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4x4x4 edge parity - is there a shorter alg that doesn't preserve corners?

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Kabuthunk
Thread starter #1
Whup, for the title, I meant to put edge-pair locations, not corners... since the parity can be spotted before even starting corners (I'm still doing a beginner method that does corners last).

Ok, first up, I'm still fairly new to cubing, and albeit I wouldn't mind going faster, I'm not currently at the point of wanting to memorize a metric ton of algorithms. Or more specifically, that 15-move algorithm for fixing the parity on a 4x4x4 when one edge pair is flipped over. As of right now, I can solve all other situations (like two corners switched), but that double edge flip I just can't get down. And every single site I've seen only has the algorithm that just... solves the cube from there with the 15 moves. I need less moves, and then I can re-solve the edges and corners later.

Thus... is there a shorter algorithm that will flip that edge, not bothering to preserve corner placements or even edge placements (so long as it doesn't create another edge pair parity :p)? I've read here and there online that apparently the two-corner-switched algorithm (which was ridiculously easy to memorize thankfully) can be used to fixed the edge-pair-flip as well, but try it as I might, once I do the two-corner algorithm and re-place all the corners, that damn edge-pair parity just comes right back again.


Any help someone could toss me... or maybe if I'm just doing the two-corner algorithm wrong (I've been trying it with the two flipped corners facing me... it's the r2 U2 r2 U2 u2 r2 u2 algorithm I learned).

As well, I also bought a 5x5x5 on boxing week sale, so if there's a shorter non-corner-preserving, non-edge-triplet-location-preserving solution for that checkerboard pattern that can come up on one edge, that'd be awesome too.
 
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Kabuthunk
Thread starter #3
That's even more turns and memorization than the 15-move algorithm :p. I'm still a beginner, and not good with memorizing big algorithms here :(.

Long-winded is the way I want to figure out, at the bare minimum so I can at least do a 4x4x4 without having to pull that piece of paper with the giant algorithm out of my wallet where it currently resides.

Aaaand unfortunately my terminology isn't the greatest yet either, so I'm not sure what you mean by slice turn, nor do I know how to fix the centers without destroying... well... the rest of the cube in general.
 
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CubeDepot
#5
That's even more turns and memorization than the 15-move algorithm :p. I'm still a beginner, and not good with memorizing big algorithms here :(.

Long-winded is the way I want to figure out, at the bare minimum so I can at least do a 4x4x4 without having to pull that piece of paper with the giant algorithm out of my wallet where it currently resides.

Aaaand unfortunately my terminology isn't the greatest yet either, so I'm not sure what you mean by slice turn, nor do I know how to fix the centers without destroying... well... the rest of the cube in general.
Did you try Dene's algorithm at all? It is extremely finger tricky, and incredibly fast.
 
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FruityDawn
#7
That's even more turns and memorization than the 15-move algorithm :p. I'm still a beginner, and not good with memorizing big algorithms here :(.

Long-winded is the way I want to figure out, at the bare minimum so I can at least do a 4x4x4 without having to pull that piece of paper with the giant algorithm out of my wallet where it currently resides.

Aaaand unfortunately my terminology isn't the greatest yet either, so I'm not sure what you mean by slice turn, nor do I know how to fix the centers without destroying... well... the rest of the cube in general.
It's really easy to remember and fast if you split it up like this and remember in parts

(Rr) U2 x
(Rr) U2 (Rr) U2
(Rr)' U2 (Ll) U2
(Rr)' U2 (Rr) U2
(Rr')' U2 (Rr)'

Don't be afraid to take a while to remember all the parts I learnt a chuck or two eacy day before going to bed.
This is also how I remembered the ugly one before Thrawst showed me this one in his 4x4 tips video.
 
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#9
r2 B2 U2 l U2 r' U2 r U2 F2 r F2 l' B2 r2

man up and learn it.
you only need this and one other alg for 4x4, and you only need that for 5x5
This. It's really not hard to learn and if I'm not mistaken, doing it from a solved state and then immediately doing it again brings your cube back to a solved state. Therefore you don't even need to be doing a solve. Just do the alg over and over again from a solved state of the cube. Also, start saying it outloud as you're doing it. Once you recognize the pattern and start watching the cube to see how things move as you do the algorithm it really does start to come naturally. You can get it, I'm confident. When I first started I too was convinced that I would never be able to learn this algorithm, now, I run it in my sleep.

