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A collection of useful <Rw,R,U> parity algorithms for 4x4x4

Do you find these algs useful?


  • Total voters
    22

Robert-Y

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I did not really find any of these algorithms. But this is how I found them:
1. I took a long list of 4x4x4 parity algs created by Kare Krig. They can be found here: http://apelgam.se/Rubik/4x4parity/
2. I pasted every alg into http://alglister.whocouldthat.be/ (created by Justin Jaffray upon personal request). It sorts all the algorithms out in QTM.
3. Then I took every short alg and tried all of them out including their mirrors, inverses, AND mirror inverses.
4. Then I was left with these algs which I feel are worth learning. I did not bother searching through any of the algorithms that affect more than one F2L slot because it's difficult to detect OLL parity for me before that point.

I have sorted the algs out by how much they affect F2L, from the least to the most.


Please let me know if I have made any mistakes and happy learning!

Flips one edge:

Algorithm and length (QTM)

Effect

Rw' U2 Rw' U2 Rw' U' R' Rw' U2 R2 U' Rw' U' R' Rw2 U' Rw' U Rw' (24)

Flips UF, antisune affect on corners

Rw' U Rw' U' Rw2 R' U' Rw' U' R2 U2 R' Rw' U' Rw' U2 Rw' U2 Rw' (24)

Flips UR, antisune effect on corners

Rw' U Rw' U' Rw2 R' U' Rw' U' R U2 Rw' U' Rw' U2 Rw' U2 Rw' (22)

Flips UF, shoots DFR to RBU

Rw' U2 Rw' U2 Rw' U' Rw' U2 R U' Rw' U' Rw2 R' U' Rw' U Rw' (22)

Flips UF, shoots DBR to FRU

Rw' U2 Rw2 U' Rw U2 Rw' U2 Rw U Rw2' U2 Rw2 R U' R' U Rw (25)

Flips UB, brings out BR pair

Rw U2 Rw2 U Rw' U2 Rw U2 Rw' U' Rw2 U2 R' Rw2 U R U' Rw' (25)

Flips UF, brings out FR pair

Rw' U' R U R' Rw2 U2 Rw2' U' Rw' U2 Rw U2 Rw' U Rw2' U2 Rw (25)

Flips UR, affects BR pair

Rw U R' U' R Rw2' U2 Rw2 U Rw U2 Rw' U2 Rw U' Rw2 U2 Rw' (25)

Flips UR, affect FR pair




Flips three edges:

Algorithm and length (QTM)

Effect

Rw' U' Rw' U2 Rw' U2 Rw' U' Rw U2 r U2 Rw U' Rw' U2 Rw' U2 Rw' U' Rw' (28)

Flips UF,UR,UB, (Pure!)

Rw' U R U2 R' U' Rw' U2 Rw' U2 R Rw' U' R' U2 R U' R' U2 Rw' (25)

Flips UF,UR,UB, twists DFR

Rw U2 R U R' U2 R U R' Rw U2 Rw U2 Rw U R U2 R' U' Rw (25)

Flips UF,UL,UB, twists DFR

Rw' U2 R' U' R U2 R' U' R Rw' U2 Rw' U2 Rw' U' R' U2 R U Rw' (25)

Flips UF,UL,UB, twists DBR

Rw U' R' U2 R U Rw U2 Rw U2 R' Rw U R U2 R' U R U2 Rw (25)

Flips UF,UR,UB, twists DBR

Rw' U' R' U' R U' R' U2 R U' Rw' U2 Rw' U2 Rw' U' R' U2 R U Rw' (25)

Flips UF,UL,UB, shoots DFR to UFR

Rw' U R U2 R' U' Rw' U2 Rw' U2 Rw' U' R U2 R' U' R U' R' U' Rw' (25)

Flips UF,UR,UB, shoots DBR to RFU

 

Christopher Mowla

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Thanks for the work. I think this process would have been easier if you would have searched first, because I already sorted ALL of Kåre's algorithms almost exactly 1 year ago, here. (You could have just created the mirrors and inverses from them, but oh well :)).

