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

[Christopher Mowla]

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.

Maybe you can share your discovery with us ?

In time.

 

[rachmaninovian]

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

 

[joey]

lol potato has laser eyes you know? :3

I don't even.

 

[rachmaninovian]

lol potato has laser eyes you know? :3

I don't even.

i insist!

 

[Christopher Mowla]

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.

 

[Christopher Mowla]

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'

 

[Christopher Mowla]

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]

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.

 

[qqwref]

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.

 

[Stefan]

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.

 

[Henrik]

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.

 

[Stefan]

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.

 

[Christopher Mowla]

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".

 

[joey]

Just post the alg.

 

[Stefan]

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

 

[Christopher Mowla]

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.

 

[Stefan]

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

I assume you mean what SiGN calls 2D.

 

[qqwref]

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.

 

[andyt1992]

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.

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.

 

[Christopher Mowla]

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).

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.