Also, like stated above, once you learn this alg. you've pretty much learned to solve a 5x5 so it is well worth it.
 
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JonnyEspinoza3
#10
It's not hard to memorize the long algorithm.
all you need to do is break it into parts like darkerarceus was saying.
lets say you're trying to memorize "(Rr)2 B2 U2 (Ll) U2 (Rr)' U2 (Rr) U2 F2 (Rr) F2 (Ll)' B2 (Rr)2"
then just break it down into sequences:
opening sequence - (Rr)2 B2
"U2" sequence - U2 (Ll) U2 (Rr)' U2 (Rr) U2
"F2" sequence - F2 (Rr) F2 (Ll)'
closing sequence - B2 (Rr)2
 
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4EverTrying
#11
It's not hard to memorize the long algorithm.
all you need to do is break it into parts like darkerarceus was saying.
lets say you're trying to memorize "(Rr)2 B2 U2 (Ll) U2 (Rr)' U2 (Rr) U2 F2 (Rr) F2 (Ll)' B2 (Rr)2"
then just break it down into sequences:
opening sequence - (Rr)2 B2
"U2" sequence - U2 (Ll) U2 (Rr)' U2 (Rr) U2
"F2" sequence - F2 (Rr) F2 (Ll)'
closing sequence - B2 (Rr)2
To help myself memorize that algorithm, I drew a picture. I guess whatever works for the individual.
 

Godmil

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Godmil
#13
I learned one from Waffles video that I thought was super easy to memorise (think it's the inverse of one listed above): r U2 r U2 r' U2 r U2 l' U2 r U2 r' U2 x' r' U2 r'
So it's just a r/l move followed by a U2 every time... if you don't write the U2's you've just got: r r r' r l' r r' x'+r' r'
note: if you turn just the inner slices you'll flip just the two edges, but if you do wide turns (which I find faster) then it flips the edges and neighbouring corners, but I do it before the OLL so that doesn't bother me at all.
 
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FruityDawn
#14
It's not hard to memorize the long algorithm.
all you need to do is break it into parts like darkerarceus was saying.
lets say you're trying to memorize "(Rr)2 B2 U2 (Ll) U2 (Rr)' U2 (Rr) U2 F2 (Rr) F2 (Ll)' B2 (Rr)2"
then just break it down into sequences:
opening sequence - (Rr)2 B2
"U2" sequence - U2 (Ll) U2 (Rr)' U2 (Rr) U2
"F2" sequence - F2 (Rr) F2 (Ll)'
closing sequence - B2 (Rr)2
That's how I remembered it except the U2 (Ll) was moved to the opening sequence for me!
 
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4EverTrying
#15
I constructed a 13 move algorithm that requires you to swap two adjacent faces after you finish executing it (which you should already know how to do if you can solve a big cube). Hence, technically only 13 moves need to be memorized.

Rw2 U2 Lw' U2 Rw U2 Rw' U2 Rw U2 Rw' x' U2 Rw2 (13)
And if we add on the piece to swap two adjacent faces,
Rw U2 Rw'
Lw' U2 Lw


, we have a 17 move algorithm (with canceling/merging moves):
Rw2 U2 Lw' U2 Rw U2 Rw' U2 Rw U2 Rw' x' U2 Rw' U2 Rw2 F2 Rw (17)


For puzzle theorists like myself, I here is the technical representation of this algorithm in single slice turns:
r2 U2 x r' U2 r U2 r' U2 r U2 r' x' U2 r2 r U2 r' l' U2 l
= [r2 U2 x: [r' U2 r, U2] (r') ] r U2 r' l' U2 l
, where the parenthesized move is the extra quarter turn.
 
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cuBerBruce
#16
Thus... is there a shorter algorithm that will flip that edge, not bothering to preserve corner placements or even edge placements (so long as it doesn't create another edge pair parity :p)?
You're going to save, like, an absolute maximum of 3-4 moves by doing this. Just learn the normal alg and don't waste the extra recognition time.
I have been somewhat curious to find out exactly how many moves (block turns) are actually required to fix OLL parity on the 4x4x4. So I've now done my own analysis, and I have believe I have exhaustively checked up to a depth of 12 block turns, and determined there is no OLL parity fix that preserves pairing of edges and correctly solved centers (but not necessarily for a supercube) up to that depth.

The standard OLL parity fix and double parity fix algs are 15 block turns. That means you can not save more than two moves if you don't care about the effects on corners and don't care about preserving edge permutation (only preserving their being paired).

I have now also found algs of 13 block turns that fix OLL parity as well as double parity (and preserves pairing of edges and solved centers). So these algs are optimal in block turns for these parity cases.

For OLL parity (only), one such alg is:

Uw B' L2 B Uw B2 Uw R2 Uw R F2 R' Uw

For double parity, one such alg is:

Rw2 B2 r' U2 Rw2 B R' B U' Rw B2 U2 Rw

There may be many other optimal algs. Most likely there exist other optimal algs that are better than these examples in terms of ease of execution or how much of the cube is preserved.
 
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4EverTrying
#17
For OLL parity (only), one such alg is:

Uw B' L2 B Uw B2 Uw R2 Uw R F2 R' Uw

For double parity, one such alg is:

Rw2 B2 r' U2 Rw2 B R' B U' Rw B2 U2 Rw

There may be many other optimal algs. Most likely there exist other optimal algs that are better than these examples in terms of ease of execution or how much of the cube is preserved.
Very impressive. I will try to find some time to decompose these algorithms and see if there are better alternatives (at least for the OLL parity (only) alg).
 
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4EverTrying
#18
Just for the OLL parity (only) algorithm, it's a non-symmetrical 6-cycle algorithm (not my strong point), so I don't know how much I can break it down as of yet (don't count on it). However, here is a different translation of it so that it can successfully be applied to a 5x5x5 as well:

On the 4x4x4,
z Rw B' U2 B Rw B2 Lw B2 Rw B D2 B' Rw z' y
On the 5x5x5,
z Rw B' U2 B Rw B2 Lw B2 Rw B D2 B' Rw z' y

In addition, this translation proves that the parity correction of this algorithm is single slice turned based (I wasn't sure before), as we can now use only single slice turns (but much less is preserved, as far as the bandaged 3x3x3 is concerned).
z r B' U2 B r B2 l B2 r B D2 B' r z' y

This really reminds me of the algorithm I finally concluded the "Wanted New Dedge Flip Algorithm" thread with, because it is not a 2-cycle either (it's a 2x2 cycle and a 4-cycle), and it doesn't really depend on the wide turns it has (they only help to preserve more of the puzzle than if it was all single slice turns).
l U2 l' F U R U' Lw' D2 r D2 r U2 Rw' U2 Lw F


Anyway, since cuBerBruce's algorithm is a 6-cycle, then we should compare it to a normal dedge-preserving 6-cycle such as:
r' U2 r U2 r U2 r2 F2 r' U2 r' U2 F2 r2 (14)
I am not positive this is the optimal algorithm for the regular move set, but if it is, then cuBerBruce's algorithm is definitely a major breakthrough for block half turns! (Of course, his quarter turn move count is superior, at a mere 17!)
 

Ton

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tonixcube
#19
Someone correct me if I'm wrong, but my understanding of OLL parity is that you have an uneven slice, so simply do a slice turn and then fix centres it should be all good. Of course that is going to be a long-winded way.
Correct , this was the first algorithm I used to solve the parity . But from this -so first move an inner slice-, using this first move I used a kind of fewest moves method to find a shorted algorithm (that was in 1986) to prevent mixing the cube to much
It will take about 30 to 35 (intuitive)moves to get a 6 cycle of edges so the corner remain in place....

So all it will take is 1 move and rebuild the centres in a specific order to get a 6 cycle
 
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cuBerBruce
#20
For whatever it's worth, I have now determined "all" optimal reduction OLL parity fixes (in block turns). Of course, by this I'm referring to algs that will convert a reduction state with odd OLL parity to a reduction state with even OLL parity. I used a bidirectional breadth-first search to find these maneuvers.

My search found 12 positions at a depth of 6 block turns that were 1 move away from position(s) of depth 6 block turns of the opposite search tree (which is really the same tree except positions have opposite edge parity from the other tree). A position, as I am using the term here, only cares about centers, where pairs of edge pieces are located (without otherwise caring which edge piece is which), and the edge parity. It also treats symmetrically equivalent positions as the same.

