# God's algorithm discovered for OLL parity edge flip (theory)



## dacubeful1 (Jan 8, 2011)

Watch - 




Edit: I cannot take credit for this video, check out Christopher Mowla's youtube account, www.youtube.com/user/4evertrying ... he's got alot of great material there..


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## y3k9 (Jan 8, 2011)

If it really is God's algorithm for oll, let's call it the "dacube's god algorithm".


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## cmhardw (Jan 8, 2011)

y3k9 said:


> If it really is God's algorithm for oll, let's call it the "*cmowla*'s god algorithm".


 
Fixed.


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## daniel0731ex (Jan 8, 2011)

I don't get it.


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## musicninja17 (Jan 8, 2011)

seconded....i also don't understand this....could somebody provide an explanation?


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## Rpotts (Jan 8, 2011)

I stopped watching when I saw the bible quote and 8 minute+ length.


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## dacubeful1 (Jan 10, 2011)

For those having trouble understanding how awesome this algorithms is, here's the video description that comes along with the video:

This is a pure edge flip algorithm which is unlike any other seen before in cubing history. In fact, it is the shortest of its kind (according to my findings).

According to my (Christopher Mowla's) theory and experience, this algorithm is in fact God's Algorithm (the briefest algorithm path) for the pure edge flip as far as quarter turn move count is concerned. In addition, this algorithm has the lowest average of half turn and quarter turn moves as well.

In fact, copy the line below:
floor(n/2)/(2-2^floor(n/2))+19.5
and paste it in the search bar at the following mathematics website, Wolfram Alpha:
http://www57.wolframalpha.com/

To calculate the average for a cube of any size (as long as the size is not too large for Wolfram Alpha to Compute), just delete the two n's and replace them with the same integer 4 or greater to represent a big cube size.


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## blade740 (Jan 10, 2011)

I hate to criticize wording, but I don't believe this algorithm has been proven to be optimal. I think it's a bit presumptuous to call it "God's Algorithm" if we haven't proven it to be.


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## Christopher Mowla (Jan 10, 2011)

Yeah, mathematically speaking, my algorithm is the shortest path that currently exists. Even in plane quarter turns (qtm), it is less than other algorithms for some cases.

The Holy Grail" is 24 qtm for cases like:









, where consecutive edge pieces from the corners to the middle need to be swapped. (It is 26 qtm for the rest of the cases).

As a comparison, a famous speedsolving algorithm is "Lucasparity". Even if the maximum number of turns are made wide, this algorithm is still 30 qtm for all cases:
Rw U2 Rw U2 r' U2 r U2 l' U2 l x U2 r' U2 x' Rw' U2 Rw'
and so is the "Standard Algorithm"
Rw2 B2 U2 l U2 r' U2 r U2 F2 r F2 l' B2 Rw2

And my other algorithm,
x' Rw2 U2 (LwM)' U2 r U2 Rw U2 x' U r U' F2 U r' U Rw2 x
is 26 qtm for all cases. But that algorithm has the lowest plane half turns (ftm) than any other algorithm, having 19. Its average between slice half turns and quarter turns is 19.5, which is pretty good. However, as I mentioned at the end of the video, the "Holy Grail" is slightly less than 19.5, even as the cube gets large.


And for those who don't know why the video is 8+ minutes long, realize that I had a brief introduction, followed by illustrating how to apply the algorithm to different size cubes and different cases on those cubes (if they are larger than the 5x5x5) because this algorithm isn't your everyday algorithm which is trivial to apply to a given case, followed by giving the formula for the average.

Also, the Bible quote was a principal that I believed in and followed: I was not trying to push Christianity on anyone. You don't have to believe in God to realize that "keep seeking, and you will find" is a good principal to live by.


EDIT


blade740 said:


> I hate to criticize wording, but I don't believe this algorithm has been proven to be optimal. I think it's a bit presumptuous to call it "God's Algorithm" if we haven't proven it to be.


I never said it was God's Algorithm. I said, "According to my theory" it is. I have many reasons to believe that it is, but I cannot expect those who did not research this particular case to take my word for it.