Anyway, since you like 1 F3L slot algorithms, out of curiosity, how do the following slice algorithms that I found compare in speed?
r' U R U2 R' U' r' U2 r' U2 r' U' R U2 R' U r' (21,17)
l' U' R U2 R' U l' U2 l' U2 l' U R U2 R' U' l' (21,17)

(Just in case you haven't seen the wiki page, I also found r' U2 F' U2 F U2 r' U2 r' U2 r' F' U2 F r' (21,15) and l U2 F' U2 F U2 l U2 l U2 l F' U2 F l (21,15) as well, and qqwref used one of them for solving very large cubes at one time...I'm not sure if he still uses them).

From the same idea, I created this alg r' U' R U' r U2 r U2 r U' R' U' r', but unfortunately, it doesn't preserve the centers, but almost. :)

Lastly, what do you think of these two algs as far as speed goes (I know they destroy more than 1 F3L slot, but I am just curious)?
Rw' U R' U2 R U' Rw' U2 Rw' U2 Rw' U' R U2 R' U Rw' (21, 17)
Rw' U' L' U2 L U Rw' U2 Rw' U2 Rw' U L' U2 L U' Rw' (21,17)
Would you recommend these to Petrus solvers?

EDIT:
That website you used isn't entirely reliable, as it counts Uw Lw' Uw' l' Uw Lw Fw' Lw2 Uw' l' Uw Lw' L' Fw Uw' as 21 qtm, when it's 18.
 
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Robert-Y

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Thanks for the work. I think this process would have been easier if you would have searched first, because I already sorted ALL of Kåre's algorithms almost exactly 1 year ago, here. (You could have just created the mirrors and inverses from them, but oh well :)).
I actually did see that list but for some reason, I thought some algs were missing in that list, but now I think I was probably mistaken.

Anyway, since you like 1 F3L slot algorithms, out of curiosity, how do the following slice algorithms that I found compare in speed?
r' U R U2 R' U' r' U2 r' U2 r' U' R U2 R' U r' (21,17)
l' U' R U2 R' U l' U2 l' U2 l' U R U2 R' U' l' (21,17)

(Just in case you haven't seen the wiki page, I also found r' U2 F' U2 F U2 r' U2 r' U2 r' F' U2 F r' (21,15) and l U2 F' U2 F U2 l U2 l U2 l F' U2 F l (21,15) as well, and qqwref used one of them for solving very large cubes at one time...I'm not sure if he still uses them).
They're pretty cool, I think they're probably worth learning too.

From the same idea, I created this alg r' U' R U' r U2 r U2 r U' R' U' r', but unfortunately, it doesn't preserve the centers, but almost. :)
Is there a way to alter this slightly to preserve centres without paying too many moves?

Lastly, what do you think of these two algs as far as speed goes (I know they destroy more than 1 F3L slot, but I am just curious)?
Rw' U R' U2 R U' Rw' U2 Rw' U2 Rw' U' R U2 R' U Rw' (21, 17)
Rw' U' L' U2 L U Rw' U2 Rw' U2 Rw' U L' U2 L U' Rw' (21,17)
Would you recommend these to Petrus solvers?
I probably would but obviously it depends on how decent their parity recognition is.

EDIT:
That website you used isn't entirely reliable, as it counts Uw Lw' Uw' l' Uw Lw Fw' Lw2 Uw' l' Uw Lw' L' Fw Uw' as 21 qtm, when it's 18.
Thanks, I've told Justin about it.
 

Christopher Mowla

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Is there a way to alter this slightly to preserve centres without paying too many moves?
Unfortunately, I don't believe so. I have looked at this from 4 different angles, and it seems that the 17 stm move algs in <U,R,r> that I already found are superior to the results I got from this.
[Route 1] We can add conjugates and get a 17 stm algorithm, but we need to use S moves.
[r2 S' r2: r' U' R U' r U2 r U2 r U' R' U' r']
[r2 S r2: r' U' R U' r U2 r U2 r U' R' U' r']
(These two algorithms are in the wiki).

