# How to use parity to simplify



## Sakarie (Jan 25, 2010)

I don't know if this have been said before, or if it's not thought about before, but I'll give it a try.

I've always experienced parity (odd swaps on edges and corners) as something bad, something that complicated everything in a terrible way. But it seems unliely that something is only bad, without the possibility to be taken advantage of. I found one.

In this example will I use M2 and BH with fixed buffer URB. But I think you can use it anything that cycles stickers, that means NOT 3OP. Also it does ONLY do any good if we have at least two cycles.

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When you have to start a new cycle, I always use the same spot, UBL, or UFR if the first one is taken. That means that I don't hesitate when choosing, and those two are the ones I'm fastest with. Also, UBL is my "parity-spot", the one I add to the cycle if I have an odd number of corners, resulting in URB and UBL switched (parity = y L2 T-perm L2). 

The ultimate thing is therefore if the last corner to shot to is UBL, that means that I don't have to do it, since the cycle would have been URB>UBL>UBL. That means that I have to shot to one corner LESS than I memorized, instead of when I have to shot to an EXTRA corner, which I usually do.

(Oh, why can't I just write it down fast and small?!)

That means that if I can force my last piece to be UBL (not LBU or BUL), I get a bonus corner. When I start the new cycle, I could chose either UBL, LBU or BUL, one of those would guarantee that I'm ending up with UBL. The only thing I have to do is to see "Which side of my buffer do I get just before I start a new cycle?" 

If your third piece in your memoanalyze is DFR, the place where your buffer is, and you can't continue the cycle, then the bufferpiece (the one that should end up on URB) always have an orientation. But you only have to look at which colour is on DFR, and translating it into which side of the bufferspace is. If *D*FR is the *B*UR-place then you only have to remember B-side, and use a very simple converting-tool to see where you should start your new cycle.

URB - start on UBL
RBU - start on BLU
BUR - start on LUB

If you are doing this, and have NOT a third cycle or extra oriented pieces, than you'll always end up with UBL as last corner-piece.

If you're not using UBL as your "parity-piece", then it's very easy to look up the same thing with any piece.

I'm not really sure what will happen if you have a third cycle or oriented pieces, but I'm sure you can use this anyway, but I'll look into how.

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I'm sorry that it became so long, but I wanted it to be so understandable so everyone could understand. Anything unclear?


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## Mike Hughey (Jan 25, 2010)

Unfortunately, this can only help a small percentage of scrambles. (Have you calculated the percentage? To me it seems like it's pretty small - something like one out of 10 or so - assuming I really understand what you're saying. You have to have 2 or more cycles, your first cycle must not include your parity piece, and you need to be able to begin your second cycle on the parity piece. Seems uncommon to me.) But it is a good idea; I may see if I can incorporate this!


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## Sakarie (Jan 25, 2010)

Well, yeah, you're right. 

One thing you can do to raise the chance of this helping is that you can use many possible parity pieces, for example all the corners in the U-layer (I will use this from now on, since it's all only PLL's). That means that you only need one of the three non-buffer pieces unsolved when strating a new cycle.


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