Solving the 3x3x3
Step 1: Centers | Step 2: Edges | Step 3: Fix parity

Theory

Just a little theory here, but one thing I think that is important to realize is that the power of centers first solving is that you reduce to a 3x3x3 cube, where you can use all of your normal speedsolving tricks. The major drawback of centers-first solving though are the two parity errors that come up. However, I think that the ability to really use your specialized 3x3 tricks makes up for that

Taking care of parity cases

So this last step is a page on how I handle the parity cases. If you want a really good page on this visit Stefan Pochmann's big cubes page. Also check out bigcubes.com.

The stuff below is how I would do each case, but there are lots of different option for how to handle them.

OLL parity

This is the parity that is caused by solving the centers such that the edge permutation is odd. If the scramble has the edges in an even permutation and you solve the centers in an odd number of inner face quarter turns you will cause the orientation parity. If the scramble starts with the edges in an odd permutation and you solve the centers in an even number of inner face quarter turns then you will also cause the parity.

This parity is not caused by the centers. I've seen that erroneously stated on many different sites and posts on the group. The one-edge flipped parity is caused by solving the centers such that the edge pieces are in an odd permutation.

Here are all the tricks I use for this case.

All cubes are in the same orientation, as defined by the below diagram,

The pure form

Here is the pure form of the alg I use,

r2 B2 U2 l U2 r' U2 r U2 F2 r F2 l' B2 r2

And here is the affect on the cube of this alg,

Speedsolve forms

This is the most general case of applying the speedsolve form,

(Rr)2 B2 U2 (Ll) U2 (Rr)' U2 (Rr) U2 F2 (Rr) F2 (Ll)' B2 (Rr)2
performed as: [(Rr) (Ll)] U2 x U2 (Ll) U2 (Rr)' U2 (Rr) [(U') (u d' D')] L2 y' x (Rr) U2 (Rr') B2 (Rr)2

And here is how that alg affects the U layer of the cube,

Using these two algs you can influence the LL a little bit,

If you use the speedsolve version of the parity alg it will leave the LL completely oriented, taking you straight into a PLL case.

If you use the pure form of the parity alg you will end with the LL completely oriented.

To solve the parity and end with oriented LL do: R2 B2 R2 (speed solve form of the parity alg) R2 B2 R2

To solve the parity and end with oriented LL do: L U L' (speed solve form of the parity alg) L U' L'

To solve the parity and end with oriented LL do: (r' l) (speed solve form of the parity alg) (r l')

PLL parity

The PLL parity is caused during the edges step. When forming the edges you only have a 50-50 chance of creating a cycle amongst those edges that has the same parity as the corner permutation. The parity of the corner and edge permutation must be the same in order for the cube to be solvable as a 3x3x3. If this is not the case, you will get the PLL parity.

There aren't really any tricks for this case, just two cases.

(Uu)2 (Ll)2 U2 l2 U2 (Ll)2 (Uu)2
performed as: [(Uu)']2 [(Ll)']2 (U')2 ([(Ll)']2 L2) (U')2 [(Ll)']2 [(Uu)']2

 Front/Left View Front/Right View

L2 D (Ff)2 (Ll)2 F2 l2 F2 (Ll)2 (Ff)2 D' L2
performed as: L2 D x [(Uu)']2 [(Ll)']2 (U')2 ([(Ll)']2 L2) (U')2 [(Ll)']2 [(Uu)']2 x' D' L2

These last two cases can be avoided almost 100% of the time with some careful planning ahead, but if you do run into one of them you should know how to solve it.

(Uu)2 (Ll)2 U2 l2 U2 (Ll)2 (Uu)2 F' U' F U F R' F2 U F U F' U' F R
performed as: [(Uu)']2 [(Ll)']2 (U')2 ([(Ll)']2 L2) (U')2 [(Ll)']2 [(Uu)']2 y [(L U' L) (U)] [(L F' L2) (U)] (L U L') (U' L F)

(Uu)2 (Ll)2 U2 l2 U2 (Ll)2 (Uu)2 R U' L U2 R' U R L' U' L U2 R' U L' U
performed as: [(Uu)']2 [(Ll)']2 (U')2 ([(Ll)']2 L2) (U')2 [(Ll)']2 [(Uu)']2 (R U') (L U2) (R' U R) (L' U' L) U2 (R' U L') (U)

Appendix A

I'm working very hard on applying ZBF2L and ZBLL to the 4x4 when solving as a 3x3. So far I have a page up to help me with ZBF2L, but I have yet to get something online for ZBLL. This is still something I'm working on, but if you're interested you can see the page.

Using ZBF2L on the 4x4x4

Step 1: Centers | Step 2: Edges | Step 3: Fix parity
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