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## blade740 (Jan 10, 2011)

cmowla said:


> I never said it was God's Algorithm. I said, "According to my theory" it is. I have many reasons to believe that it is, but I cannot expect those who did not research this particular case to take my word for it.


 
I was referring more to the title of this topic than anything you said. I do like the question mark in your signature.


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## MiSenIn (Jan 10, 2011)

exciting!


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## TMOY (Jan 10, 2011)

Is it a big surprise if I tell you that the algs are not pure ? (At least the 4^3 alg, I stopped watching after that. For those who want to know, it does two 2-cycles on centers.)


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## Christopher Mowla (Jan 10, 2011)

Why do you persist?! Because the 4x4x4 is THE ONLY big cube which can actually have a center-preserving odd permutation algorithm, I don't think you should even consider these algorithms to be pure in the sense of center-preservation.  It is their nature to force centers out of place. The way you use the term pure should only apply to even permutation algorithms. One exception (the 4x4x4) to an infinite number of big cubes does not justify that a common term to describe an odd permutation algorithm should change to your definition of pure.

Do we discard an outlier or do we allow an outlier to dominate the general trend?


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## TMOY (Jan 10, 2011)

So the word pure should have different meanings when applied to even and odd permutations ? Yeah, sure it makes a lot of sense, not confusing at all.


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## Christopher Mowla (Jan 10, 2011)

Obviously you know of a much less confusing term to refer to this type of algorithm, or you wouldn't insist I am confusing everyone. I know all kinds of odd permutation algorithms, so be sure to pick a good term (and not a confusing one). Enlighten me. Should we call it a "2-cycle of wings within the same composite edge and 2(n-2) center swapper)?

"Hey everyone, I have made a 2-cycle of wings within the same composite edge and a 2(n-2) center piece swapper, you wanna see?" I bet everyone (this includes those who don't know what a super cube is, those that don't blindsolve, those who have not seen my derivation videos, those who just learned how do solve a big cube, etc.) will immediately assume I mean "the pure edge flip". Oh, that's a lot less confusing to me.

Surely we cannot call it non-pure because this, this, this, and this are all non-pure algorithms to me. Categorizing this in the same category as the others is not only confusing to beginners, but also unpractical.

Even better. Show a beginner this:
"Hey, did you know that this is pure, but this is not"? Without explanation (for example, having a supercube to demonstrate), that person would look at you like you were stupid. So in all honesty, is it really that confusing? No. You only want to win an argument on technicality. That's just about it.

Lastly, let's take a look at the definition of confusing, according to thefreedictionary.com.
"To cause to be unable to think with clarity or act with intelligence or understanding; throw off."

By debating on whether or not an odd permutation algorithm is pure for one and only one cube size, when it has no meaning at all for all other big cube sizes (except for when an even cube is treated like a 4x4x4), you are throwing everyone off of the big picture. That's confusion to me.

Differentiating the visual effect of this from the 4+ or more other types of odd parity algorithms by calling it pure is not in any way confusing. In addition, it is a straight-forward compact expression which everyone understands.


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## TMOY (Jan 10, 2011)

Well, "semi-pure", apparently pure", "visually pure" all sound better to me than just "pure".
And beginners are not idiots you know. Everybody with half a brain is able to understand that an alg can have hidden effects on centers of the same colour. And I don't even need a supercube to show them, trying to apply the alg to a cube a Fw (or something similar) away from solved is convincing enough.


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## Christopher Mowla (Jan 10, 2011)

TMOY said:


> Well, "semi-pure", apparently pure", "visually pure" all *sound better* to me than just "pure".


Sounds wrong\( \ne \)confusing. It sounds wrong to you because YOU have experimented with algorithms. YOU have seen algorithms on supercubes. Those who have not thought about this don't know about it. One cannot know what one did not learn. It has nothing to do with brain capacity, only with information introduced to the brain. I have seen several cubers over the years think that the center commutator swaps two pieces (instead of 3). These people can solve a nxnxn cube, but they don't have a brain? I have never heard of anyone who solves big cubes say that they solved one of the _ of _ solved positions of the big cube. They say, "I have solved this _x_x_ cube in _ amount of time". (Applause please...)

