Mixup Cube

Need to flip edges at FR and BR? We have options. I could use either of the two edge flippers I know for the 3x3x3 cube. Or I could treat them as centers and use the center twisting alg where you move them to the top and twist them. But when we were taking Rory and Roark to the airport yesterday I came up with a new method that is the best of all of them.

(E 45 degrees right; R2; E 45 degrees left; R2) x 2

3x3x4 Mixup Plus

I scrambled it. I solved it. I scrambled it. I tried some reducing. I got pretty far but decided to check on old notes. I abandoned trying to reduce the E-layer edges and followed the notes below. Here is what I found:

3x3x4 Mixup Plus Scramble

1. Thin layers. 180° on perpendicular layers; 45x° on thin layers. Some scrambling of the white and yellow 3x3s will take place.
2. White and Yellow Edges. Break up the inner edge pieces from the outer edge pieces.
3. Corners. Scramble the corners as if it were a 3x3x3.

3x3x4 Mixup Plus Solve

1. Yellow and White Centers
2. Reduce the White and Yellow Edges. Line up a white outer edge at BU with a white inner edge at FD. M up 45°, U2, M down 45°. This works well if the cube is flat. I do not know how it would be if it were shape-shifted. I shape-shifted it to see. It still works but with a little added care. Store each reduced edge in R or L. That way if a 45° turn is needed to flatten an edge piece before joining it to its edge, nothing already reduced gets messed. Use simple setup moves or the Move to move edges around.
3. Orient all the E-layer pieces. This is a simple process. Take them to the top, twist it 90°, and take it back to the E-layer.
4. Permute All Center Pieces to Center Locations Ignoring Color, Use the 3x3x2 Corner Commutator. You don’t have to turn an inner slice since the corners aren’t solved yet. 
5. Corners
6. Yellow and White Edges
7. E-layer Center Re-orientation then Permutation. Permuate using The Move, similar to solving the edges of a 3x3x2.
8. E-layer Outer Edges using the 3x3x2 method. If you get down to a single swap of corners needed hold the cube so the two that need to swap are neither on the lower left and do U R2 U R2 U R2 U R2 U. The centers are good and the corners will solve now.
9. E-layer Inner Edges. ((u 45° left) L2 (u 45° right) R2) x 2 moves A to B to C. A’s flatness stays; the flatness of B and C change. This is the 3x3x2 Corner Commutator where A is on the top layer in the front.

Mixup Cube

Although I do not remember my favorite way to solve this I vaguely remember that I do have a favorite way. Basically it is a 3x3x3, but with 45º slices possible, so that centers can move to edge spots and edges can move to center spots. hmmm, maybe I should start with the corners!

Haha! The corners are solved and the yellow center happened to be in the midst of the yellow corners, but the white center is in a yellow edge spot! Weird.

After focusing on the centers, I proceeded to solve it as much as possible using the Corners First Method. I used the center twisting algorithm to twist edges when needed.

I vaguely remember that what I would do in the past when I got to a certain point was count how many swaps were needed and if it was odd, or even?, then I would give the middle layer a 45º turn. I didn't do this this time and the parity was not an issue. But I did have an interesting situation. One middle layer edge is flipped. Center twister alg to the rescue!

After several more scrambles and solves I did run into the parity at the end and had to give the middle layer a 45º turn then resolve the middle layer centers along with the edges. One thing bothers me. I have this notion that I had some clever way to twist edges other than using the center twister alg. But I can't remember. So finally I decided to see if I had ever made any notes mentioning it. So far here is all I have found in the Solution Guides Pre Fall 2013 file:

White and Yellow Layers; check # of swaps in Middle Layer; Make it even with 45˚ twists if necessary; 3-cycles to solve Middle Layer.

In the Solution Guides file it goes into greater detail:

1. Count how many odd swaps are needed. In other words a swap is 1. A 3-cycle = a double swap = 0 odd swaps.
2. An even numbered cycle is an odd number of swaps. Each pair of odd swaps = an even swap.
3. If there is 1 swap needed after all the math is done, there will be after solving as much as possible too. So do a 45˚ twist before solving anything.

Is that hilarious or what?

In the Notes section of that page it tells about the "clever way to twist edges" that I haven't been able to remember.

So basically I am solving Corners First. It took several solves to see that getting the white and yellow edges could have some fun little twists. Like the one going in does not have to be in the back corner all the time. So you can situate it conveniently to orient other edges along the way when doing the F twist.

Now let's see if I can actually do it!