[Route 2] We can insert an interior piece in <U2,r> which swaps 3 1x2 blocks in slice r, merge that with all existing <U2,r> moves, and use CubeExplorer to find the optimal <U2,r> solution, but doing so makes a (31,21) solution.
r' U' R U'
U2 r2 U2 r2 U2 r' U2 r U2 r' U2 r2 U2 r2 U2
U' R' U' r'
= r' U' R U r2 U2 r2 U2 r' U2 r U2 r' U2 r2 U2 r2 U R' U' r'
But this is exactly the same as an algorithm I already have in the wiki:
(r' U' R U r)(r U2 r2 U2 r' U2 r U2 r' U2 r2 U2 r)(r U R' U' r'), where the middle piece is the center preserving checkerboard 2-gen alg.

[Route 3] We can obviously just add moves to the end to restore centers, but it's ugly:
(r' U' R U' r U2 r U2 r U' R' U' r') (U2 x r2 u2 r2 u2 x')

[Route 4]
If we remove the R moves from this alg, we have a non-visually pure checkerboard 4-cycle in U.
r' U' U' r U2 r U2 r U' U' r'
You've probably seen this before, and probably what's coming to mind now is what if we split some two U2 moves is our beloved <U,r> algorithm for the checkerboard case, r' U2 r2 U2 r U2 r' U2 r U2 r2 U2 r', and insert R moves in between. We would get a 17 stm algorithm, but I have tried all possibilities and none of them are dedge preserving algorithms.
I also found a (21,15) <U, Rw, R> algorithm of a similar effect to my (15,13) slice turn algorithm:
Rw' U2 Rw2 U Rw U2 Rw' U2 Rw U Rw2 U R2 U Rw
(I just took out some moves from one of Kåre's algorithms to make it), but again, I don't see any promises.


I wonder, how fast can Sameer do my pure 3 flip double parity alg?
Rw' U2 r U2 Rw' x' U2 r' U' R' U' Rw' U2 Rw U R U' Rw R U2 x (24 sqtm,19 stm)

EDIT:
Just in case anyone wants to know how I found that 3 flip by hand, here's its decomposition (it's like a derivation if you start with the commutator and then add the remaining pieces...you factor in the x cube rotation last):
[x' U2 R2: [r': [U2, U' R' U' Rw'] ] U2 Rw2 [Rw' F2: r'] U2 R2]'
 
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Robert-Y

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cubizh found these:

(y) Rw U R Rw' U' Rw' U' Rw U Rw U' Rw' U' R Rw' U Rw U R' U' R' (U)
(y) R' U' R' U Rw U R Rw' U' Rw' U' Rw U Rw U' Rw' U' R Rw' U Rw (U)
R' U Rw U R Rw' U' Rw' U' Rw U Rw U' Rw' U' R Rw' U Rw U R' (U')

They also work on odd number cubes! (They will preserve +centres if they are all solved)
 
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Christopher Mowla

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cubizh found these:

(y') Rw U R Rw' U' Rw' U' Rw U Rw U' Rw' U' R Rw' U Rw U R' U' R' (U)
(y' R' U' R' U Rw U R Rw' U' Rw' U' Rw U Rw U' Rw' U' R Rw' U Rw (U)
R' U Rw U R Rw' U' Rw' U' Rw U Rw U' Rw' U' R Rw' U Rw U R' (U')

They also work on odd number cubes! (They will preserve +centres if they are all solved)
They are neat and all, but don't you think the alg I found by hand around 2 years ago is better?
(Rw' U R U Lw' U2 Rw' U2) r2 (U2 Rw U2 Lw U' R' U' Rw)

It also works on odd cube sizes as well as every wing edge orbit of all cube sizes > 3.
 

Robert-Y

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I'm not sure I haven't learnt nor tested them yet.

Yours is easier to learn probably but I think cubizh's algs might be better since I can almost do them without regripping much.

