# <M,U> 3-cycles



## blah (Jun 1, 2011)

Here's a list of all non-isomorphic cases and their optimal algs:

M U2 M' U2 (4) - Good M
U M U2 M' U (5) - Good T
M U M U2 M' U M' (7) - Bad T
M U M' U2 M U M' (7) - Middle U
M2 U M U2 M' U M2 (7) - Normal U
M U M' U M U M' U (8) - Dog Cat
M U2 M U M' U2 M' U' (8) - Duck Duck
M U M U M' U M U M2 (9) - Cat Cat
M U M U2 M U2 M2 U' M' (9) - Goose Duck
U' M U M U2 M' U M' U (9) - Weird M
U' M U M' U M U M' U2 (9) - Duck Goose
U2 M U2 M U M' U2 M' U (9) - Dog Dog
M U M U2 M U M' U2 M' U2 M' (11) - Cat Dog
M U M U' M' U' M U' M' U2 M' (11) - Coffee
M U M' U' M U' M' U' M U2 M' (11) - Side U
M2 U M U' M' U' M U' M' U2 M2 (11) - Goose Goose
U2 M U M U M U2 M' U M' U' M' U2 (13) - Bad M

So apparently 17 of the 27 cases can be done with MU algs  But it really isn't hard at all to see why 

Related to this thread on <R,U> 3-cycles. Names come from this thread on my classification of BH cases(the 27 cases also come from this thread).


----------



## sa11297 (Jun 1, 2011)

how did you get all of those algs?


----------



## blah (Jun 1, 2011)

Perl.


----------



## Nickmaovich (Jun 1, 2011)

Nice ones. But, how should it be used?


----------



## irontwig (Jun 1, 2011)

Non-isomorphic:

M U2 M' U2 
U M U2 M' U 
M U M U2 M' U M' 
M U M' U2 M U M' 
M2 U M U2 M' U M2 
M U M' U M U M' U 
M U2 M U M' U2 M' U' 
M U M U M' U M U M2 
M U M U2 M U2 M2 U' M' 
M U M2 U2 M' U2 M' U' M' 
M U2 M' U M U2 M U' M2 
M2 U M U M' U M U M 
U' M U M U2 M' U M' U 
U M U M U2 M' U M' U' 
U' M U M' U M U M' U2 
U2 M U M' U M U M' U' 
U2 M U2 M U M' U2 M' U 
U M U2 M U M' U2 M' U2


----------



## blah (Jun 1, 2011)

Nickmaovich said:


> Nice ones. But, how should it be used?


Use these instead of supercube-safe commutators on a 3x3x3?


----------



## blah (Jun 1, 2011)

Completely redone. Check the first post again.


----------



## cmhardw (Jun 1, 2011)

Chester, this is really great! I've always thought that using these will greatly speed up 3x3x3 edge execution whenever an easy case comes up. Awesome stuff!


----------



## lucarubik (Jun 1, 2011)

interesting... I will take a look of this and see if i can improve any case on BLD


----------



## Owen (Jun 1, 2011)

Here comes a stupid question: 

What are these cases for?


----------



## Stefan (Jun 1, 2011)

Owen said:


> Here comes a stupid question:
> 
> What are these cases for?


 
I'm guessing you missed that this is about blindsolving...


----------



## RyanReese09 (Jun 1, 2011)

Owen said:


> Here comes a stupid question:
> 
> What are these cases for?


 
The only stupid questions are those that go unasked.

Part of edge commutators for BLD, as Stefan mentioned.


----------



## Stefan (Jun 2, 2011)

RyanReese09 said:


> Part of edge commutators for BLD, as Stefan mentioned.


 
Commutators?


----------



## RyanReese09 (Jun 2, 2011)

Stefan said:


> Commutators?


 
Stefan?


----------



## Diniz (Jun 2, 2011)

RyanReese09 said:


> Stefan?


 
They are not commutators.. But yeah, you can use them for blind..


----------



## blah (Jun 2, 2011)

M U2 M' U2 (4) - Good M
[M, U2]

U M U2 M' U (5) - Good T
[U: M, U2]

M U M U2 M' U M' (7) - Bad T
[M U: M, U2]

M U M' U2 M U M' (7) - Middle U
[M U: M', U2]

M2 U M U2 M' U M2 (7) - Normal U
[M2 U: M, U2]

M U M' U M U M' U (8) - