# 3x3x3 "Parity"



## hawkmp4 (Sep 18, 2008)

Edit: Oops. Sorry mods >.< I don't know how but this got posted in the wrong forum. Could you move it to off topic?

This might belong in the blindsolving forum because that's where its discussed most, but its a general topic... So, I was thinking about this, and I know that on 3x3 corners and edges are completely independent. So then, how does Y perm come about, where 2 edges are swapped and 2 corners are swapped, seemingly an odd permutation of edges and an odd permutation of corners.
So... set up a Y perm. Then do U' so that the UL edge is correct. Now solve the cube using only algorithms that affect JUST edges or JUST corners, you can do it, yeah?
I guess this all comes out of my frustration at the concept of parity on 3x3, odd permutations are not possible, really. It may not have the most pieces correct but an AUF shows clearly it can be solved with 3 cycles. Right?


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## shelley (Sep 18, 2008)

If you have an odd permutation of edges and an odd permutation of corners, that's an even permutation.

Edges and corners aren't *completely* independent. Every time you turn a face of a cube, you affect both corners and edges. You use the AUF to show that a Y perm can be solved as 3-cycles of edges and corners. When you turn U, you're affecting both the edge permutation and the corner permutation. Yes, you can solve everything using 3-cycles. But the corner/edge PLL algorithms make things much easier and quicker.

A 3-cycle is just swapping two pairs of pieces, e.g. UR/UF and UF/UL. That's what all the PLLs do.


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## TMOY (Sep 18, 2008)

Because of the possibility of odd permutations of both edges and corners, you can't always solve your cube using only 3-cycles. You must have a parity correction somewhere. Ans yes, a single U or U' is enough for that, but it's necessary.


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