New 4x4 parity algs using R, Rw, U

[mr. giggums]

I would be intrested if you did a search with <U,R,Rw> but instead of just the LL unsolved have U and R unsolved.

Just like Rw' U R U Rw' U2 Rw' U2 Rw' U2 Rw2 U R' U' Rw2 U' R' U Rw' but if possible shorter. Also if there isn't one shorter can you post all other algs at similar length so I can see which one flows faster.

[uberCuber]

I would be intrested if you did a search with <U,R,Rw> but instead of just the LL unsolved have U and R unsolved.

Ooo, I see where you're going with this; that could be cool

As a similar type of thought, it would be interesting to see <U,R,Rw> algs that could mess with both the U layer and M layer

[cmowla]

Just for fun, here's a 4-cycle double parity that messes up two 1x2 center blocks in M (in addition to the U and R slices).

Rw U2 Rw U2 Rw U2 Rw2 U' R U Rw2 U R U' Rw2 (21,15)

EDIT:

Here's another one which I made from one of Kåre's algs. It destroys the U Layer, two 1x2 center blocks in M, and destroys only one F3L slot.
Rw U2 Rw2 U' Rw' U2 Rw U2 Rw' U' Rw2 U' R2 U' Rw' (21,15)

[mr. giggums]

Ooo, I see where you're going with this; that could be cool

As a similar type of thought, it would be interesting to see <U,R,Rw> algs that could mess with both the U layer and M layer

It would be pointless because you coun't move the DFl and DBl wings so when they get paired back together the other wings the DF and DB edges will be solved so you would end up with only LL scrambled.

[uberCuber]

It would be pointless because you coun't move the DFl and DBl wings so when they get paired back together the other wings the DF and DB edges will be solved so you would end up with only LL scrambled.

And there's me failing to think something through again...

[cmowla]

I have now also searched for sequencens using only Rw U. Sadly those are 25 moves long (21 if one f2l pair is unsolved).
Dumping long lists of algs in the forum seems to be a bit impractical, so Gunnar kindly provided some webspace for a simplistic list of my results.

http://apelgam.se/Rubik/4x4parity/

Beautiful collection. Did Gunnar not add all of the algs you listed in this thread (I know some of them are there)? Also, there are algorithms which only mess up the U Layer in categories which claim to mess up more?

Anyway, I just studied the OLL Parity (not double parity) algorithms which destroy the FR F3L slot, and I have took off a move. These solutions mess up the U and R layers (Petrus).

Rw U2 Rw2 U' Rw' U2 Rw U2 Rw' U Rw2 U2 Rw2 U R2 U' Rw' (25,17)
Rw U2 Rw2 U Rw' U2 Rw U2 Rw' U' Rw2 U2 r2 U R2 U' Rw' (25,17)
Rw' U2 Rw2 U Rw U2 Rw' U2 Rw U' Rw2 U2 Rw2 U' R2 U Rw (25,17)
Rw' U2 Rw2 U' Rw U2 Rw' U2 Rw U Rw2 U2 r2 U' R2 U Rw (25,17)


mr. giggums,
Are these algs (well, I really just listed 2 algs, and only one is fast) are an example of what you wanted? I wonder what the minimum btm move counts are for <U, Rw, R>, considering that the minimum for all moves allowed is 13.

[KingTim96]

am i doing something wrong here? im using the very first alg posted, the first 19 move one, and each time it is flipping a different edge, what am i doin wrong?

[cmowla]

am i doing something wrong here? im using the very first alg posted, the first 19 move one, and each time it is flipping a different edge, what am i doin wrong?

You're doing it correctly. It just flips the edge in the back. You have to add U' at the end of the alg to flip the same edge each time:
Rw U2 Rw U2 Rw U R Rw U2 R2 U Rw U R Rw2 U Rw U' Rw U'

[Pyjam]

Rw U2 Rw2 U' Rw' U2 Rw U2 Rw' U Rw2 U2 Rw2 U R2 U' Rw'

Wonderful. Many thanks.

I do {thumb on F} (Rw U2' Rw2' U') {thumb on U} (Rw' U2 Rw U2' Rw' U) (Rw2' U2' Rw2 U R2' U') {thumb on U} Rw'

[cmowla]

Even though I posted this algorithm here, I wanted to add it to this thread. It's another "Petrus Parity", only this one is shorter than the (25, 17) I derived from Kåre's algorithms, and it's a lot less complicated. I indirectly derived it from cuBerBruce's algorithm.

Rw' U R' U2 R U' Rw' U2 Rw' U2 Rw' U' R U2 R' U Rw' (21, 17) (Not double parity).

If we rewrite my algorithm as the following, you can see that this algorithm is no more than (Rw' U2)4 Rw' with some <U, R> insertions!
(Inserted moves are red.)

Rw' U R' U2 R U' Rw' U2 Rw' U2 Rw' U' R U2 R' U Rw'

It should be very easy to remember, as the red moves are just setup moves to the first and last U2s.

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In addition, although this algorithm is not in <U, Rw, R>, if we adjust this algorithm, we can have an inner slice version which just affects the FR F3L slot and the last layer.

r' U R U2 R' U' r' U2 r' U2 r' U' R U2 R' U r' (21, 17) (Not double parity)

Again, this algorithm can be visualized as being (r' U2)4 r' with some move insertions, and therefore it can be easy to remember.

r' U R U2 R' U' r' U2 r' U2 r' U' R U2 R' U r'

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The only difference between the inner slice version and the wide turn version is that the first two R moves are inverted in the inner slice version (obviously all slice turns are wide in the wide turn version, and all slice turns are inner turns in the inner slice version).

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I can't help but remember Stefan's algorithm when I see my (21,17) wide turn version because he made his double parity algorithm

Rw' U R U (Rw' U2)3 Rw2 U R' U' Rw2 U' R' U Rw' (24, 19)

several years ago using an adjustment of (Rw' U2)4 Rw' as well. (Here is his derivation).

Rw' U R U (Rw' U2)3 Rw2 U R' U' Rw2 U' R' U Rw'