I then used an IDA* depth-first search to find optimal algs for these positions, and from there generated the length-13 maneuvers corresponding to the optimal OLL parity fixes (from a reduction state to a reduction state).

To reduce the amount of text to show the various optimal maneuvers, I've done the following things. (See spoiler below.)

Instead of listing out each maneuver in full, I list the first 7 moves and the last 6 moves separately. These starting and ending maneuvers are grouped, so for instance there might be 3 "starting" maneuvers followed by 9 "ending" maneuvers. Any of the three starting maneuvers can be combined with any of those 9 ending maneuvers. So these really represent 27 maneuvers in all.

A wide turn such as Uw could be replaced by a wide turn on the opposite side (Dw, in this case) if the rest of the alg is converted appropriately. I only use the U face for the wide turns in the algs. (Wide turns on F/B and L/R axes were not needed.)

I also only show a wide turn for the first move of each starting maneuver, and only a wide turn for the final move of each ending maneuver. These wide turns could also be an inner layer turn (either inner layer for the same axis). (I note they could also be replaced by a wide turn on the opposite side, but I only considered wide turns on one side for each axis as mentioned above.)

Maneuvers that are symmetrically equivalent are only listed in one form.

See this spoiler for the actual maneuvers. I have arbitrarily assigned letters A-L for the 12 positions mentioned earlier (and A', B', etc. for the corresponding positions in the "ending" search tree.) The maneuvers are grouped according the which of these positions occur in the maneuvers.

A -> A'

Starts:
Uw B' L2 B Uw B2 Uw
Uw B' L2 B u B2 Uw
Endings:
R2 Uw R F2 R' Uw
R2 u R F2 R' Uw

Starts:
Uw B' L2 B Uw B2 d
Uw B' L2 B u B2 d
Endings:
B2 Uw B R2 B' Uw
B2 u B R2 B' Uw

A -> K'

Starts:
Uw B' L2 B Uw B2 u
Uw B' L2 B u B2 u
Endings:
R2 Uw R' F2 R Uw
R2 d B' R2 B Uw

B -> C'

Starts:
Uw B L2 B' u B2 Uw
Uw B L2 B' u B2 u
Ending:
R2 d B R2 B' Uw

B -> B'

Start:
Uw B L2 B' u B2 d
Ending:
B2 u B' R2 B Uw

C -> B'

Starts:
Uw R' B2 R d B2 Uw
Uw R' B2 R d B2 u
Ending:
R2 u R' F2 R Uw

D -> D'

Starts:
Uw B2 Uw F2 Uw2 L2 Uw
Uw B2 Uw F2 Uw2 L2 u
Uw B2 u F2 Uw2 L2 Uw
Uw B2 u F2 Uw2 L2 u
Uw R2 d F2 Uw2 L2 Uw
Uw R2 d F2 Uw2 L2 u
Uw B2 Uw F2 u2 L2 Uw
Uw B2 Uw F2 u2 L2 u
Uw B2 u F2 u2 L2 Uw
Uw B2 u F2 u2 L2 u
Uw R2 d F2 u2 L2 Uw
Uw R2 d F2 u2 L2 u
Uw F2 Uw B2 d2 L2 Uw
Uw F2 Uw B2 d2 L2 u
Uw F2 u B2 d2 L2 Uw
Uw F2 u B2 d2 L2 u
Uw L2 d B2 d2 L2 Uw
Uw L2 d B2 d2 L2 u
Endings:
F2 Uw2 L2 Uw R2 Uw
F2 Uw2 L2 u R2 Uw
F2 Uw2 L2 d B2 Uw
F2 u2 L2 Uw R2 Uw
F2 u2 L2 u R2 Uw
F2 u2 L2 d B2 Uw
F2 d2 R2 Uw L2 Uw
F2 d2 R2 u L2 Uw
F2 d2 R2 d F2 Uw

Starts:
Uw B2 Uw F2 Uw2 L2 d
Uw B2 u F2 Uw2 L2 d
Uw R2 d F2 Uw2 L2 d
Uw B2 Uw F2 u2 L2 d
Uw B2 u F2 u2 L2 d
Uw R2 d F2 u2 L2 d
Uw F2 Uw B2 d2 L2 d
Uw F2 u B2 d2 L2 d
Uw L2 d B2 d2 L2 d
Endings:
R2 Uw2 F2 Uw B2 Uw
R2 Uw2 F2 u B2 Uw
R2 Uw2 F2 d L2 Uw
R2 u2 F2 Uw B2 Uw
R2 u2 F2 u B2 Uw
R2 u2 F2 d L2 Uw
R2 d2 B2 Uw F2 Uw
R2 d2 B2 u F2 Uw
R2 d2 B2 d R2 Uw