*Even if they know that they have solved one of the _ visually solved states of whatever big cube they solved, they don't tell others that. They say they solved the big cube. Why? Because they _do not want to confuse people_. If someone is interested in knowing the _theory_ behind what they are doing, they can ask.

In short, to be clear to everyone and not just to those who are familiar with the exact effects of algorithms (especially that I put this video on Youtube and anyone can watch it), I will continue to use the terminology I use unless there is a need to explain more. I only have gone on talking this long because you commented on my video. For me, a pure algorithm for just one cube size is worthless to me and to most other people. An algorithm which does not affect anything else visually is all the majority of people need.


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## AvGalen (Jan 10, 2011)

I agree with TMOY. Redefining "pure" is a bad idea. And people that will understand this topic will SURELY have encountered "pure" in the meaning of NOT influencing centers (supercube safe)


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## freshcuber (Jan 10, 2011)

The alg doesn't look very practical for speedsolving but the theory behind it is interesting and that it works on different sized cubes is cool.


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## TMOY (Jan 10, 2011)

freshcuber said:


> The alg doesn't look very practical for speedsolving


 
And thus probbly won't be used by all those lovely beginners who don't need algs to be pure. How sad it is that they don't need them to be optimal either.


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## Johannes91 (Jan 10, 2011)

cmowla said:


> Yeah, mathematically speaking, my algorithm is the shortest path that currently exists.


You're amazing.


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## cmhardw (Jan 10, 2011)

I agree with cmowla. It seems that people are defining "pure" when referred to a parity algorithm as "supercube safe". As Chris said, this is *only* possible on the 4x4x4 supercube. Every other cube size will have other effects on the centers by changing the parity of a wing orbit. If you want proof of this, see my supercube parity states matrix method. It seems pointless to me to talk about whether an algorithm is supercube safe on the 4x4x4 or not. Also, what is the problem of saying that an algorithm is the God's Algorithm (assuming this is proven) for the n x n x n cube, and by that I mean *regular* cube and *not* supercube? It makes perfect sense to me. We don't care about the locations of centers on a regular cube when solving, so why would we start when considering this parity algorithm?

It would be theoretically possible to construct a _minimally destructive_ parity algorithm on any cube size larger than 4x4x4 supercube, but it is *impossible* to have a completely supercube safe parity algorithm on any cube larger than the 4x4x4 supercube. My supercube parity matrix is the proof of this, so read it if you still need to be convinced.

--edit--
Ok looking at the parity states matrix of the even n x n x n cube there is one exception to this. If you change the parity of *every* wing orbit on the even n x n x n supercube, then this will not affect the parities of any of the center orbits. However, since this is just a bandaged 4x4x4 cube, I still think the argument stands that "pure" in the sense of "supercube safe" applies only to the 4x4x4 cube, or changing the parity of every wing orbit on the even n x n x n supercube. This seems like a very clumsy definition to me.


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## Lars (Jan 10, 2011)

this is for Fewest moves, curiosity and mathmatics


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## AvGalen (Jan 10, 2011)

I have read that proof about the specialty of 4x4x4 from you a loooong time ago (5 years?). But "pure" has the properties of "supercube safe, can be used for blindfolded" associated with it. That is the only complaint I have about using that word, not interfering with anything else in this discussion that seems like great work



Lars said:


> this is for Fewest moves, curiosity and mathmatics


 
For Fewest Moves, parity should be avoided in totally different ways. Adding 20 moves for 2 pieces is completely unacceptable.
Curiosity, mathematics and advancing cube theory I totally agree with


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## cmhardw (Jan 10, 2011)

AvGalen said:


> I have read that proof about the specialty of 4x4x4 from you a loooong time ago (5 years?). But "pure" has the properties of *"supercube safe, can be used for blindfolded"* associated with it. That is the only complaint I have about using that word, not interfering with anything else in this discussion that seems like great work


 
I don't know of any "pure" algorithms for the parity of the wings edges then, and I certainly don't use pure algorithms when I solve blindfolded.

