# Odd parity Algorithms (specifically, single edge "flip")



## Christopher Mowla (Sep 18, 2009)

Is there an edge flip algorithm less than 25 quarter turn moves?


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## Lucas Garron (Sep 19, 2009)

http://www.speedsolving.com/forum/showthread.php?p=164072#post164072
http://archive.garron.us/paste/text/dp_lrU2F2B2D2.txt
Hence both my OLL parities are 25q. Note what kind of algs you are referring to (Domino).


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## qqwref (Sep 19, 2009)

Dan Cohen said he used ACube to search for all algs in <r,l,U2,B2,D2,F2> and that there were none in fewer than 25 quarter turns. Theoretically there might be a parity alg shorter than that, but I don't think we'll find one with the conventional approach.

EDIT: Lucas's file seems to include "nonpure" algorithms that adjust the last layer by U2, such as the following:
r2 F2 r U2 r U2 x U2 r U2 r' U2 r U2 r2 U2

EDIT: I'm dumb, that was a 25qtm one, but here's a 23:
r' D2 l B2 r' U2 r U2 l' B2 U2 D2 r U2 r'


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## Stefan (Sep 19, 2009)

Here's an old one with 24:
http://games.groups.yahoo.com/group/speedsolvingrubikscube/message/13700


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## fanwuq (Sep 19, 2009)

StefanPochmann said:


> Here's an old one with 24:
> http://games.groups.yahoo.com/group/speedsolvingrubikscube/message/13700



Thanks!
(Rr)' U R U
[(Rr)' U2] * 3
(Rr)2 U R' U' (Rr)2
U' R' U (Rr)'
This alg is awesome. Finally I have an excuse to use Petrus for speedsolving the 4x4x4.


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## Lucas Garron (Sep 19, 2009)

StefanPochmann said:


> Here's an old one with 24:
> http://games.groups.yahoo.com/group/speedsolvingrubikscube/message/13700


Nice alg, but that's not what the original post was asking for. 
(Adding R2 U2 R' U2 could qualify, though.)


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## Stefan (Sep 19, 2009)

Lucas Garron said:


> Nice alg, but that's not what the original post was asking for.


Maybe it's not what he wanted, but I think it still is a valid answer. At least it definitely is an "odd parity algorithm". The OP was a bit ambiguous, making us guess what exactly he means and even what puzzle he's talking about. Also... do you think he counts R2 as two turns but an inner slice quarter turn as one turn? Seems counter-intuitive to me, so I think with his lower case letters he meant double layer turns rather than inner slice turns, and thus the algs he presented do affect other pieces as well, just like mine. Plus he explicitly mentioned _"without messing up the centers"_ but said nothing about the other edges/corners (except "single edge flip" implies the other edges shouldn't be flipped).


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## Christopher Mowla (Sep 20, 2009)

*He's correct*



Lucas Garron said:


> StefanPochmann said:
> 
> 
> > Here's an old one with 24:
> ...



Yes Lucas, you are correct. That is not what I was looking for. As you probably have realized, I meant a pure edge "flip" which does not affect the cube at all (besides distorting-not discoloring-the centers and "flipping the one edge").


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## Christopher Mowla (Sep 20, 2009)

StefanPochmann said:


> Lucas Garron said:
> 
> 
> > Nice alg, but that's not what the original post was asking for.
> ...



I am sorry for the confusion. I meant a pure edge flip, much like the ones which you have on your website:

http://www.stefan-pochmann.de/spocc/other_stuff/4x4_5x5_algs/?section=FixOrientationParity

In fact, I am glad that you answered this post. I wanted to ask you about what you say to be Chris Hardwick's pure edge flip algorithm. Did he really come up with it. I noticed on your site that you ask "how was this found". Has he ever told you? I have always been curious about how, that algorithm was found. I have private messaged Chris and emailed him, but he didn't respond.

Lastly, do you think that there is a way to logically come up with a pure edge flip alg, which is around 25q?


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## Christopher Mowla (Sep 20, 2009)

qqwref said:


> Dan Cohen said he used ACube to search for all algs in <r,l,U2,B2,D2,F2> and that there were none in fewer than 25 quarter turns. Theoretically there might be a parity alg shorter than that, but I don't think we'll find one with the conventional approach.
> 
> EDIT: Lucas's file seems to include "nonpure" algorithms that adjust the last layer by U2, such as the following:
> r2 F2 r U2 r U2 x U2 r U2 r' U2 r U2 r2 U2
> ...



Thanks for the 23q alg. for double parity (even though I was seeking the pure one-edge flip). Please tell me, who found this algorithm and how? Did he/she use a computer, trial and error, or logical reasoning?


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## Christopher Mowla (Sep 20, 2009)

Lucas Garron said:


> http://www.speedsolving.com/forum/showthread.php?p=164072#post164072
> http://archive.garron.us/paste/text/dp_lrU2F2B2D2.txt
> Hence both my OLL parities are 25q. Note what kind of algs you are referring to (Domino).



Oh, and I was referring to algorithms for regular big cubes (.i.e. the 4X4X4-> NXNXN).


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## cmhardw (Sep 20, 2009)

cmowla said:


> In fact, I am glad that you answered this post. I wanted to ask you about what you say to be Chris Hardwick's pure edge flip algorithm. Did he really come up with it. I noticed on your site that you ask "how was this found". Has he ever told you? I have always been curious about how, that algorithm was found. I have private messaged Chris and emailed him, but he didn't respond.



I did not come up with the alg. In 1998 I learned how to solve the 5x5x5 completely by intuition, except for the "parity" case. I went to www.excite.com to look up algorithms for solving this.

Doing so linked me to a simple text only HTML page that had several algs listed for the parity case. I don't remember how many were listed but it was less than 10. I chose the one that had the fewest number of turns (fewest in written notation). I have not been able to find the same page since.

--edit--
The only parity alg I did come up with on my own is the r2 U2 r2 U2 u2 r2 u2 for 4x4x4 PLL parity - just to be clear. I was trying to adapt the same concept as (R2 U2)*3 on 3x3x3.



> Lastly, do you think that there is a way to logically come up with a pure edge flip alg, which is around 25q?



I see two ways to do this. Either we can invent algorithms that are short and are intuitive, or we can try to understand the algorithms already given.

Also, are you certain that every single short algorithm known is not understood by everyone? That's a pretty big assumption.

Chris


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## Christopher Mowla (Sep 20, 2009)

cmhardw said:


> Also, are you certain that every single short algorithm known is not understood by everyone? That's a pretty big assumption.
> Chris



To be more specific, I was not so much referring to all algorithms, only odd parity (especially the one edge "flip").

I know that it is possible for someone to study an initially unobvious algorithm long enough until he/she believes that he/she has a good understanding of the algorithm; however, this involves a timely study, and, is that understanding a real understanding?

I might be missing it, but think of math. Now, I have not taken advanced calculus yet, but tell me if I am wrong (and I am serious, because I know you majored in math). Take for example the formal definition of the limit. I honestly do not know any students who fully understand what a limit is. They usually just think of "plug in the number which x approaches" into f(x): if none of the indeterminate forms is not obtained, then the limit is found...otherwise do L'hospital's rule, algebra, trig identities, etc..to evaluate it...if it exists at all.
From an advanced calculus student's perspective, one who has understood all of the proofs and logic behind the limit, would define a limit much differently than a freshman year calculus student.

Similarly, studying a brief "one edge correction" algorithm long and hard might help develop a light undertanding of what is happening to a cube, but not an understanding that is good enough to be confident in.

If that confidence was great, then that person should be able to write 100s of algorithms for the single "edge flip". Obviously all could not be the same length in moves, but, many algorithms should intuitively come out of that person's head (many of them very brief). Furthermore, that person should be able to prove what is the briefest possible algorithm for the one edge "flip" (without tools such as a computer).

If I understand one integration problem, does that make me an expert at integration?


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## qqwref (Sep 20, 2009)

cmowla said:


> Thanks for the 23q alg. for double parity (even though I was seeking the pure one-edge flip). Please tell me, who found this algorithm and how? Did he/she use a computer, trial and error, or logical reasoning?



A computer of course. Did you look at his file? There are hundreds of algorithms there... nobody would waste their time looking for algs like this by hand when computers can do it much faster and guarantee optimality (assuming you entered in the right assumptions).



cmowla said:


> If that confidence was great, then that person should be able to write 100s of algorithms for the single "edge flip". Obviously all could not be the same length in moves, but, many algorithms should intuitively come out of that person's head (many of them very brief). Furthermore, that person should be able to prove what is the briefest possible algorithm for the one edge "flip" (without tools such as a computer).



I don't think the things you say are possible except for certain easy cases, unless you are willing to do a non-humanly-possible amount of work. Cubing is not as easy as mathematics in a way - there are no simple theorems that guarantee a solution of a given length (or any algorithms that always generate a reasonably short solution without brute force trial and error). A few things such as parity considerations and certain subgroups are guaranteed but beyond that you are really on your own. No matter how much you know of cube theory, I don't think there is any known way at all to prove optimality without a certain measure of brute force (and the less brute force you want, the more algorithms you need to store in the form of pruning tables).

Here is one intuitive way to deal with parity, though: Do a z rotation and use only R2, u slice, and d slice moves. Then the middle two layers can be thought of as two layers which each have four corners and four "edges". Flipping a 4x4 edge in this layer is a matter of swapping the two corners lying directly above one another. (However, since an even permutation of the middle layers will cause the rest of the cube to be an R2 off, in practice you also need to swap one or three pairs of identical 'edges'.) So algs can be generated in this way. I could personally generate a lot of different move sequences for this but there would be no point since a computer could generate more and more efficient sequences (and I would, again, have no way to prove optimality without an impossible amount of work).


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## Stefan (Sep 20, 2009)

cmowla said:


> From an advanced calculus student's perspective, one who has understood all of the proofs and logic behind the limit, *would define a limit much differently* than a freshman year calculus student.


What?! Why?



cmowla said:


> If that confidence was great, then that person should be able to write 100s of algorithms for the single "edge flip".


Well, many of us easily could.



cmowla said:


> Furthermore, that person should be able to prove what is the briefest possible algorithm for the one edge "flip" (without tools such as a computer).


No. I'm afraid some things in life simply require brute force, and some too much to do by a human.


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## Christopher Mowla (Sep 20, 2009)

qqwref said:


> A computer of course. Did you look at his file? There are hundreds of algorithms there... nobody would waste their time looking for algs like this by hand when computers can do it much faster and guarantee optimality (assuming you entered in the right assumptions).



Which site? Can you show me. I would like to add it to my bookmarks!


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## qqwref (Sep 20, 2009)

It isn't a site, it's a program, called ACube (the version I use is JACube, same thing though). This program only does 3x3 but you can add any move constraints you want, so in this case you can simulate the 4x4 middle slices by only allowing R, L, U2, D2, F2, B2 and ignoring the middle slice of the 3x3.

There is a more general program out there called ksolve which can be used to solve pretty much anything (you could even optimally solve 4x4 positions if you had enough computing power/time) but it takes more work to set up and I don't think you would find any good solutions that are not in <r,l,U2,F2,B2,D2>.


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## Stefan (Sep 20, 2009)

qqwref said:


> I don't think you would find any good solutions that are not in <r,l,U2,F2,B2,D2>.


Well, here's one of length 28 that I just made up:
Dw' L' U F (r U2 r U2 r U2 r U2 r) F' U' L d L' d' L D L' d L
Ok, so it's a bit longer. But I'm only human.


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## Stefan (Sep 20, 2009)

qqwref said:


> here's a 23:
> r' D2 l B2 r' U2 r U2 l' B2 U2 D2 r U2 r'


Make that a 21:
r' D2 l B2 r' U2 r U2 l' B2 E2 l U2 l'


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## Christopher Mowla (Nov 6, 2009)

StefanPochmann said:


> qqwref said:
> 
> 
> > I don't think you would find any good solutions that are not in <r,l,U2,F2,B2,D2>.
> ...



I think that's the record without the use of a computer. I am impressed. .

Most other algorithms one-edge flip algorithms (not computer generated) that I have seen are not in the sub 30 range. But, as always, I am suprised of how little I know (there could be more out there besides Stefan's).:fp


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## deadalnix (Nov 20, 2009)

fanwuq said:


> (Rr)' U R U
> [(Rr)' U2] * 3
> (Rr)2 U R' U' (Rr)2
> U' R' U (Rr)'
> This alg is awesome. Finally I have an excuse to use Petrus for speedsolving the 4x4x4.



Is it a good way to scramble the cube, or something I don't get ?

EDIT: OK, say no more, I get it. But how the hell did you find this alg ?


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## Stefan (Nov 20, 2009)

deadalnix said:


> But how the hell did you find this alg ?


Follow the link.


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## Christopher Mowla (Nov 21, 2009)

Lucas Garron said:


> (Adding R2 U2 R' U2 could qualify, though.)


 
Instead of that, it might be better to add F' L' U' L F U R2 U R' *:*

(Rr)' U R U
[(Rr)' U2] * 3
(Rr)2 U R' U' (Rr)2
U' R' U (Rr)'
F' L' U' L F U R2 U R'

from there, all you need to do is perform *one* corner cycle (with the single incorrect corner in the bottom layer and the two incorrect corners in the top layer) and orient the left and back composite edges.

In summary,
(Rr)' U R U
[(Rr)' U2] * 3
(Rr)2 U R' U' (Rr)2
U' R' U (Rr)'
F' L' U' L F U R2 U R'
[1 3 corner cycle]
[orient left and back composite edges]

This procedure will swap Front composite edge <-->right composite edge and swap the winged edges of the original right composite edge (a double parity fix between the front and right edges, where the original right edge appears to be flipped).


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## Ron (Dec 5, 2009)

(Rr)' U R U
[(Rr)' U2] * 3
(Rr)2 U R' U' (Rr)2
U' R' U (Rr)'

R2 U2 R U R2 U2 R2 U R2


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## Christopher Mowla (Dec 6, 2009)

Ron said:


> (Rr)' U R U
> [(Rr)' U2] * 3
> (Rr)2 U R' U' (Rr)2
> U' R' U (Rr)'
> ...


 
That's even better. How did you find that?


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## Christopher Mowla (Dec 16, 2009)

qqwref said:


> Dan Cohen said he used ACube to search for all algs in <r,l,U2,B2,D2,F2> and that there were none in fewer than 25 quarter turns. Theoretically there might be a parity alg shorter than that, but I don't think we'll find one with the conventional approach.


 
You are right about the theory, qqwref.

For those interested in God's algorithm for big cubes, I have just lowered the move lower bound for the "one edge flip" case (again). At the beginning of the thread, qqwref mentioned the theory that there may exist "one edge flip algorithms" shorter than 25q but not using the conventional approach. The three algorithms below are (as far as I know) the shortest found (and publically known) using that approach.

r2 B2 U2 l U2 r' U2 r U2 F2 r F2 l' B2 r2 (25 q, 15 h)
r' U2 l F2 l' F2 r2 U2 r U2 r' U2 F2 r2 F2 (25 q, 15 h)
r2 B2 r' U2 r U2 F2 r F2 l' U2 l U2 B2 r2 (25 q, 15 h)

I now have just found a *23q* pure edge flip algorithm (by hand of course). I previously found a 24q algorithm on August 17, 2009. Since then I have found several more 24qs. I didn't think that there could be a shorter algorithm (in quarter turn moves) than 24, but I proved myself wrong just a few days ago (December 13, 2009).

But as for half turn moves, I still haven't found anything below 15h: the lowest I have come has been 18h. The computers could be right on that one (using the conventional approach).

I am aiming for 21q because I can see based from how I found my 23q that the constraints are strict, but there still is a (great) possibility for less than 23q. I guess only the future will tell (whether I find it or someone else does).

Again, I am mentioning this comment for those interested in the theory--*a 23q has been found*. For speedcubing purposes, you probably would prefer to execute already known algorithms (25-27q), not the ones I have found.


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## Kenneth (Dec 16, 2009)

If you have an alg that is 25 q to solve a case, then it is impossible to have an alg of 24 q to solve the same case...

Parity comes from a odd number of q-turns, if it is even it is not a parity. So, 22 is not possible either.

I have no idea how your 24 q can solve this case, did you ignore a ending U turn?


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## Christopher Mowla (Dec 16, 2009)

Kenneth said:


> I have no idea how your 24 q can solve this case, did you ignore a ending U turn?


 

No, I did not. The 24q and moreover, the 23q, are complete algorithms. They correct the "one edge flip" to a *completely solved cube state.*

Edit:
It is a privilege to hear from you first. I have read your occupation in your public profile. You and I appear to have the same passion (finding algorithms).


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## Kenneth (Dec 16, 2009)

cmowla said:


> Kenneth said:
> 
> 
> > I have no idea how your 24 q can solve this case, did you ignore a ending U turn?
> ...



Hehe, well, that was like 2 years ago, then I found you can setup the same cases but for corners on a 3x3 and use a solver to do the work for me, then I lost intrest...

If you claim you got an alg of 24 q then I'm sure you do not know what you are talking about and/or don't know how to count your turns.

All algs that solves this case MUST have a uneven number of quarterturns, there are no hidden secrets we do not know about yet. That's why i'm sure you are wrong somehow...


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## Stefan (Dec 16, 2009)

Kenneth: I'd count R r Rw' as three quarter turns.


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## Christopher Mowla (Dec 16, 2009)

Kenneth said:


> All algs that solves this case MUST have a uneven number of quarterturns, there are no hidden secrets we do not know about yet. That's why i'm sure you are wrong somehow...


 
No. I am not miscounting my moves. In order to correct/induce an inner-layer odd permutation *(of pure form),* an algorithm *must *have the sum of the inner-layer turns for a pair of complimentary layers to be *odd* and the sum of the outer-layer moves to be *even*.

The odd number of inner layer turns induces/fixes the inner layer odd permutation.
The even number of outer layer turns preserves the permutation of the outer layer.

My algorithms satisfy this requirement.


Edit:
Let me ask you a question. Maybe I am wrong on counting my moves.
If you don't count the following as 10q, then, I am counting wrong: (Rr) B r U L D S E F2.

Otherwise, if I am not mistaken, every possible individual move on a 4X4X4 (or NxNxN) is considered a quarter turn and, multiple layer turns which are parallel, touching, and being turned in the same direction one time are considered one quarter turn move.

Edit:
And of course, this can always be proven with move equivalences. For example, F=([all back layers]' z).
Edit:
If what I just mentioned about multiple layer turns is not true, then a 25q algorithm for the “one edge flip” on a 5X5X5 cube would not be 25q anymore on a 7X7X7 cube (if 2 pairs of winged edges needed to be permuted): there would be a whole lot more quarter turn moves. And, using the 7X7X7 as an example, as I just mentioned, if all the winged edges on a single composite edge needed to be fixed on a 7X7X7 and you chose to perform the usual algorithm:
r2 B2 U2 l U2 r' U2 r U2 F2 r F2 l' B2 r2
then, the r and l turns would be touching each other and thus, the procedure would still be considered 25q.

What about if you are solving a 20X20X20 and you have 3 non-touching sets of complimentary winged edges which needed to be swapped. According to my move interpretation, then the move count would be more than 25q because they are not touching. If it is still considered 25q just because the layers are parallel and being turned in the same direction, then my 23 alg is even less moves--but this is not how I count quarter turn moves: I believe they must be touching (and this way of counting can be proven using move equivalences yet again).

In summary, here is how I count quarter turn moves. If I am wrong here, then I am wrong about all of this. If this is correct, then my claim is legitimate (I assure you).

On a 4X4X4,
(Rr): 1q
Fb': 2q
(Ffb'): 1q
FS: 1q
FS':2q
L R': 1q

On a 5X5X5 (when I say M' , I just mean the central slice)
L' M' R: 2qßbecause I can do l r' x instead.
l'M' 1q
etc…


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## Kenneth (Dec 16, 2009)

"If you don't count the following as 10q, then, I am counting wrong: (Rr) B r U L D S E F2."

Really depends, if you count slices as quarter turns, then it is ok but then specify it is in slice metric because I would count that as 13 q-turns (face turns and wide face turns).


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## Christopher Mowla (Dec 16, 2009)

So in other words, in quarter turn moves,

On 4X4X4,
F B' =2q
S=2q
(Rr)=2q
M=2q
(Ffb')=1q

and on 5X5X5,
l'M'=2q
(l'M'r)=2q

But in slice metric, they are:
On 4X4X4,
F B' =1q
S=1q
(Rr)=1q
M=1q
(Ffb')=1q

and on 5X5X5,
l'M'=1q
(l'M'r)=1q

Am I understanding you correctly?

Edit:
For cubes greater than the 3X3X3, why would a quarter turn move refer to the same thing as on a 3X3X3? At least M, E, and S should be one quarter turn move just like on a 3X3X3, right? Why are they considered multiple quarter turns? This just doesn't make sense to me. *I know* that many people use a 3X3X3 solver to find the shortest algorithms for big cubes, but why does that make the moves for big cubes considered to be as 3X3X3 moves?
Anyway, according to what you regard as moves, my algorithms are still 24q and 23q, but with slice metric.

Even Stefan counts M, E, and S as quarter turn moves (see his algorithms which he gave earlier in this thread).


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## Kenneth (Dec 16, 2009)

There are for mayor metrics

QTM, single face quarter turns
HTM, single face half turns
SQTM, slice quarter turns
STM, slice turn metric

If you do not specify I (and most people) assumes you are talking about face turns. This because the "normal" metric is HTM.

If you use a M, S or a E in FMC it is always counted as two turns because there turns are counted in the normal metric...


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## Christopher Mowla (Dec 16, 2009)

Kenneth said:


> There are for mayor metrics
> If you use a M, S or a E in FMC it is always counted as two turns because there turns are counted in the normal metric...


 
Well, for my algorithms, I don't have to use M, S, or E, but how about 
(Uu)--on the 4X4X4 or 5X5X5; or (UuE')--on the 5X5X5, where E is just the central row....you can you just send me a link with the specifications if you want.


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## qqwref (Dec 18, 2009)

Kenneth said:


> There are for mayor metrics
> 
> QTM, single face quarter turns
> HTM, single face half turns
> ...



For cubes greater than 3x3, this post is wrong and completely nonsensical.

Apart from the distinction between half and quarter turn metrics (since every metric can be considered with either quarter or half turns), there are three useful metrics on larger cubes:
- block turn metric, where any group of contiguous slices moving the same way is counted as one move
- layer turn metric, where the only allowed moves are moves of a single slice layer
- multislice turn metric, where the only allowed moves are moves that move slices 1 through n on a given face in the same way
I believe what you are using, cmowla, is the block quarter turn metric. I prefer the block (half) turn metric for pattern-making because it is the least restrictive without adding moves that don't feel like moves. It reduces to STM/SQTM on 3x3, as does the layer turn metric; the multislice metric reduces to HTM/QTM on 3x3.


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## Christopher Mowla (Dec 18, 2009)

qqwref said:


> I believe what you are using, cmowla, is the block quarter turn metric.


 
Your explanation makes a lot more sense, qqwref.

According to how you described the block quarter turn metric, my alg is 23q. According to the block quarter turn metric, I believe the usuall algs that I have listed in this thread (which use the conventinal method) are still 25q.

In cubetwister, my alg is 28qtm, while the usuall algs that I have listed already in this thread (which use the conventional method) are 34qtm. 

I can understand why you like block half turn metric, qqwref, but I personally (probably most people don't) feel that a half turn is 2 moves (I guess I like leaning on the math more). Thus, I lean toward block quarter turn metric.

Based on my 24q (in block turn metric) algorithm, I don't believe one can find an algorithm that is less than 15h, as the algorithms found by the computer have. And, I also must say that I am 100% positive that 23q is the optimal algorithm for block quarter turn moves (and my 23q alg happens to be the least in qtm on cube twister--one of my 24s is as well). However, 15h is definitely optimal for block half turn moves.

In short, for the "pure edge flip algorithm", the optimal algorithms, according to my findings, are:

For block half turn moves, 15 (computer-generated algorithms with conventinal approach).
For block quarter turn moves, 23 (my alg).
For qtm, according to cube twister, 28 (my alg).

Edit:
I just found another 23 block quarter turn alg, and it is *26qtm*, according to cube twister.


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## Christopher Mowla (Dec 28, 2009)

I did it again. I lowered the upper bound for the pure single edge flip in block quarter turn moves!

I have found a *22 BQTM* alg. It is still *26 qtm*, according to cube twister (so the qtm lower bound remains 26).


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## deadalnix (Dec 28, 2009)

Maybe you can share your discovery with us ?


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## Stefan (Dec 28, 2009)

cmowla said:


> I have found a *22 BQTM* alg





cmowla said:


> I am *100% positive that 23q is the optimal algorithm* for block quarter turn moves


..


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## Christopher Mowla (Dec 28, 2009)

StefanPochmann said:


> cmowla said:
> 
> 
> > I am *100% positive that 23q is the optimal algorithm* for block quarter turn moves
> ...


 
I am actually quite happy to prove myself wrong this time!
I always suspected the possibility for a 22 BQTM algorithm, but I wasn't sure if I would ever find it or not and had no real way to prove that it could exist except by my theory. I decided to give it a shot, and it is by that theory that I found this alg (well, I have actually found two 22 BQTM algs, not just one).

I know for a fact that I personally will not be able to achieve 21 BQTM or less, whether 22 BQTM is God's Algorithm or not. That is something I have been sure of ever since I found my 23 earlier this month (and I had no clue about any of this when I found my very first 24 at the end of August). As I have said before, there are just too many constraints for 21 (even though I have come so close to finding it in at least 5 different approaches: it is so close to being valid that I shake my head).

In short, 22 was never really out of the question in my mind, but 21 definitely is (thus I am concluding that God's Algorithm for the Pure Edge Flip is 22 BQTM). But maybe when I explain my method in the future, someone else might tell me different (which I am not against) or if computers become advanced enough to overtop me/confirm that God's Algorithm for this specific case is 22 BQTM.



deadalnix said:


> Maybe you can share your discovery with us ?


 In time.


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## rachmaninovian (Dec 28, 2009)

lol it really doesnt harm just to post your alg here, before anyone questions you lol
lol potato has laser eyes you know? :3


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## joey (Dec 28, 2009)

rachmaninovian said:


> lol potato has laser eyes you know? :3


I don't even.


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## rachmaninovian (Dec 29, 2009)

joey said:


> rachmaninovian said:
> 
> 
> > lol potato has laser eyes you know? :3
> ...



i insist!


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## Christopher Mowla (Dec 30, 2009)

Although this doesn't match the name of the thread perfectly,
I have now found a *18 BQTM pure algorithm *for the two directly opposite winged edges (usually, I usually use l' U2 l' U2 F2 l' F2 r U2 r' U2 l2) to fix this case. (Thus, 19 BQTM is no longer the shortest pure alg for that case, if it was believed to be before).






And for the *diagonal case*, I have found a *pure 19 BQTM alg* (I am not sure if that is the shortest, but it's pretty brief).




Both I found by hand as I did with my 22 BQTM pure edge flip.


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## Christopher Mowla (Jan 3, 2010)

I have just found a nonpure alg that does the diagonal case (shown in my previous post) in very few moves (it swaps top front left with top back right).

It is very "unpure" and thus is ideal for the 3X3X3 reduction method, when pairing up the last two composite edges. And I will actually post this one:

17 BQTM, 11 BHTM
r U2 r U2 r2 U2 r x2 U2 l F2 r' x'


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## Christopher Mowla (Jan 7, 2010)

I now have found a *20 BQTM* pure edge flip *for the 4X4X4 cube and only for the 4X4X4 cube* (or higher even cubes treated as a 4X4X4, where the entire composite edge appears to be flipped).

*The important thing to note is that I did not find it using the approach which I have been using* (not exactly, anyway). Thus, *I am not contradicting my previous claim* because when I boldly claimed that I could not achieve less than 22 BQTM before , I had in mind the method which I was using at that time (and besides, this algorithm only holds for the 4X4X4 form anyway).

This algorithm, unlike my 22's, 23's, and 24's, is *very ugly*, despite sufficient cube rotations. Due to the way I found this algorithm, I know that it is specifically designed for the 4X4X4. I will not make any claims which state that I cannot use this new approach to find 20 BQTM or even 21 BQTM for all size cubes (and all forms of the pure edge flip), but...:fp

Though I do not know too much on what makes the 4X4X4 cube different from all other big cubes (besides the obvious size difference), I can recall one difference from information related to my "Supercube centers and odd parity" thread. The 4X4X4 cube is the only _big_ cube which one can technically swap just two pieces (this can be done by performing a one edge flip alg, followed by a 180 degree rotation of the top center).

If it turns out that 20 BQTM is God's algorithm for the pure edge flip for the 4X4X4 and 22 BQTM is God's algorithm for pure edge flip for bigger cubes (other than large even cubes treated as a 4X4X4), then, in my (small) opinion, it might just be an unexpected phenomena. The 4X4X4 is an extraordinary cube, I do admit!