D -> L'

Starts:
Uw B2 Uw F2 Uw2 L2 Uw'
Uw B2 Uw F2 Uw2 L2 u'
Uw B2 u F2 Uw2 L2 Uw'
Uw B2 u F2 Uw2 L2 u'
Uw R2 d F2 Uw2 L2 Uw'
Uw R2 d F2 Uw2 L2 u'
Uw B2 Uw F2 u2 L2 Uw'
Uw B2 Uw F2 u2 L2 u'
Uw B2 u F2 u2 L2 Uw'
Uw B2 u F2 u2 L2 u'
Uw R2 d F2 u2 L2 Uw'
Uw R2 d F2 u2 L2 u'
Uw F2 Uw B2 d2 L2 Uw'
Uw F2 Uw B2 d2 L2 u'
Uw F2 u B2 d2 L2 Uw'
Uw F2 u B2 d2 L2 u'
Uw L2 d B2 d2 L2 Uw'
Uw L2 d B2 d2 L2 u'
Endings:
L2 Uw2 F2 Uw' R2 Uw
L2 Uw2 F2 u' R2 Uw
L2 Uw2 F2 d' F2 Uw
L2 u2 F2 Uw' R2 Uw
L2 u2 F2 u' R2 Uw
L2 u2 F2 d' F2 Uw
L2 d2 B2 Uw' L2 Uw
L2 d2 B2 u' L2 Uw
L2 d2 B2 d' B2 Uw

Starts:
Uw B2 Uw F2 Uw2 L2 d'
Uw B2 u F2 Uw2 L2 d'
Uw R2 d F2 Uw2 L2 d'
Uw B2 Uw F2 u2 L2 d'
Uw B2 u F2 u2 L2 d'
Uw R2 d F2 u2 L2 d'
Uw F2 Uw B2 d2 L2 d'
Uw F2 u B2 d2 L2 d'
Uw L2 d B2 d2 L2 d'
Endings:
B2 Uw2 L2 Uw' F2 Uw
B2 Uw2 L2 u' F2 Uw
B2 Uw2 L2 d' L2 Uw
B2 u2 L2 Uw' F2 Uw
B2 u2 L2 u' F2 Uw
B2 u2 L2 d' L2 Uw
B2 d2 R2 Uw' B2 Uw
B2 d2 R2 u' B2 Uw
B2 d2 R2 d' R2 Uw

E -> F'

Starts:
Uw' R2 Uw F2 Uw R2 Uw'
Uw' R2 Uw F2 Uw R2 u'
Uw' R2 u F2 Uw R2 Uw'
Uw' R2 u F2 Uw R2 u'
Uw' F2 d F2 Uw R2 Uw'
Uw' F2 d F2 Uw R2 u'
Uw' R2 Uw F2 u R2 Uw'
Uw' R2 Uw F2 u R2 u'
Uw' R2 u F2 u R2 Uw'
Uw' R2 u F2 u R2 u'
Uw' F2 d F2 u R2 Uw'
Uw' F2 d F2 u R2 u'
Uw' F2 Uw L2 d R2 Uw'
Uw' F2 Uw L2 d R2 u'
Uw' F2 u L2 d R2 Uw'
Uw' F2 u L2 d R2 u'
Uw' L2 d L2 d R2 Uw'
Uw' L2 d L2 d R2 u'
Endings:
B2 Uw B2 Uw' L2 Uw
B2 Uw B2 u' L2 Uw
B2 Uw B2 d' B2 Uw
B2 u B2 Uw' L2 Uw
B2 u B2 u' L2 Uw
B2 u B2 d' B2 Uw
B2 d L2 Uw' F2 Uw
B2 d L2 u' F2 Uw
B2 d L2 d' L2 Uw

Starts:
Uw' R2 Uw F2 Uw R2 d'
Uw' R2 u F2 Uw R2 d'
Uw' F2 d F2 Uw R2 d'
Uw' R2 Uw F2 u R2 d'
Uw' R2 u F2 u R2 d'
Uw' F2 d F2 u R2 d'
Uw' F2 Uw L2 d R2 d'
Uw' F2 u L2 d R2 d'
Uw' L2 d L2 d R2 d'
Endings:
R2 Uw R2 Uw' B2 Uw
R2 Uw R2 u' B2 Uw
R2 Uw R2 d' R2 Uw
R2 u R2 Uw' B2 Uw
R2 u R2 u' B2 Uw
R2 u R2 d' R2 Uw
R2 d B2 Uw' L2 Uw
R2 d B2 u' L2 Uw
R2 d B2 d' B2 Uw

F -> E'

Starts:
Uw F2 Uw' R2 Uw R2 Uw'
Uw F2 Uw' R2 Uw R2 u'
Uw F2 u' R2 Uw R2 Uw'
Uw F2 u' R2 Uw R2 u'
Uw R2 d' R2 Uw R2 Uw'
Uw R2 d' R2 Uw R2 u'
Uw F2 Uw' R2 u R2 Uw'
Uw F2 Uw' R2 u R2 u'
Uw F2 u' R2 u R2 Uw'
Uw F2 u' R2 u R2 u'
Uw R2 d' R2 u R2 Uw'
Uw R2 d' R2 u R2 u'
Uw L2 Uw' F2 d R2 Uw'
Uw L2 Uw' F2 d R2 u'
Uw L2 u' F2 d R2 Uw'
Uw L2 u' F2 d R2 u'
Uw F2 d' F2 d R2 Uw'
Uw F2 d' F2 d R2 u'
Endings:
B2 Uw L2 Uw B2 Uw'
B2 Uw L2 u B2 Uw'
B2 Uw L2 d L2 Uw'
B2 u L2 Uw B2 Uw'
B2 u L2 u B2 Uw'
B2 u L2 d L2 Uw'
B2 d F2 Uw L2 Uw'
B2 d F2 u L2 Uw'
B2 d F2 d F2 Uw'

Starts:
Uw F2 Uw' R2 Uw R2 d'
Uw F2 u' R2 Uw R2 d'
Uw R2 d' R2 Uw R2 d'
Uw F2 Uw' R2 u R2 d'
Uw F2 u' R2 u R2 d'
Uw R2 d' R2 u R2 d'
Uw L2 Uw' F2 d R2 d'
Uw L2 u' F2 d R2 d'
Uw F2 d' F2 d R2 d'
Endings:
R2 Uw B2 Uw R2 Uw'
R2 Uw B2 u R2 Uw'
R2 Uw B2 d B2 Uw'
R2 u B2 Uw R2 Uw'
R2 u B2 u R2 Uw'
R2 u B2 d B2 Uw'
R2 d L2 Uw B2 Uw'
R2 d L2 u B2 Uw'
R2 d L2 d L2 Uw'

G -> J'

Starts:
Uw F2 L2 Uw L B' U
Uw F2 L2 u L B' U
Uw L2 B2 d L B' U
Endings:
B' Uw2 R2 Uw' R2 Uw2
B' Uw2 R2 u' R2 Uw2
B' Uw2 R2 d' F2 Uw2
B' u2 R2 Uw' R2 Uw2
B' u2 R2 u' R2 Uw2
B' u2 R2 d' F2 Uw2
B' d2 L2 Uw' L2 Uw2
B' d2 L2 u' L2 Uw2
B' d2 L2 d' B2 Uw2

Starts:
Uw F2 L2 Uw L B' u'd
Uw F2 L2 u L B' u'd
Uw L2 B2 d L B' u'd
Endings:
L' Uw2 B2 Uw' B2 Uw2
L' Uw2 B2 u' B2 Uw2
L' Uw2 B2 d' R2 Uw2
L' u2 B2 Uw' B2 Uw2
L' u2 B2 u' B2 Uw2
L' u2 B2 d' R2 Uw2
L' d2 F2 Uw' F2 Uw2
L' d2 F2 u' F2 Uw2
L' d2 F2 d' L2 Uw2

H -> I'

Starts:
Uw F2 L2 Uw L' B D'
Uw F2 L2 u L' B D'
Uw L2 B2 d L' B D'
Endings:
B Uw2 R2 Uw' R2 Uw2
B Uw2 R2 u' R2 Uw2
B Uw2 R2 d' F2 Uw2
B u2 R2 Uw' R2 Uw2
B u2 R2 u' R2 Uw2
B u2 R2 d' F2 Uw2
B d2 L2 Uw' L2 Uw2
B d2 L2 u' L2 Uw2
B d2 L2 d' B2 Uw2

Starts:
Uw F2 L2 Uw L' B u'd
Uw F2 L2 u L' B u'd
Uw L2 B2 d L' B u'd
Endings:
L Uw2 B2 Uw' B2 Uw2
L Uw2 B2 u' B2 Uw2
L Uw2 B2 d' R2 Uw2
L u2 B2 Uw' B2 Uw2
L u2 B2 u' B2 Uw2
L u2 B2 d' R2 Uw2
L d2 F2 Uw' F2 Uw2
L d2 F2 u' F2 Uw2
L d2 F2 d' L2 Uw2

I -> H'

Starts:
Uw2 R2 Uw R2 Uw2 B' D
Uw2 R2 u R2 Uw2 B' D
Uw2 F2 d R2 Uw2 B' D
Uw2 R2 Uw R2 u2 B' D
Uw2 R2 u R2 u2 B' D
Uw2 F2 d R2 u2 B' D
Uw2 L2 Uw L2 d2 B' D
Uw2 L2 u L2 d2 B' D
Uw2 B2 d L2 d2 B' D
Endings:
B' L Uw' L2 F2 Uw'
B' L u' L2 F2 Uw'
B' L d' B2 L2 Uw'

Starts:
Uw2 R2 Uw R2 Uw2 B' ud'
Uw2 R2 u R2 Uw2 B' ud'
Uw2 F2 d R2 Uw2 B' ud'
Uw2 R2 Uw R2 u2 B' ud'
Uw2 R2 u R2 u2 B' ud'
Uw2 F2 d R2 u2 B' ud'
Uw2 L2 Uw L2 d2 B' ud'
Uw2 L2 u L2 d2 B' ud'
Uw2 B2 d L2 d2 B' ud'
Endings:
R' B Uw' B2 L2 Uw'
R' B u' B2 L2 Uw'
R' B d' R2 B2 Uw'

J -> G'

Starts:
Uw2 R2 Uw R2 Uw2 B U'
Uw2 R2 u R2 Uw2 B U'
Uw2 F2 d R2 Uw2 B U'
Uw2 R2 Uw R2 u2 B U'
Uw2 R2 u R2 u2 B U'
Uw2 F2 d R2 u2 B U'
Uw2 L2 Uw L2 d2 B U'
Uw2 L2 u L2 d2 B U'
Uw2 B2 d L2 d2 B U'
Endings:
B L' Uw' L2 F2 Uw'
B L' u' L2 F2 Uw'
B L' d' B2 L2 Uw'

Starts:
Uw2 R2 Uw R2 Uw2 B ud'
Uw2 R2 u R2 Uw2 B ud'
Uw2 F2 d R2 Uw2 B ud'
Uw2 R2 Uw R2 u2 B ud'
Uw2 R2 u R2 u2 B ud'
Uw2 F2 d R2 u2 B ud'
Uw2 L2 Uw L2 d2 B ud'
Uw2 L2 u L2 d2 B ud'
Uw2 B2 d L2 d2 B ud'
Endings:
R B' Uw' B2 L2 Uw'
R B' u' B2 L2 Uw'
R B' d' R2 B2 Uw'

K -> A'

Starts:
Uw' R' F2 R Uw' R2 u'
Uw' B' R2 B d' R2 u'
Endings:
B2 Uw' B' L2 B Uw'
B2 u' B' L2 B Uw'

L-> D'