The two parity algs I use are:
l' U2 l' U2 F2 l' F2 r U2 r' U2 r2

and the old standard:
r2 B2 U2 l U2 r' U2 r U2 F2 r F2 l' B2 r2

Now I could make these pure on the 4x4x4 by using an alg to rotate one center group 180 degrees, but I could never make a pure alg on the 5x5x5 supercube as that is impossible.

Neither of these algs is pure, yet I still use them for blindfold solving the 4x4x4 and 5x5x5 supercubes. Also, I would argue that not very many of us are crazy enough to solve the larger supercubes blindfolded, and remember that it is *impossible* to have a "pure" parity alg on the odd n x n x n supercube. So for solving the 5x5x5 supercube blindfolded, there does not exist any "pure" alg. You will have to make do with a _minimally destructive_ parity alg, and account for its effects on the cube.

--edit--
Also, it was my understanding that "pure" when applied to a parity alg meant that you were only turning single inner slice turns rather than multi-slice groups. I thought that was all that "pure" meant for a parity alg. Where is it defined in the literature anywhere that "pure" is related to whether or not it is "supercube safe"? I have not seen that before to be honest.


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## ben1996123 (Jan 10, 2011)

Pure alg. Also, I was already watching the video whilst I found this thread. Can't wait for the derivation video


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## TMOY (Jan 10, 2011)

cmhardw said:


> I don't know of any "pure" algorithms for the parity of the wings edges then, and I certainly don't use pure algorithms when I solve blindfolded.


The one I'm using is:
U l U' l' U' l' U l U l' U' l' U' l D x' d2 l' d2 l x U D'
which swaps the UFl and UBl wings and does nothing else on the 4^3. On the 5^3, it also swaps the Ul and Dl +-centers and that's all.
A bit longer than your algs, but it doesn't really matter concerning an alg I only use once every second solve, and the gain of being able to do centers at the end (which I really feel more comfortable with) is much bigger for me.


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## DavidWoner (Jan 11, 2011)

So can we no longer refer to M' U' M' U' M' U' M' U2 M' U' M' U' M' U' M' as a pure 2flip because it rotates centers?


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## TMOY (Jan 11, 2011)

You're missing the point. If you apply your 2-edge flip to a scrambled 3^3, you will always get 2 edges flipped as the only apparent result no matter how you scrambled your cube before. So yes it is pure as a 3^3 alg (but not as a supercube alg of course). This is not true for a dedge flip on the 4^3 which rotates centers.
On a group-theoretical point of view: on the 3^3, the group H of center rotations is a normal subgroup of the group G of permutations of the supercube, hence the quotient G/H, which is the set of permutations of the normal 3^3, has a natural group structure induced from the group structure of G. Unfortunately this doesn't work for big cubes, and we musr consider the full supercube group as the group of permutations of the 4^3.


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## Christopher Mowla (Jan 11, 2011)

TMOY said:


> You're missing the point.


We should ask ourselves why did this intelligent individual miss your point? (Oh, I know exactly why->find the *). I never said my alg was pure for the supercube, but you insisted that it shouldn't be considered a pure algorithm for regular cubes! More importantly, think about the context I was indicating how it was pure...for users who use reduction, k4, or some other method which solves centers to non-supercubes first. (I never said, "Oh and to the blindfold solvers, this algorithm even works if you solve centers last, and to supercube solvers, this algorithm affects the minimal centers on the nxnxn!"). This is probably THE number one reason why I bet most of the people viewing your posts about pure odd permutations algorithms are confused.


TMOY said:


> If you apply your 2-edge flip to a scrambled 3^3, you will always get 2 edges flipped as the only apparent result no matter how you scrambled your cube before.


All those who solve centers first on non-supercubes will say, "And you won't for a 'pure edge flip' for the nxnxn?"