Thus, the upperbound for God's algorithm for the 4X4X4 pure edge flip is now lowered to 20 BQTM, while all other big cube sizes, in general, remain 22 BQTM.

Again, for speedcubing purposes, it is definitely _not_ _faster_ than the standard 25 BQTM (or even longer algorithms). My 23 BQTM is decent (and my 22 BQTM follows closely behind the 23), but as for the 20 BQTM, it is slower to execute (and I don't think I can memorize this one very easily either...the alg is very random throughout and seems to utilize many different silces...very messy).


----------



## reThinking the Cube (Jan 7, 2010)

cmowla said:


> I now have found a *20 BQTM* pure edge flip *for the 4X4X4 cube and only for the 4X4X4 cube* (or higher even cubes treated as a 4X4X4, where the entire composite edge appears to be flipped).



Congrats!

cmowla - Thanks. Nice post.


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## qqwref (Jan 7, 2010)

cmowla said:


> Thus, the upperbound for God's algorithm for the 4X4X4 pure edge flip is now lowered to 20 BQTM, while all other big cube sizes, in general, remain 22 BQTM.



I don't think you can really make such a claim without backing it up. Cube theory (just like mathematics) is a collaborative venture; if you just declare something to be true, or say "I have a proof of this theorem" without publishing it, nobody will believe you. (In fact, if what you're declaring is non-obvious but you provide no evidence, the only logical decision is to not believe you.) There are many cases in mathematics where someone has thought they proved or discovered something when it turned out they were mistaken or even lying, which is why things are only considered true once they are publicly proven. So I would say that it's not right to say "the upper bound is now lowered to 20 bqtm" until the community has access to a 20-move algorithm or some kind of non-constructive proof that one exists.

For instance: I have just found a 15 bqtm parity algorithm. Of course, I won't tell anyone the algorithm; however I am sure you will believe me anyway! I suggest you start looking for a 14-move one now.


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## Stefan (Jan 7, 2010)

cmowla said:


> *The important thing to note is that I did not find it using the approach which I have been using* (not exactly, anyway). Thus, *I am not contradicting my previous claim* because when I boldly claimed that I could not achieve less than 22 BQTM before , I had in mind the method which I was using at that time (and besides, this algorithm only holds for the 4X4X4 form anyway).


Yes you *are* contradicting your previous claim, cause it didn't say anything about a restriction to some method. Doesn't matter what you had in mind. And that's one of the big problems with you and your claims and "proofs". You make general claims ignoring alternatives. And then turn out to be wrong again and again.

Please stop being childish.


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## Henrik (Jan 7, 2010)

I have nothing to add to this thread, the only thing Im asking is that you post the algs you have found.
I hear the number go down all the time, but I have only seen a few. 

I would like see them even if they are ugly. Mostly just for fun, but also for understanding.


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## Stefan (Jan 7, 2010)

Henrik said:


> the only thing Im asking is that you post the algs you have found.



Unlikely to happen. He's apparently still dreaming of making lots of money by selling his stuff as a book.


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## Christopher Mowla (Jan 7, 2010)

StefanPochmann said:


> Please stop being childish.


I am trying not to be. I know that I made claims in the past which have proven myself wrong, but notice that in my most recent post, I did not say that 20 BQTM *is* God's algorithm for the pure one edge flip for 4X4X4 or that 22 BQTM *is* God's algorithm for pure one-edge flip for all cases in general. I just said what the upper-bound at most must be for the 4X4X4 and all other cubes, respectively (I am trying to improve).

_And for those who don't believe me, I completely understand...I can hardly believe it myself_. _Nonetheless, I had to mention it (I couldn't resist)._

By the way, when I do release these algs, in what notation do you guys prefer for multiple layer turns? The reason I ask is because there are many double layer turns, e.g. (Uu), and even triple layer turns sometimes. I know I could type (Uue') for the top three layers clockwise, but how about Uw3? This is the custom notation I have made for cubetwister, and I like it a lot. Uw2 therefore represents (Uu) and Uw has no meaning at all (in my notation) because I only type "w" if it is a multiple layer turn, and, how many consecutive layers turned is specified after the "w".


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## joey (Jan 7, 2010)

Just post the alg.


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## Stefan (Jan 7, 2010)

Preferably one of the notations you find here:
Lucas' tool with 3u2 example


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## Christopher Mowla (Jan 7, 2010)

StefanPochmann said:


> Preferably one of the notations you find here:
> Lucas' tool with 3u2 example


So, for example, to do "d", is the only way I can input it (d D')?

Edit:
I think I will use "Superset".
Edit:
Never mind. Thanks Stefan. I think I will use SiGN.


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## Stefan (Jan 7, 2010)

cmowla said:


> So, for example, to do "d", is the only way I can input it (d D')?


I assume you mean what SiGN calls 2D.


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## qqwref (Jan 7, 2010)

cmowla said:


> And for those who don't believe me, I completely understand...I can hardly believe it myself[/I]


This is exactly what peer review is for 

SiGN is the best notation to use (in my opinion) for algorithms involving various weird block turns. The basic way it works is:
- turns of only layer 1, 2, 3, etc. are R, 2R, 3R, ...
- turns of layers 1-2, 1-3, etc are r, 3r, ...
- turns of layers A-B are A-Br (for instance you can use 2-3r as a replacement for an M' move on the 4x4) - this doesn't HAVE to be used but it's far less ambiguous than the normal slice turns and probably easier to understand too.


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## andyt1992 (Jan 7, 2010)

StefanPochmann said:


> Henrik said:
> 
> 
> > the only thing Im asking is that you post the algs you have found.
> ...



HAHAHAHAHAHA its very unlikely he has a good alg.
2 small points:

1. Why wouldn't the thousands of other people not have found it since the cubes were invented it is very unlikely he'd be the first.
2. If he did have them, he'd sell one book and they'd be over the internet within the day.


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## Christopher Mowla (Jan 7, 2010)

andyt1992 said:


> HAHAHAHAHAHA its very unlikely he has a good alg.
> 2 small points:


As I mentioned, these algs are *not* good for speedsolving. This is strickly theory. So if "good" to you means "fast", then yes, you are correct. However, if you were implying "good" as in the algs I found are not shorter in BQTM than the computer-generated algs, then, that's your decision (as I said, I completely understand if you don't believe me--it's mind-blowing, to me at least).



andyt1992 said:


> 1. Why wouldn't the thousands of other people not have found it since the cubes were invented it is very unlikely he'd be the first.


I wonder the same thing. I never said I was the first (although I strongly implied the possibility), but no one else is telling me that I am not (as in, they are or know someone who has), even though I have not given out the algs *yet*.


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## Henrik (Jan 7, 2010)

I will repeat my self.

I dont care if this alg is suitable for speedcubing, Im just interested in understanding some theory about the parity algs. 

So I would still like to see those algs you have found.

Henrik


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## reThinking the Cube (Jan 7, 2010)

qqwref said:


> cmowla said:
> 
> 
> > And for those who don't believe me, I completely understand...I can hardly believe it myself[/I]
> ...



+1. 

Here is a pictorial representation of SiGN that was perpetrated by the usual suspects:

http://twistypuzzles.com/forum/viewtopic.php?p=121194#p121194


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## Faz (Jan 7, 2010)

I just found a 13 BQTM alg for a pure edge flip but I won't tell anyone because I'm going to make a book about it and become a millionaire.

But seriously, erm what is the reason you aren't posting your algorithm?
If you were to publish a book on it, I highly doubt any more than 10 people would buy it... 

Oh yeah, you can't just publish a book with a click of your fingers. There needs to be a market for it. I doubt people would walk into a book store, and buy it.

Well, the book was just a lmao idea. 

What's the reason? Because right now, I don't think many people believe you at all.


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## Stefan (Jan 8, 2010)

fazrulz said:


> Oh yeah, you can't just publish a book with a click of your fingers.


Welcome to the 21st century.


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## rachmaninovian (Jan 8, 2010)

meh, why are you holding on to the algs you found?
I always share my algs =P


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## Faz (Jan 8, 2010)

rachmaninovian said:


> meh, why are you holding on to the algs you found?
> I always share my algs =P



cos he's very lmao


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## ChrisBird (Jan 8, 2010)

My guess is that he hasn't found one and just wants us to think he is smart.


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## Lucas Garron (Jan 8, 2010)

ChrisBird said:


> My guess is that he hasn't found one and just wants us to think he is smart.


My guess is that he's found one, but he's just not ready to share it.
I'm pretty sure he can count the number of moves correctly, and I don't think he would lie about something like that. Neither do I think he's going to pull a Stieltjes on us.

Meanwhile, I'm perfectly content going on without knowing it for now. It just means there's more interesting stuff out there.


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## Christopher Mowla (Jan 9, 2010)

I have now found a 21 BQTM algorithm which gets rid of OLL parity from a scrambled "3X3X3" state on the 4X4X4.

Thus, the alg is not a pure one, but is does break the odd permutation and reunites all centers and edges in just 21q.

*This is not a double parity alg.*


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## nlCuber22 (Jan 9, 2010)

cmowla said:


> I have now found a 21 BQTM algorithm which gets rid of OLL parity from a scrambled "3X3X3" state.
> 
> Thus, the alg is not a pure one, but is does break the odd permutation and reunites all centers and edges in just 21q.
> 
> *This is not a double parity alg.*





fazrulz said:


> cos he's very lmao



yeah


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## Christopher Mowla (Jan 9, 2010)

nlCuber22 said:


> cmowla said:
> 
> 
> > I have now found a 21 BQTM algorithm which gets rid of OLL parity from a scrambled "3X3X3" state.





nlCuber22 said:


> cmowla said:
> 
> 
> > Thus, the alg is not a pure one, but is does break the odd permutation and reunites all centers and edges in just 21q.
> ...


 
*Believe me now?*

r U2 r' U2 r D2 r D2 r' F L' F' U' r' D2 r

or in single slice turns:
r U2 r' U2 r D2 r D2 r' F L' F' U' r' D2 r

I have decided to show this alg to let everyone know that none of this is a joke (since you couldn't take my word for it before). Believe what Lucas Garron says, because he couldn't be more right.

And all who give this alg to others (to use for any purpose), give me credit. I found it by hand, and it is officially (because the public has seen it) the *briefest* algorithm to break *only* OLL parity (with edge and center preservation). In actuality, my 20 BQTM pure edge flip is more briefer to solely break OLL parity (not double parity, that's 19 BQTM--I have found 3 of those by hand too), but I haven't released it yet for it to be officially the most optimal. "Come on, a pure algorithm is more optimal than a non-pure?" YES, at least in this case, as far as my findings have said.

On the contrary, for the digaonal swap of individual winged-edge pieces, my non-pure 17q (which swaps the top-front-left winged edge with the top-back-right winged edge):
r U2 r U2 r2 U2 r x2 U2 l F2 r' x'
is 2 BQTM shorter than my pure diagonal swap (which is 19 BQTM).


Date: 1/9/10


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## Henrik (Jan 9, 2010)

This is cool, thanks  funny alg, even though I dont know if I vile ever use it.

Did you say you had found a pure alg in 20 BQTM?
Can we see that one too. I think its cool you found these by hand.


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## Christopher Mowla (Jan 9, 2010)

Henrik said:


> Did you say you had found a pure alg in 20 BQTM?
> Can we see that one too. I think its cool you found these by hand.


 
Yes. And not right now. Yes, I think it's cool too. I actually like finding the briefest algorithms in the world by hand for fun. I never was interested in using computers (and I never learned how to use them either, although I wrote a TI-83 plus calculator program that pairs up the last layer edges k4 style).


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## Christopher Mowla (Jan 13, 2010)

I now found a *19 BQTM* pure edge flip algorithm for the 4X4X4 and only for the 4X4X4 (or even cubes treated as a 4X4X4, where it appears the entire composite edge needs to be flipped).

I used the same method that I used to find the 20 BQTM.

This alg is even more ugly than the 20 BQTM pure edge flip alg because it doesn't contain anymore half turn moves (it is composed only of block quarter turn moves).

Hence, it's 19 BQTM/19 BHTM.

Another interesting thing is that it is still 26 qtm in cube twister (if you have been reading this entire thread, you will notice that I mentioned before that I could not achieve less than 26 qtm with any of the other algs which I have previously found). Interesting.

_For all who doubt me, don't worry because I will actually consider releasing these algs (my 24's, 23's, 22's, 20, and 19) to the public in the near future. I highly doubt it will be for a price. Instead it will just be a documentation of some kind where I give a plausible derivation (which will be pretty long, especially for the 19 and 20 BQTMs) for each (and where I can clearly get officially credited for these algs and the process to find them...anyone who uses my method*s* cannot get credit for any algs found from them without mentioning my name as well as theirs). In addition, I *will* be in favor of people displaying the algs I have found on Youtube, on their website(s), or anywhere as long as I am given credit (that includes not crediting computer solvers, which I *did not* use to find these algs)._

_Any suggestions on how I can do officially establish my credit is welcomed. But please, keep it to a minimum in this thread, for that is not puzzle theory (pm me if you can)._

_1/12/10 6:43pm central time USA_


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## fanwuq (Jan 13, 2010)

cmowla said:


> Henrik said:
> 
> 
> > Did you say you had found a pure alg in 20 BQTM?
> ...



Could you share the code?


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## Christopher Mowla (Jan 13, 2010)

fanwuq said:


> Could you share the code?


 
Sure. Just give pm me your email and I will send you the application (which you can use Ti-connect to download it to your calc). I will also send you a pdf explaining how to input the positions of winged edges of your cube. _Note: You need to have solved the LL corners first, just like k4. Then, you can use it to solve the LL winged edges for every set of complimentary winged edges, e.g., the 7X7X7 cube, etc, but you must solve one complimentary set at a time)._

Once you input the information (which is very easy), it will give you all the moves (in several steps, just like k4...commutators--ones that I have come up with..and the 2 cycles are common ones which you have seen before) to solve the cube. Follow the moves exactly (including cube rotations). These moves are not necessarily the most efficient to solve the cube. Instead, it comes very close to how humans solve the LL edges. Like Thom Barlow said in his guide, it takes about 3 algorithms to solve the LL edges...this program does it at most 4 different algorithms (most of the time, it puts in two pieces at a time..and if the solve permits, 3 at a time). It solves the winged edges primarily with 3 cycles, and, if there is parity, then the last algorithm is a 2 cycle (which can be any of the forms of odd parity that comes with the solve).

The notation is the regular notation from Chris Hardwicks 4X4X4 solution page.


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## Stefan (Jan 13, 2010)

cmowla said:


> _clearly get officially credited for these algs and the process to find them...anyone who uses my method*s* cannot get credit for any algs found from them without mentioning my name as well as theirs). In addition, I *will* be in favor of people displaying the algs I have found on Youtube, on their website(s), or anywhere as long as I am given credit_


Looks like I'm not gonna read your stuff, as I want nothing to do with that kind of mentality...


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## Christopher Mowla (Jan 13, 2010)

StefanPochmann said:


> Looks like I'm not gonna read your stuff, as I want nothing to do with that kind of mentality...


What? All I am really trying to say is I want to be credited for my discoveries, just as others have been credited for their contributions.


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## miniGOINGS (Jan 13, 2010)

cmowla said:


> StefanPochmann said:
> 
> 
> > Looks like I'm not gonna read your stuff, as I want nothing to do with that kind of mentality...
> ...



If it's worth being credited, it will be.


----------



## Kirjava (Jan 13, 2010)

cmowla said:


> I wrote a TI-83 plus calculator program that pairs up the last layer edges k4 style



Maybe your wording is incorrect, but you don't pair edges on the K4 last layer.



cmowla said:


> Instead, it comes very close to how humans solve the LL edges. Like Thom Barlow said in his guide, it takes about 3 algorithms to solve the LL edges...this program does it at most 4 different algorithms (most of the time, it puts in two pieces at a time..and if the solve permits, 3 at a time).



The maximum (not average) number of algorithms should be three.


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## miniGOINGS (Jan 13, 2010)

Wow, just went to the wiki to find out more about K4 and realized the page is a DNF. http://www.speedsolving.com/wiki/index.php/K4

Found the website though (http://snk.digibase.ca/k4/).


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## Christopher Mowla (Jan 13, 2010)

Kirjava said:


> The maximum (not average) number of algorithms should be three.


 
Well, the program does 3 cycles the entire time, and, if there is parity, it does the proper 2 cycle at the end.

I noticed on your guide that you also mention two-2 cylcle algs and 4 cycles...maybe if you consider those in the maximum algorithm count of 3. But, as I said, my program does 3 cycles for everything (except for a 2 cycle at the end, if there is parity). It doesn't count two 2 cycles as one alg, and it doesn't do 4 cycles.

Edit:


Kirjava said:


> Maybe your wording is incorrect, but you don't pair edges on the K4 last layer.


Yeah, I think I did word it incorrectly, because it puts the winged edges into their correct positions directly (that's what I really meant).


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## blade740 (Jan 13, 2010)

cmowla said:


> _For all who doubt me, don't worry because I will actually consider releasing these algs (my 24's, 23's, 22's, 20, and 19) to the public in the near future. I highly doubt it will be for a price. Instead it will just be a documentation of some kind where I give a plausible derivation (which will be pretty long, especially for the 19 and 20 BQTMs) for each (and where I can clearly get officially credited for these algs and the process to find them...anyone who uses my method*s* cannot get credit for any algs found from them without mentioning my name as well as theirs). In addition, I *will* be in favor of people displaying the algs I have found on Youtube, on their website(s), or anywhere as long as I am given credit (that includes not crediting computer solvers, which I *did not* use to find these algs)._
> 
> _Any suggestions on how I can do officially establish my credit is welcomed. But please, keep it to a minimum in this thread, for that is not puzzle theory (pm me if you can)._



I'm sorry, but this is the biggest ego trip I've ever seen. You found a few algs that are a bit shorter than the commonly-known versions (and even then only in QTM, which nobody but you cares about). If anyone ever does talk about your alg (which is unlikely, since it's not useful for anything), you want them to put your name there to make sure you get credit for your alg? And make sure to note that you didn't use a computer? 

This is NOT what cubing is about.


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## Christopher Mowla (Jan 13, 2010)

blade740 said:


> This is NOT what cubing is about.


So what's your definition of cubing? Not all cubing is speedsolving. This is the theory section. And I think 6q is a significant amount less.


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## PHPJaguar (Jan 13, 2010)

Not the part about the alg not being suitable for speedsolving, but the bit where you think/expect people are going to worship you for it. You've obviously not been very friendly to the people here, and I don't know why that makes you think you'll be a cubing celebrity.


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## Christopher Mowla (Jan 13, 2010)

PHPJaguar said:


> Not the part about the alg not being suitable for speedsolving, but the bit where you think/expect people are going to worship you for it. You've obviously not been very friendly to the people here, and I don't know why that makes you think you'll be a cubing celebrity.


What makes you say that? How have I been rude? All I have been doing is explaining that this is theory.

People constantly tell me how worthless everything I do is. I am not answering their negative comments back rudely.

Stop reading every word I write as hostility, because I am just talking calmly. And I don't understand how I have been mean to fanwuq, since I did send him the code.

What is it with you guys? People write very rude comments to me, and everyone supports it. I write regular statements and people call them rude? I don't get it.

In all honesty, the only time I got out of hand was when I went at Lucas Garron. But now, me and him are cool. So please reconsider your judgement of me.


----------



## blade740 (Jan 13, 2010)

cmowla said:


> blade740 said:
> 
> 
> > This is NOT what cubing is about.
> ...



It's not a "definition of cubing" It's about how the cubing community works:
Cubing is, and has been for as long as I've been part of it, a collaboration. Information is freely shared. It's not about getting credit, or personal glory. Like someone already said, if you deserve respect, it will come. But demanding recognition is the WRONG way to get it. 

I think of cubing culture as similar to hacker culture



> Like most cultures without a money economy, hackerdom runs on reputation. *You're trying to solve interesting problems, but how interesting they are, and whether your solutions are really good, is something that only your technical peers or superiors are normally equipped to judge.*
> 
> Accordingly, when you play the hacker game, you learn to keep score primarily by what other hackers think of your skill (this is why you aren't really a hacker until other hackers consistently call you one). This fact is obscured by the image of hacking as solitary work; also by a hacker-cultural taboo (gradually decaying since the late 1990s but still potent) against admitting that ego or external validation are involved in one's motivation at all.
> 
> Specifically, hackerdom is what anthropologists call a gift culture. *You gain status and reputation in it not by dominating other people, nor by being beautiful, nor by having things other people want, but rather by giving things away.* Specifically, by giving away your time, your creativity, and the results of your skill.


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## DavidWoner (Jan 13, 2010)

cmowla said:


> In all honesty, the only time I got out of hand was when I went at Lucas Garron. But now, me and him are cool. So please reconsider your judgement of me.



Do not think we have forgotten the very first thread you created here. First impressions are very hard to overcome. You have been told from the beginning that being secretive with your work is highly frowned upon. It seems that you have forgotten what was said there.

Perhaps you do not understand one of the underlying problems with hoarding your work, so I will do my best to explain. The cubing community is a collaborative one: someone shares their discovery, others give feedback, improvements are made, and _everyone_ benefits. However, not sharing says two things.

1.) You do not deserve to see my work. It is above and beyond you. 
2.) There is nothing I can gain from sharing with you. You are incapable of helping me in any way.

While these may not be your thoughts or motives, that is the impression that I (and likely others) get from your behavior. Please do not misconstrue this as a personal attack. You asked what our problem was, and I am attempting to explain.


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## Henrik (Jan 13, 2010)

As far as I know and remember, no one has gotten credit by demand. When someone has gotten credit for single algorithms or sets of algs that has the same purpose, others has given them credit for the algs. An example is me, Jason Baum has given me credit for finding parity algs for his sq1 method. Even though only a few of the algs I found are online if any, Jason still credited me for helping him.

If others has their name on a method or gets credited with a name, it is for a method. MGLS is a new way of doing almost half the puzzle, ZZ is a whole new way of seeing how to solve 3x3x3. BH is a method and a collection of algs on how to solve the cube blindfolded.
Those has just put their name one the method so it can be recognized from others.

As far as I know no one had demanded credit for single algs, or methods, they have but their name on a method in the hopes of others to use it.

I think the quote Blade740 posted is very telling of how the cubing community works. Thanks

Now it is up to you to decide if you want to post the algs, and then you can hope for others to credit you.


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## rachmaninovian (Jan 13, 2010)

i just found a dedge flip which is rather useful for me...

l r U2 l U2 r' U2 r U2 r' U2 l U2 l2
which is 21qtm =P

and by doing l r U2 l U2 r' U2 r U2 r' U2 l U2 l2 + l2 U2 l2 U2 l2
I get l r U2 l U2 r' U2 r U2 r' U2 l' U2 l2, a double parity with 21qtm too.

however, these are NOT useful for reduction =p


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## PatrickJameson (Jan 13, 2010)

cmowla said:


> _For all who doubt me, don't worry because I will actually consider releasing these algs (my 24's, 23's, 22's, 20, and 19) to the public in the near future. I highly doubt it will be for a price. Instead it will just be a documentation of some kind where I give a plausible derivation (which will be pretty long, especially for the 19 and 20 BQTMs) for each (and where I can clearly get officially credited for these algs and the process to find them...anyone who uses my method*s* cannot get credit for any algs found from them without mentioning my name as well as theirs). In addition, I *will* be in favor of people displaying the algs I have found on Youtube, on their website(s), or anywhere as long as I am given credit (that includes not crediting computer solvers, which I *did not* use to find these algs)._
> 
> _Any suggestions on how I can do officially establish my credit is welcomed. But please, keep it to a minimum in this thread, for that is not puzzle theory (pm me if you can)._
> 
> _1/12/10 6:43pm central time USA_



I lol'd. You do realize that because you are being like this, and the algs are basically useless to most people, you won't be remembered for the algorithms. Instead, at this point, you will be remembered usually with the prefix 'lol' added to your name.

If you had released these algs as you found them, without putting up such a fight, whenever this would come up in a conversation, people would think, 'oh, I should find that thread that cmowla made to find that alg'.

Lucas Garron released his version of the OLL parity on here, and it is very often referred to as 'lucas's parity' or something similar.

Not sure if there's much you can do at this point to bring your reputation back up, but as a start you should probably just release all of your work, as it would be much better for you than to just keep it a secret, or even possibly, like this post describes, have people pay to see it.


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## Mr Cubism (Jan 13, 2010)

....."Pride before a fall".......


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## Christopher Mowla (Jan 13, 2010)

Mr Cubism said:


> ....."Pride before a fall".......


 
I was never "up" in this community to fall. People hated me ever since I typed my first post about me finding brief algs by hand (a thread that no longer exists--my first thread ever--this was my second thread), instead of using computers. Ever since I began mentioning things like that, I have been holding firm against all who tried to criticize me into giving them my algs because I feared that I wouldn't get credited for my algs based on their behavior towards me.

Only individuals like Henrik showed that if he was to see my algs, he would give me credit (not necessarily respect...but he has shown that too) for them (even though he didn't have any use for them except curiousity of the possibility and theory).

I personally don't have enough energy to come up with these algs by hand and not get credit for them. It was not easy to find them, especially since it was against all "odds", considering I even believed that there could be no pure edge flip algs shorter than 25q.

The way my mind works, getting credit for my work and getting respect from this community are two different things. I never demanded respect, but I do believe that if I came up with these algs, that I should be given credit for finding them. I know that was too much to ask (from most of those who responded afterwards, at least). That's really all I was trying to say. Not to demand fame. Instead, to request credit (not respect) for where it is due, just as people must cite their papers if something is not their original work. With that example, the writer doesn't have to respect the author of the source he/she is quoting or paraphrasing, but must give credit to him/her regardless.

Despite all of what I just said, I know from experience with this community, that someone is going pervert what I just said (making it mean something that I didn't intend it to mean). All I can hope for is for everyone who took sides with those who believed I demanded respect (instead of credit) for my work would reconsider.

I have learned a lesson so far...I have given out other algorithms, and most of what I got in return was criticism, ridicule, and butchery. I have nothing further to say except this:
Notice that I said in the post that everyone was commenting on lately, for people to pm me. No one has done this...they all have instead written it on this thread...this thread was good before, but now has lost the cube theory entirely (by the community's choice...I guess they did it for entertainment). 

There has been thousands of views on this thread, and I can only hope that a portion of those individuals can understand my reasoning more than those who have posted irrelevant and insulting comments to me.

If someone still wants to take something I said and put it out of my good intentional context, then, I really think this community is not even worth trying to be a part of or to waste my time writing posts and trying to contribute.


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## DavidWoner (Jan 13, 2010)

cmowla said:


> I feared that I wouldn't get credited for my algs based on their behavior towards me.



At no point did I get this impression from anyone. How did you come to this conclusion? I cannot recall an instance where someone has not received due credit for their contributions. As you said, we do not have to respect you, but credit should (and will) always be given where it is due. If your only reason for not releasing your algs before now is that you fear your work will go uncredited, then I urge you to reconsider. Though we may seem cruel to you, we still follow a code.



cmowla said:


> There has been thousands of views on this thread, and I can only hope that a portion of those individuals can understand my reasoning more than those who have posted irrelevant and insulting comments to me.



Once again, you mistake constructive criticism for insults. Are you so thin-skinned that you cannot see past our words and know that *we are trying to help you*? I would like to see you succeed, and I take from your words that you only seek to be credited for your work, and recognized as the creator. However, you must bear in mind that you cannot be credited for unpublished work. Yes, there are rude, cruel, and insulting people who will scorn new ideas. That is how the world and, especially, the scientific community often works. Your victory will come from proving the naysayers wrong, not from retreating.


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## Christopher Mowla (Jan 14, 2010)

DavidWoner said:


> cmowla said:
> 
> 
> > I feared that I wouldn't get credited for my algs based on their behavior towards me.
> ...





PatrickJameson said:


> I lol'd. You do realize that because you are being like this, and the algs are basically useless to most people, you won't be remembered for the algorithms. Instead, at this point, you will be remembered usually with the prefix 'lol' added to your name.



Another thing I forgot to mention was that I was shocked everyone substituted "respect" in for "credit". The only person who commented who actually read what I wrote was miniGOINGS.


miniGOINGS said:


> cmowla said:
> 
> 
> > StefanPochmann said:
> ...


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## DavidWoner (Jan 14, 2010)

cmowla said:


> DavidWoner said:
> 
> 
> > cmowla said:
> ...



He is saying that *you* won't be remembered for your algs, that doesn't mean that we will forget that the *algs* were created by you. And I was hoping you could provide an older post, one that inspired your initial fears.


Another thing I forgot to mention was that I was shocked everyone substituted "respect" in for "credit". The only person who commented who actually read what I wrote was miniGOINGS.


miniGOINGS said:


> cmowla said:
> 
> 
> > StefanPochmann said:
> ...


[/QUOTE]

Generally only respected work is worth mentioning/borrowing/using/etc, and therefore required credit. Going off what minigoings said, respected work is generally worth being credited. Even if people do not respect you as a person, your work can still speak for itself and earn respect on its own.