Starts:
Uw' R2 Uw F2 Uw2 L2 Uw
Uw' R2 Uw F2 Uw2 L2 u
Uw' R2 u F2 Uw2 L2 Uw
Uw' R2 u F2 Uw2 L2 u
Uw' F2 d F2 Uw2 L2 Uw
Uw' F2 d F2 Uw2 L2 u
Uw' R2 Uw F2 u2 L2 Uw
Uw' R2 Uw F2 u2 L2 u
Uw' R2 u F2 u2 L2 Uw
Uw' R2 u F2 u2 L2 u
Uw' F2 d F2 u2 L2 Uw
Uw' F2 d F2 u2 L2 u
Uw' L2 Uw B2 d2 L2 Uw
Uw' L2 Uw B2 d2 L2 u
Uw' L2 u B2 d2 L2 Uw
Uw' L2 u B2 d2 L2 u
Uw' B2 d B2 d2 L2 Uw
Uw' B2 d B2 d2 L2 u
Endings:
L2 Uw2 F2 Uw' B2 Uw'
L2 Uw2 F2 u' B2 Uw'
L2 Uw2 F2 d' R2 Uw'
L2 u2 F2 Uw' B2 Uw'
L2 u2 F2 u' B2 Uw'
L2 u2 F2 d' R2 Uw'
L2 d2 B2 Uw' F2 Uw'
L2 d2 B2 u' F2 Uw'
L2 d2 B2 d' L2 Uw'

Starts:
Uw' R2 Uw F2 Uw2 L2 d
Uw' R2 u F2 Uw2 L2 d
Uw' F2 d F2 Uw2 L2 d
Uw' R2 Uw F2 u2 L2 d
Uw' R2 u F2 u2 L2 d
Uw' F2 d F2 u2 L2 d
Uw' L2 Uw B2 d2 L2 d
Uw' L2 u B2 d2 L2 d
Uw' B2 d B2 d2 L2 d
Endings:
F2 Uw2 R2 Uw' L2 Uw'
F2 Uw2 R2 u' L2 Uw'
F2 Uw2 R2 d' B2 Uw'
F2 u2 R2 Uw' L2 Uw'
F2 u2 R2 u' L2 Uw'
F2 u2 R2 d' B2 Uw'
F2 d2 L2 Uw' R2 Uw'
F2 d2 L2 u' R2 Uw'
F2 d2 L2 d' F2 Uw'

L -> L'

Starts:
Uw' R2 Uw F2 Uw2 L2 Uw'
Uw' R2 Uw F2 Uw2 L2 u'
Uw' R2 u F2 Uw2 L2 Uw'
Uw' R2 u F2 Uw2 L2 u'
Uw' F2 d F2 Uw2 L2 Uw'
Uw' F2 d F2 Uw2 L2 u'
Uw' R2 Uw F2 u2 L2 Uw'
Uw' R2 Uw F2 u2 L2 u'
Uw' R2 u F2 u2 L2 Uw'
Uw' R2 u F2 u2 L2 u'
Uw' F2 d F2 u2 L2 Uw'
Uw' F2 d F2 u2 L2 u'
Uw' L2 Uw B2 d2 L2 Uw'
Uw' L2 Uw B2 d2 L2 u'
Uw' L2 u B2 d2 L2 Uw'
Uw' L2 u B2 d2 L2 u'
Uw' B2 d B2 d2 L2 Uw'
Uw' B2 d B2 d2 L2 u'
Endings:
F2 Uw2 L2 Uw B2 Uw'
F2 Uw2 L2 u B2 Uw'
F2 Uw2 L2 d L2 Uw'
F2 u2 L2 Uw B2 Uw'
F2 u2 L2 u B2 Uw'
F2 u2 L2 d L2 Uw'
F2 d2 R2 Uw F2 Uw'
F2 d2 R2 u F2 Uw'
F2 d2 R2 d R2 Uw'

Starts:
Uw' R2 Uw F2 Uw2 L2 d'
Uw' R2 u F2 Uw2 L2 d'
Uw' F2 d F2 Uw2 L2 d'
Uw' R2 Uw F2 u2 L2 d'
Uw' R2 u F2 u2 L2 d'
Uw' F2 d F2 u2 L2 d'
Uw' L2 Uw B2 d2 L2 d'
Uw' L2 u B2 d2 L2 d'
Uw' B2 d B2 d2 L2 d'
Endings:
L2 Uw2 B2 Uw R2 Uw'
L2 Uw2 B2 u R2 Uw'
L2 Uw2 B2 d B2 Uw'
L2 u2 B2 Uw R2 Uw'
L2 u2 B2 u R2 Uw'
L2 u2 B2 d B2 Uw'
L2 d2 F2 Uw L2 Uw'
L2 d2 F2 u L2 Uw'
L2 d2 F2 d F2 Uw'
 
Last edited:
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