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Parity Errors

dChan

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Currently I just have to count how many corners I have to permute to see if I have a parity error. But yesterday I came across a pecuilar problem on my 8th solve where the UFR and UBR corners needed to be switched and also the FR and BR corners needed to be switched as well. I believed that I had fixed the parity already so is this just a matter of me forgetting to do one more edge in my cycle? Or is it a parity? My 7th solve was definetly a parity because I had a T-pattern at the end but this one I can't tell.
 

tim

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Everything in a 3-cycle system where you have only 2 pieces to swap is a parity.
A parity is either a Corner Parity, an Edge Parity or (very ugly) a mixture of both (2 corner pieces + 2 edge pieces). To fix a parity bring the 4 pieces to your U or D layer (F and B are not allowed, cause they destroy the orientation of your corners) and use one of your PLL algorithms. The setup moves required to bring 2 corners and 2 edges to U or D are in my opinion the hardest part in bld cubing. (Except your T-Permutation :))

In your particular situation i would have done something like this:
U2 L2 to bring the corners to D.
D' F' to bring edge 1 to the up layer.
D2 B to bring edge 2 to the up layer.
D' L2 to bring the corners back to the up layer.

And then you can execute the F permutation algorithm on U.

After reading this long list of moves i'm sure there's a shorter solution, but i can't figure it out at the moment (i need some sleep...).
 

dChan

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Thanks cin, this helps alot! Parities are still a mystery to me so I don't full understand them beyond just doing the T-perm after corner permutation to fix it. The only thing stopping me from an actually successful solve is parities because my last two solves were the closes I've ever been to have a solved cubed while blindfolded. I just needed to fix the parity! Thanks a bunch.
 

tim

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Originally posted by watermelon@May 16 2007, 10:59 PM
After reading this long list of moves i'm sure there's a shorter solution, but i can't figure it out at the moment (i need some sleep...).
Here's what I thought of:
d2 L' S' (T Permutation) S L d2

Enjoy!
That's awesome. At first time i saw your post, i thought: "he's using a L move, what about the orientation?". And then i got it. I've never thought of middle layer moves as setup moves, until now. That simplifies a lot, thanks :).


(That sounds like a dumb TV commercial where they say nothing more than "Wow, that's so great, where did you get that?" :D)
 

KJiptner

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I would handle it with much less headache...

TPerm -> solves Corners, swaps UR and UL
F' B setup to bring Edges in U -> H-Perm -> B'F

I often handle the parity like this: do a PLL alg to solve the corners and swap two uninvolved (!) edges, then swap those 2 edges back along with the 2 from the Parity with an H-Perm (on any Layer) or Z-Perm (not on L or R)
 
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