit "ugly" for some cases, I'll clean it up a bit and post it here later.


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## blah (Aug 4, 2008)

Okay so here's my idea, it's nothing new, it's just a more systematic way of doing things.

Generate an algorithm to swap UB-DF and UFR-UBL. And generate another algorithm to swap the exact same pieces, but this time, with the centers off by M2 (hope you get what I mean). Choose the "nicer" of the 2 algorithms and stick to it. (or you could just use the ~M function with ACube)

The 2 edges should be solved with whatever algorithm you've got, so now all you have to worry about is the corners. I did a bit of probability calculation, and here's what I got:

1/28 - Solved
3/28 - H Perm + U2
4/28 - A Perm
4/28 - The most annoying case*
8/28 - "Q Perm" (FR'F'R)*3
8/28 - 3-cycle (2 diagonal U corners and 1 D corner)

*2 diagonal U corners and 2 adjacent D corners

All cases require at most 1 setup move (AUF or ADF), except the most annoying case, which I haven't figured out an efficient way to solve yet. Algs, anyone?

And for Tyson, since most of the time you have UFR as one of your unsolved corners, the (conditional) probability of you getting the nasty case is even lower than 1/7, so yeah.


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## KJiptner (Aug 4, 2008)

Try D2 M' D2 M' very short and leaves you with UF and UB swapped. M-Slice must be incorrect (no M2 to adjust first).


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## Mike Hughey (Aug 4, 2008)

KJiptner said:


> Try D2 M' D2 M' very short and leaves you with UF and UB swapped. M-Slice must be incorrect (no M2 to adjust first).



Or, I use M' F2 M' F2 - does the exact same thing. Masterofthebass told me about that, and I've used it ever since. Solve the last piece wherever it might be using typical M2 setups, then do this. Ever since learning this, parity seems outrageously easy, and some of my fastest solves now include parity.


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## KJiptner (Aug 4, 2008)

Mike Hughey said:


> KJiptner said:
> 
> 
> > Try D2 M' D2 M' very short and leaves you with UF and UB swapped. M-Slice must be incorrect (no M2 to adjust first).
> ...



Thank you Mike, pretty nice with an x before


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## Swordsman Kirby (Aug 6, 2008)

Tyson said:


> I am a blindfolding noob...



Heheheheeh.

By the way, Dan Cohen uses FD instead of DF.


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## blah (Aug 6, 2008)

Swordsman Kirby said:


> Tyson said:
> 
> 
> > I am a blindfolding noob...
> ...



And Erik and Joel.


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## tim (Aug 6, 2008)

blah said:


> Swordsman Kirby said:
> 
> 
> > Tyson said:
> ...



And Kai.


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## KJiptner (Aug 6, 2008)

tim said:


> blah said:
> 
> 
> > Swordsman Kirby said:
> ...



Yip.


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## joey (Aug 6, 2008)

KJiptner said:


> Yip.


Kai Yiptner?


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