--- In [email protected], "Per Kristen Fredlund"
<[EMAIL PROTECTED]> wrote:

> 
> My idea to deal w parity is to change my own cage method so that i 
> would solve complete first layer then opposite layer. Then middle 
> layers edges (with trivial inner layer quarter-turn parity fix) and 
> no equivalent to the permutation parity of the pairing-up method. 
> Then finally do the rest of the centers. One could also use 
> empty "dedge"s on those first 2 layers while solving the middle 
> layers edges. Im sure it can be fast, but a bit unusual :-) As for 
> doing the last 4 centers im sure it can be fast. Once u reach the 
> state where all unsolved centers are on opposite faces u need 
> maximum 2 algs and u are done :-) And those algs are short. For the 
> 5x5x5 cube im not really that convinced that this new approach will 
> be more efficient than my current approach (or the pairing-up).
> 
> Cheers!
> 
> -Per

Hey now.  It's not weird to do it that way.  The only difference
between my method and the one you described is that I leave out 1 edge
group from each face, essentially turning my sovle into a Roux solve.

The parity fix is easy to spot and takes 13 moves to fix.
lU2l'U2lU2l'U2rU2rU2r' (U2).  It shuffles also 3 blocks of centers in
the M slice, as well as swapping the UB and DB edge pairs.

I played around a lot with counting edges and things and eventually
realized that discounting extremely special cases, it's quicker to
just move on and finish the edge pairing, and use the parity fixer if
it comes up.  This saves time on solves without parity, and loses only
a trivial amount of time on the solves with parity.

-Mike Bennett





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