*Most people solve centers first on non-supercubes, so this has absolutely no meaning to the majority of cubers in the world, not even including the supercube in the equation. That IS why my algorithm can be considered "pure" in their eyes because it swaps two wings in the same composite edge "no matter what scrambled state the composite edges and corners were in". This is just as valid reason to consider an algorithm pure as is yours for solving the centers last in 4x4x4 bld because that is the method they use.

*Algorithm Terminology Proposal.*
Instead of saying my algorithm is "visually pure", how about we call your algorithm (and all other algorithms which do not affect centers for any size supercube) "supercube safe" or "supercube pure" and refer to algorithms which are visually pure as pure.

Why? "Majority rules" can have a place here too. Think about the future generation of cubers replacing every description of algorithms (which visually affect only non-center pieces, but affect the centers) with the term "visually pure". Do you know how many fast/short algorithms would need their description enlarged? As a programmer, this is definitely a no no, if I have any hope to same code space. If I can have less code to make sense to the computer, I will use it, as my computer's RAM is limited.




By the way, your supercube pure algorithm for the 4x4x4 is pretty neat.
U l U' l' U' l' U l U l' U' l' U' l D x' d2 l' d2 l x U D' = [U l U' l' U', l'] (l') [l', U'] [U' D: [f2, l']] 

It swaps two wings and permutes 6 X-center pieces (with a 2 3-cycle),
[U l U' l' U', l'] (l') [l', U']
and then restores the 6 X-center pieces with a very brief 2 3-cycle [f2, l']
, whose set-up moves, U' D, (to move all X-center pieces affected into slice 2L) partially cancel with the first piece!


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## TMOY (Jan 11, 2011)

In othr words: most people are clueless, so let's keep them in their cluelessness ? Well, at least they can see how great an opinion you have about them.


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## Christopher Mowla (Jan 11, 2011)

TMOY said:


> In othr words: most people are clueless, so let's keep them in their cluelessness ? Well, at least they can see how great an opinion you have about them.


You missed my point, or you are just being stubborn. I wasn't saying that most people are "clueless", I am saying that I want to save people the trouble of describing something in fewer words than what you are wanting. AND, according to how they solve and what kind of cube they solve, the "fewer words" is a legitimate description of what they are doing.


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## TMOY (Jan 11, 2011)

cmowla said:


> You missed my point


We should ask ourselves why did that intelligent individual miss your point. ,


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## Christopher Mowla (Jan 11, 2011)

TMOY said:


> We should ask ourselves why did that intelligent individual miss your point. ,


Yeah, the intelligent individual failed to read my entire post:


cmowla said:


> Think about the future generation of cubers replacing every description of algorithms (which visually affect only non-center pieces, but affect the centers) with the term "visually pure". Do you know how many fast/short algorithms would need their description enlarged? As a programmer, this is definitely a no no, if I have any hope to same _(I meant to write "save", not "same", but I still think anyone could have guessed that)_ code space. If I can have less code to make sense to the computer, I will use it, as my computer's RAM is limited.


or is purposely being stubborn (which is now definitely more of a possibility).

EDIT:
If you were implying the single sentence I wrote:


cmowla said:


> This is probably THE number one reason why I bet most of the people viewing your posts about pure odd permutations algorithms are confused.


Take note in what David said below this post. I meant they were confused because you are going against common terminology. However unclear that sentence was, there was no legitimate reason to misinterpret what my point:


cmowla said:


> I am saying that I want to save people the trouble of describing something in fewer words than what you are wanting. AND, according to how they solve and what kind of cube they solve, the "fewer words" is a legitimate description of what they are doing.


because of the portion I first pointed out in this post.


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## DavidWoner (Jan 11, 2011)

TMOY said:


> You're missing the point.


 
No, you seem to be missing my point. There's a big difference between what is technically correct and what is the commonly accepted terminology. You're the only one stressing the importance of the first one. We still refer to "PLL Parity" as a parity case, even though it technically isn't. However, _in the context of solving with the reduction method_ it is a parity case. Context is everything regarding terminology in cubing. If you would like to refer to this alg as "visually pure" in the context of 4BLD and supercube solving then you are more than welcome to. However, cmowla's algs have always been (this thread is certainly no exception) in the context of speedsolving all even-ordered bigcubes, therefore drawing a distinction in this case is wholly unnecessary.