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## fanwuq (Jan 14, 2010)

Cmowla,

The problem was the way you initially presented yourself. You were being a bit vain. Don't worry about whether or not others will credit you with your discoveries. People who find and share things are usually credited for their discoveries. Just enjoy finding your algs and don't bother seeking social approval. Look at blade740's quote.
Just share everything and everyone will be happy. 
At first, I was pretty annoyed when you were making claims without any real evidence. Then, you provided some cool algs, and I and reThinker did recognize you for your work. MiniGoings is right, "If it's worth being credited, it will be."

You made some interesting algs that will be recognized in time. Right now people (you and your criticizers) are too concerned with petty matters.

I did not have the chance to find my calculator cable yet, but I'll download the program onto the calculator when I get the chance. Thanks for sending it!


Patrick,

Your comment was completely unnecessary and tasteless. You were not involved in this thread at all. All you did was come in for a lol and bang on this guy. That's not cool, man. Go back to #rubik. Cmowla will be remember for what he did and reveal, not for his imperfections. I can see that you are trying to offer cmowla some advice on how he should present himself, but I don't like your tone. Your advice will not accepted if you don't present yourself in an acceptable way. Therefore, the purpose of that post of yours was inherently mocking. If you have nothing positive or puzzle theory related to contribute, do not post anything.
Thanks.

Now can we go back to cube theory?

Edit:
Joey,

I will not make another post that is not cube theory related.



joey said:


> fanwuq said:
> 
> 
> > That's not cool, man. Go back to #rubik.
> ...


You can ask, but doesn't mean that I will answer.
I dare you to post the address of this post on #rubik right now. But don't do it if you know what is good for the forums. There is no need for trolling in the puzzle theory section. Thanks.
You just need to know that I will be critical next time team # does another mass trolling. I'm cool with y'all as people, but some of the things you discuss on there are quite petty. If what I thought was wrong, prove me wrong through action (or rather inaction). If I was right, you can trashtalk about me all you like and I will still appreciate the cubing community as a whole. 

Now can we go back to cube theory?


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## joey (Jan 14, 2010)

fanwuq said:


> That's not cool, man. Go back to #rubik.


Can I ask what you mean by that?


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## miniGOINGS (Jan 14, 2010)

Wow, I didn't know that my sentance would be so appreciated (signature change maybe?). 

But yea, credit is different than respect. If I found something that could potentially be important or effect future cubing, I would like credit where credit is due. I wouldn't demand respect, but I think that the OP does deserve a certain amount of credit if this truly is what he says it is.


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## PatrickJameson (Jan 14, 2010)

fanwuq said:


> Patrick,
> 
> Your comment was completely unnecessary and tasteless.


Tasteless, maybe, but unnecessary? I was simply attempting to put some sense into him, and since other methods that people have tried have failed, it was necessary to attempt a new approach.



fanwuq said:


> You were not involved in this thread at all.


 Doesn't mean I haven't been following it.



fanwuq said:


> All you did was come in for a lol and bang on this guy. That's not cool, man.



I did not just 'come in for a lol and bang on this guy', I attempted to get him to realize how silly he has been.



fanwuq said:


> Go back to #rubik.


What does #rubik have to do with this?



fanwuq said:


> Cmowla will be remember for what he did and reveal, not for his imperfections.


Why? This entire thread is basically pointing out his 'imperfections', what would make him not be remembered for that?

Also, as you point out later in your post, I did make suggestions on how he could improve his reputation. I'm simply stating facts about how he will, if he doesn't change, mostly be remembered for.



fanwuq said:


> Therefore, the purpose of that post of yours was inherently mocking.


Don't change/add any implied meaning to my post. This is not what I meant it to be and you know it.



fanwuq said:


> If you have nothing positive or puzzle theory related to contribute, do not post anything.


Why are you not also pointing this toward cmowla as well? He has not provided very much actual cube theory, but rather most of his posts are him gloating about how awesome he is for finding something.



fanwuq said:


> I dare you to post the address of this post on #rubik right now. But don't do it if you know what is good for the forums. There is no need for trolling in the puzzle theory section.


Huh? Firstly, many many posts on here have already been posted and discussed on #rubik. Secondly, what will posting this on #rubik do? Besides, it has already been posted once or twice. And thirdly, I'm not trolling. You implying/making up meanings of my actions are getting quite annoying. If you think this is a troll, it is not. It is merely defending your attack on me.


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## Ron (Jan 14, 2010)

Come on guys! Make love not war.

I have been following this thread and the other thread about the parity algorithms. I check it at least twice a day for new finds. Always looking for improvements found by smart members of our community.

People will get automatically credited if they publish stuff that's new AND useful.
My credit goes to Lucas Garron for his latest parity algorithm. For me that one is the fastest orientation parity for reduction method. I am already using it, except for cases where I can do set up moves to skip OLL. That is where I use the other parity algorithm by Lucas. ;-)

Btw. the thread is called: Odd parity Algorithms (specifically, single edge "flip"). Note the 'single edge "flip"'.

CMOWLA, welcome to our community. Please publish your on topic findings and I will gladly credit you if there are good. I am disappointed every day when I check the thread and I see you still haven't published.

Have fun!


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## reThinking the Cube (Jan 14, 2010)

Ron said:


> People will get automatically credited if they publish stuff that's new AND useful. My credit goes to Lucas Garron for his latest parity algorithm. For me that one is the fastest orientation parity for reduction method. I am already using it, except for cases where I can do set up moves to skip OLL. That is where I use the other parity algorithm by Lucas. ;-)



I'm curious as to which Lucas alg you are referring - lucasparity™ or lucaspaypal19q™, or some other alg(s)? 

*lucasparity™ - r U2 x r U2 r U2 r' U2 l U2 r' U2 r U2 r' U2 r '*

What about this new alg below for OLL parity?

*DoubleTrouble™ - r U2 r' U2 r' D2 r D2 x' r' U2 r U2 r' U2 2s2  *

SiGN notation r=(Rr), and 2s2=(fb)2=(y'M2)


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## Ron (Jan 14, 2010)

> I'm curious as to which Lucas alg you are referring - lucasparity™ or lucaspaypal19q™, or some other alg(s)?


In regular cases the reverse of lucasparity.
In OLL skip cases: Rw2U2 Rw'U2 Rw'U2 RwU2 F2RwF2Rw'F2 U2Rw2
I filtered that one from Lucas' long list of algorithms.


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## Christopher Mowla (Jan 15, 2010)

DavidWoner said:


> However, you must bear in mind that you cannot be credited for unpublished work.


Well, I did some research on copyright, free use, and publishing.

My work would most likely fall under "Fair Use" for the public, since I will not intend for it to be for a price, and it can be classified under scientific discoveries (just like all cube theory).
http://www.lib.umn.edu/copyright/fairuse.phtml

According to the US government, copyright is instantly given as soon as a work is in a "tangile form of expression", e.g., in forums on the internet (I don't need to publish it or purchase copyright rights from the government). Copyright does not protect my idea itself, but it does protect my credit for my original work.
http://www.alllaw.com/articles/intellectual_property/article11.asp

And, because my work falls under fair use, people can freely use my idea/methods, but still cannot declare it their original idea (if they do, they *are* breaching copyright...this is all I have been cautious about, not the rest--I want people to use my ideas, as long as they acknowledge that they are using my original work). They *do not* need permission to quote my work (though they must quote it, nonetheless) or use my idea, but they cannot use it to commercially benefit themselves.

They may only claim it their original work if I deliberately "hand over" my copyrights on my original work to them *in writing*.


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## Christopher Mowla (Jun 22, 2010)

*A Sub 25q Is Finally Here*

Although this is not my main approach for brief pure edge flip algorithms in quarter turns, it is a method from which generates a very fast 23q/16h (single slice turn algorithm). I have found it most recently, getting bored with my main method (I have come to a dead end with it). I have only told Lucas Garron about a the 16h/23q single slice turn pure edge flip algorithm you are about to see. I hope you enjoy! I know it's structure is a little awkward compared to what everyone is use to. Give it a shot! Memorize it and finger-trick it: you might be surprised on its speed (personally to me, it is the fastest single edge flip parity algorithm there is). For those who mention it to others, please give me credit. 



StefanPochmann said:


> cmowla said:
> 
> 
> > I have found the briefest pure edge flip in the world
> ...


This...

*SEE AND BELIEVE!* Sub 25q algorithms DO exist. _Although, with this method, (as far as I can see) there are a limited number of brief algorithms which are not conjugates of each other._

_All algorithms are in SiGN notation. So, those who are not familiar with this notation, just click the links and write down the algorithm in your own notation._

Based on how I found this algorithm (by hand), I cannot replicate this algorithm as far as both the half turn and move count combination (as far as I can see right now, it is unique. _Well, basically--see italicized note after algorithm is presented._). I tried my hardest to find another 16h, but I only ended up with a conjugate of this same algorithm over and over again. Due to this, I couldn't help but give it a name.

