Another 4x4x4 challenge

[Robert-Y]

Scramble using only R, r, and U moves, and try to solve it using only these moves.

Besides using reduction, are there any other good strategies for solving the 4x4x4 using these moves?

Using reduction, I've almost finished, I just need to figure out how to do the parities.

Has anyone found any algorithms for the following:

1. Flipping 2, 4, or 6 edges (ignoring corners)

2. OLL parity

3. PLL parity

4. (Bonus ) OLL+PLL parity without just solving one parity, then the other parity.

If you have, please type them in spoiler tags, so that you wont spoil the challenge for others

If you're bored of this challenge, you could also try just using r, U, and u moves as another challenge, if you haven't done so already

 

[TMOY]

Well, centers last won't work since there is no nice way to perform center commutators
I tried to solve corners, then centers, then edges with commutators, and it works well. I didn't get a parity case, but I know how to handle it. (Spoiler: (U2r)^5)

 

[Stefan]

For flipping even numbers of dedges:

Spoiler

(Rw U2 Rw') (U' R U) (Rw U2 Rw')
Should be easy to understand and generalize.

 

[Muesli]

Oh my. I could never do that. Are you allowed Cube Rotations?

 

[AvGalen]

Oh my. I could never do that. Are you allowed Cube Rotations?

You are allowed cube rotations, but then the moves you are allowed to perform will change as well so they are mostly useless.

If cube rotations were allowed all you would need to solve anyway was u and U

 

[masterofthebass]

I find <RrU> harder than <RrUu>, but both are pretty simple. I also find them both easier on 5x5 than 4x4

 

[qqwref]

This sounded like fun, but also I thought I remembered how to do it, so I took an average of 5 of <R,r,U>:
(46.57) 1:03.61 (1:04.26) 49.06 47.76 => 53.48
To be honest I was quite lucky, no PLL parities at all and I think only one OLL parity. OLL parities are accomplished with r U2 etc (and some 3-cycles) and PLL parities are just a bunch of 3-cycles (I don't know any better alg.)


As for <R,r,u>, I don't know how to do it I tried <r,U,u> instead which is equivalent but I think much easier to visualize. Anyway it's pretty easy to fix the u ring - edges don't move, and you can place each center by r U r' type moves and use u moves to set up - so that it becomes equivalent to <r,U>. Then, you can fix everything but the U wings by making the D center and then putting two 'columns' of three pieces in. After that, well, I have no idea I've never been able to solve <r,U> either... Anyone know an edge 3-cycle?