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## AvGalen (Jan 12, 2011)

Let's compromise on the following:
pure is badly defined and confusing. So:
cmowla will use visually pure from now on
and tmoy will use supercube safe from now on
Problem solved from now on


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## TMOY (Jan 12, 2011)

DavidWoner said:


> No, you seem to be missing my point. There's a big difference between what is technically correct and what is the commonly accepted terminology. You're the only one stressing the importance of the first one. We still refer to "PLL Parity" as a parity case, even though it technically isn't. However, _in the context of solving with the reduction method_ it is a parity case. Context is everything regarding terminology in cubing. If you would like to refer to this alg as "visually pure" in the context of 4BLD and supercube solving then you are more than welcome to. However, cmowla's algs have always been (this thread is certainly no exception) in the context of speedsolving all even-ordered bigcubes, therefore drawing a distinction in this case is wholly unnecessary.


 
Sorry but your example is a bad example. PLL parity has no meaning outside the context of reduction+Fridrich method, so we can freely use it as a shorthand for "the case which corresponds to the PLL parity case in the reduction+Fridrich method", and its meaning is perfectly clear. This is not the case with "pure". Yes I know pretty well that cmowla is misusing it, but if a random cuber tells me "I've found a pure alg" without context, how am I supposed to tell what he's talking bout without checking his alg ?


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## afrizal (Jan 12, 2011)

i hate big cubes


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## TMOY (Jan 12, 2011)

cmowla said:


> You have been ignoring every post I have been posting.



True


Spoiler



You should do the same with mine. Really.


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## oll+phase+sync (Jan 21, 2011)

would you mid to post the Holy Grail in standard notation - thanks.


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## Christopher Mowla (Jan 22, 2011)

oll+phase+sync said:


> would you mind to post the Holy Grail in standard notation - thanks.


I prefer not to for the 6x6x6 and 7x7x7 (just see the cube applet below for them, play one move at a time, and write it in your own notation).

On the 4x4x4:
z (Dd)' M D *(Ll)'* (Uu)' r' (Uu) *(Ll)* (Uu)' *(Ll)'2* (Bb)' r' (Bb) (Rr)' R' *u* y' M' (Uu) x2 z' 
= z Dw' M D Lw' Uw' r' Uw Lw Uw' Lw'2 Bw' r' Bw Rw' R' u y' M' Uw x2 z' 

For the 5x5x5, just include the central slice with the bold moves above.


On the inner-orbit of the 6X6X6: 20q/19h
z 3d' 4m D 3l' 3u' 3R' 3u 3l 3u' 3l'2 2R' 3b' 3R' 3b 3r' R' 2-3u y' 4m' 3u x2 z' 

On the outer-orbit of the 6X6X6: 19q/19h
z 3d' 4m D 3l' 3u' 2R' 3u 3l 3u' 3l'2 3R' 3b' 2R' 3b 3r' R' 2-3u y' 4m' 3u x2 z' 
=
z 3d' 4m D 3l' 3u' 2R' 3u 3l 3u' 4l 3l 3b' 2R' 3b 3r' R' 2-3u y' 4m' 3u x2 z' 

On the inner-orbit of the 7X7X7: 20q/19h
z 3d' 5m D 4l' 3u' 3R' 3u 4l 3u' 4l'2 2R' 3b' 3R' 3b 3r' R' 2-4u y' 5m' 3u x2 z' 

On the outer-orbit of the 7X7X7: 19q/19h
z 3d' 5m D 4l' 3u' 2R' 3u 4l 3u' 4l'2 3R' 3b' 2R' 3b 3r' R' 2-4u y' 5m' 3u x2 z' 
=
z 3d' 5m D 4l' 3u' 2R' 3u 4l 3u' 5l 4l 3b' 2R' 3b 3r' R' 2-4u y' 5m' 3u x2 z'


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