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

[Ron]

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!

 

[reThinking the Cube]

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)

 

[Ron]

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.

 

[Christopher Mowla]

However, you must bear in mind that you cannot be credited for unpublished work.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

 

[Christopher Mowla]

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.

I have found the briefest pure edge flip in the world

Proof, please.

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).

 

[Christopher Mowla]

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

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

 

[unsolved]

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!

 

[Christopher Mowla]

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.)

 

[unsolved]

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.

 

[Christopher Mowla]

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.

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.

 

[Herbert Kociemba]

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.

 

[Herbert Kociemba]

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.

 

[Christopher Mowla]

@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.