I present: cmowlaparity. (16h/23q)

*Speed Form (All Wide Turns)*
On the 4X4X4 (and other even cubes):
x' r2 U2 l' U2 r U2 r U2 x' U r U' F2 U r' U r2 x 

On the 5X5X5 (and other odd cubes):
x' 2r2 U2 3l' U2 2r U2 2r U2 x' U 2r U' F2 U 2r' U 2r2 x

*Pure Form (Speed Version)*
On the 4X4X4 (Even Cubes):
x' r2 U2 l' U2 2R U2 r U2 x' U 2R U' F2 U 2R' U r2 x

On the 5X5X5 (Odd Cubes):
x' 2r2 U2 3l' U2 2R U2 2r U2 x' U 2R U' F2 U 2R' U 2r2 x

*Pure Form (All single slices/non-speed Version)
*For all size cubes:
x' r2 U2 l' U2 r U2 l x U2 x' U r U' F2 U r' U r2 x (4X4X4)
x' r2 U2 l' U2 r U2 l x U2 x' U r U' F2 U r' U r2 x (5X5X5)


_One last note: if the single U moves are reversed we still have a pure edge flip algorithm, but the speed form (all wide turns) destroys the cube. Hence, this algorithm is unique in the fact that it is a legitimate algorithm to apply wide turns to without any problems. So, technically, there is another 16h/23q algorithm:
_x' r2 U2 l' U2 2R U2 r U2 x' U' 2R U F2 U' 2R' U' r2 x
_In my opinion, I think the other version of this alg (previous) is faster with the individual U turns going that way instead of like the algorithm directly above anyway (which is a plus!)._

-------------
Now, a 25q 3-Edge Flip algorithm can result from adding two set-up moves to the speed-form of cmowlaparity
On Even Cubes:
x' U' r 2R U2 l' U2 r U2 r U2 x' U r U' F2 U r' U r' 2R' U x
On Odd Cubes:
x' U' r 2R U2 l' U2 r U2 3r U2 x' U r U' F2 U r' U r' 2R' U x

-------------
Here is a K4 Alg for swapping two adjacent wing edges (21q/15h)
On Even Cubes: (notice that for the 4X4X4, you can merge the last two slice turn moves as M' l')
2L'2 U l U2 2R' U2 r' U2 x U' 2R' U x' U2 x U' 2R 2L'2
On Odd Cubes:
2L'2 U l U2 2R' U2 3r' U2 x U' 2R' U x' U2 x U' 2R 2L'2

 
I have found an algorithm that is possibly as close as it can get to rethinking the cube's request as far as the algorithm being OLL parity (not double parity) and being the fastest OLL parity which takes full advantage of the front-right F2L slot and U-layer. I have posted that alg in that thread. @Rethinker, it took me 6 months to come across something that fits your description, but now it's finally here (on the forums).

_I DID NOT use a computer solver to form any of the algorithms I have (or will) release. I have derived them all by hand._


By Christopher Mowla. Date: Jun 22, 2010

EDIT: I just made a video on youtube for cmowlaparity. However, I don't call it that there.
EDIT: The speed-form of this algorithm is 23 plane quarter turns--the least number I have ever seen for a center-preserving algorithm which also preserves F(N-1)L. The second best I have seen is one of my pure edge flip algorithms: it is 24 plane quarter turns for some cases and 26 plane quarter turns for the rest.

EDIT:
I just redid my video. I updated the link above as well. I think it's much better now (it also includes the 3-edge flipper from cmowlaparity).


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## Christopher Mowla (Jul 16, 2010)

The same set-up moves applied to the speed version of cmowlaparity.


cmowla said:


> Now, a 25q 3-Edge Flip algorithm can result from adding two set-up moves to the speed-form of cmowlaparity
> On Even Cubes:
> x' U' r 2R U2 l' U2 r U2 r U2 x' U r U' F2 U r' U r' 2R' U x
> On Odd Cubes:
> x' U' r 2R U2 l' U2 r U2 3r U2 x' U r U' F2 U r' U r' 2R' U x


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## unsolved (May 20, 2015)

Wow that really silenced all of the non-believers. And not one subsequent post praising your work, so let me be the first.

Congratulations Chris, very nicely done!


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## Christopher Mowla (May 22, 2015)

unsolved said:


> Wow that really silenced all of the non-believers. And not one subsequent post praising your work, so let me be the first.
> 
> Congratulations Chris, very nicely done!


Thank you very much!

For those new to the forums viewing this thread, I finally released my groundbreaking algorithms in Methods for Forming Parity Algorithms, and I started New Two-Corner Swap Algorithm Technique for Big Even Cubes (PLL Parity) for the development and discussion of two corner swap PLL parity algorithms.


I wasn't expecting this thread to see the light of day again. However, since I did delete a lot of my posts from this thread (out of frustration), I believe it's fair for me to provide a means by which people can see my deleted posts (even though one can see at least a portion of some of them because they were quoted by other members). Before I deleted _most_ of them, I saved the thread for offline viewing.

Here is a link to my saved thread with most of my posts of this thread for a more complete reading.

In addition, here is a link to the saved version of the sister thread, WANTED: New Dedge Flip Algorithm!, before I deleted my posts there.

(To my knowledge, I did not delete any of my posts which are after the last posts in these saved threads.)

It might be worthy to note that the accusation which started around here about reThinking the Cube modifying my alg to create his alg "reParity™" might have indeed been coincidental, but I later did some further investigation (see below the dashed line).

I just thought that I would mention all of this to give a better historical account of what happened in these two very chaotic but barrier breaking parity algorithm threads.

EDIT:
I forgot to mention that I found the following algorithms by hand later which much better matched what reThinking the Cube was looking for:
2R' U2 F' U2 F U2 2R' U2 2R' U2 2R' F' U2 F 2R' (21,15)
2L U2 F' U2 F U2 2L U2 2L U2 2L F' U2 F 2L (21,15)
2R' U R U2 R' U' 2R' U2 2R' U2 2R' U' R U2 R' U 2R' (21,17)
2L' U' R U2 R' U 2L' U2 2L' U2 2L' U R U2 R' U' 2L' (21,17)

And the following are very fast "Petrus Parity" algorithms I found as well for those who enjoyed Stefan's 24q double parity algorithm,
r' U R U (r' U2)3 r2 U R' U' r2 U' R' U r' (24,19),
from the beginning of this thread. Note that these are not double parity algorithms.

r' U R' U2 R U' r' U2 r' U2 r' U' R U2 R' U r' (21,17)
r' U' L' U2 L U r' U2 r' U2 r' U L' U2 L U' r' (21,17)

It also turns out that the most compact "OLL Parity" algorithm which has a repeating sequence in it (like Stefan's alg) is my move optimal adjacent double parity algorithm. It can be written like so: (2R2 F r' F') 2R' (2R' U2)4 (F r F' 2R2) (23,16).


(All of these algorithms are on the 4x4x4 parity algorithms page now along with the rest of the parity algorithms I found.)


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## unsolved (May 24, 2015)

cmowla said:


> It also turns out that the most compact "OLL Parity" algorithm which has a repeating sequence in it (like Stefan's alg) is my move optimal adjacent double parity algorithm. It can be written like so: (2R2 F r' F') 2R' (2R' U2)4 (F r F' 2R2) (23,16).
> 
> 
> (All of these algorithms are on the 4x4x4 parity algorithms page now along with the rest of the parity algorithms I found.)



I have a question.

Now that I am working on a 3-stage solver where all of the middle edges are solved first, I was wondering if there are any algs showcasing the longest solve involving unsolved corners.

Example:

https://alg.cubing.net/?alg=U_F-_U-_(L_R2_F2_B-)4_U_F_U-
&puzzle=4x4x4

I thought the "deepest corner" solve was around 11 moves or so (from all of the corner pruning results posted by some programmers). Is there a much faster solve for the position shown above? I haven't given it to my solver yet, it is still working on some puzzles from the Fewest Moves Challenge.


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## Christopher Mowla (May 24, 2015)

unsolved said:


> I have a question.
> 
> Now that I am working on a 3-stage solver where all of the middle edges are solved first, I was wondering if there are any algs showcasing the longest solve involving unsolved corners.
> 
> ...


I started a thread in the past which is actually relevant to what you seek (because this topic has nothing to do with parity algorithms). So it might be good to post there if you have any further questions or wish to start any discussion on the topic.

In my thread, I was given this source. Search for "Analysis of 3x3x3 corners only" to find that the number you are seeking is *14* (*11* is when we ignore all of the puzzle except for corners, meaning that we are able to destroy other piece types in order to solve the corners themselves optimally). Similar data on the middle edges is directly below this corner data, and as you can see the work is still in progress for some of the edge data.


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## Herbert Kociemba (May 24, 2015)

unsolved said:


> https://alg.cubing.net/?alg=U_F-_U-_(L_R2_F2_B-)4_U_F_U-
> &puzzle=4x4x4
> 
> I thought the "deepest corner" solve was around 11 moves or so (from all of the corner pruning results posted by some programmers). Is there a much faster solve for the position shown above? I haven't given it to my solver yet, it is still working on some puzzles from the Fewest Moves Challenge.



Since you not only have to solve the corners but also have to keep the edges, the shortest solution is longer. Since every 3x3x3 cube position can be solved in <= 20 moves your given 22 move generator of course can be shortend. The shortes solution using only outer face turns is 18 moves: U (B' U2 D' F2)^4 U' (18f*).

Theoretically there is some chance that also using inner slice moves there is a shorter solution, but that is not very likely.


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## Herbert Kociemba (May 24, 2015)

unsolved said:


> https://alg.cubing.net/?alg=U_F-_U-_(L_R2_F2_B-)4_U_F_U-
> &puzzle=4x4x4
> 
> I thought the "deepest corner" solve was around 11 moves or so (from all of the corner pruning results posted by some programmers). Is there a much faster solve for the position shown above? I haven't given it to my solver yet, it is still working on some puzzles from the Fewest Moves Challenge.



Since you not only have to solve the corners but also have to keep the edges, the shortest solution is longer. Since every 3x3x3 cube position can be solved in <= 20 moves your given 22 move generator of course can be shortend. The shortes solution using only outer face turns is 18 moves: U (B' U2 D' F2)^4 U' (18f*).

Theoretically there is some chance that using inner slice moves there is a shorter solution, but that is not very likely.


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## Christopher Mowla (May 28, 2015)

@unsolved, as I mentioned in my first response to you, this is NOT relevant to this thread.

So please either start a new topic or find one which is relevant to post in. You have to think about those who are going to view this thread in the future. They are not going to be happy seeing you starting a whole new topic in an existing one.

Thank you for your consideration.


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