However you can modify yours slightly to make it a bit better I think:
Mirror the algorithm along the "S plane":

(Rw U' R' U' Lw U2 Rw U2) r2 (U2 Rw' U2 Lw' U R U Rw')

Now just convert it to <Rw,R,U,B>:

(Rw U' R' U' Rw B2) (Rw B2 r2 B2 Rw') (B2 Rw' U R U Rw')

Which is a bit nicer I think :)

Thanks for sharing again!

I should look at that wiki page of parity algs more :p
 

uberCuber

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cubizh found these:

(y') Rw U R Rw' U' Rw' U' Rw U Rw U' Rw' U' R Rw' U Rw U R' U' R' (U)
(y' R' U' R' U Rw U R Rw' U' Rw' U' Rw U Rw U' Rw' U' R Rw' U Rw (U)
R' U Rw U R Rw' U' Rw' U' Rw U Rw U' Rw' U' R Rw' U Rw U R' (U')

They also work on odd number cubes! (They will preserve +centres if they are all solved)
Rw U Rw' R U' Rw' U' Rw U Rw U' Rw' U' Rw' R U Rw U R' U' R' is nearly regripless o_____O

I wonder if he could find similarly cool algs for the O perms?
 

Robert-Y

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He's trying :)

It'll take some time I think. Hopefully there'll be some results tomorrow?

You can try this for now: R U R' U R' U' R2 U' R' U R2 U Rw U R Rw' U' Rw' U' Rw U Rw U' Rw' U' R Rw' U Rw

I think you can understand how I created that^ :p
 

cubizh

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W Perm


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

New algs (Jan 2nd):

R2 U' R' U' R U2 Rw U R Rw' U' Rw' U' Rw U Rw U' Rw' U' R Rw' U R Rw
Rw R U Rw' R U' Rw' U' Rw U Rw U' Rw' U' Rw' R U Rw U2 R U' R' U' R2
 
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Robert-Y

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^I just want to say, I forgot to tell cubizh to search in qtm, so that's why these algs are long. He'll research this case again in qtm, hopefully there'll be better algs :p
 

cubizh

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Just a small update on this O perm, since it's taking a very long time:


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

More algs found (Jan 2nd):

R2 U' Rw U Rw2 U R2 U' Rw2 U' Rw' U' Rw2 U' Rw2 U' R2 U R2 Rw2 U R2 Rw2
R2 U' Rw' U Rw2 U R2 U' Rw2 U' Rw U' Rw2 U' Rw2 U' R2 U R2 Rw2 U R2 Rw2
R2 U' R' U' R U R U R2 Rw2 U2 Rw U2 Rw2 U2 Rw2 U2 Rw U2 R' Rw2 U' R
R2 U' R' U' R U R U R2 Rw2 U2 Rw' U2 Rw2 U2 Rw2 U2 Rw' U2 R' Rw2 U' R
R2 U' R' U' R2 U R2 Rw2 U2 Rw U2 Rw2 U2 Rw2 U2 Rw U2 R' Rw2 U R U2 R
R2 U' R' U' R2 U R2 Rw2 U2 Rw' U2 Rw2 U2 Rw2 U2 Rw' U2 R' Rw2 U R U2 R
 
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Robert-Y

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(Rw' R2 U' R' U R' Rw U' R U2' R' U' R' Rw U R Rw' U' Rw' F Rw2 U' Rw' U') (Rw U Rw' F')

Breakdown:
3 wing cycle: (Rw' R2 U' R' U R' Rw U' R U R')
Another 3 wing cycle: (R U R' U' R' Rw U R U' Rw')
Wide T perm: (Rw U Rw' U' Rw' F Rw2 U' Rw' U' Rw U Rw' F')
6 moves cancelled.

I know it's not <Rw,R,U>, but I thought it was worth sharing anyway :)
 

cubizh

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Algs for the other O perm (clockwise)
Seem pretty terrible but it's short I suppose.


Rw' U Rw U R' Rw U' Rw' U R' U' R' U' R2 U Rw' U' R' Rw U R Rw U R' Rw'

(UPDATED: Jan 3rd)

R' Rw' U R Rw U R' Rw U' Rw' U R2 U' R' U' R' U Rw' U' R' Rw U Rw U Rw'
 
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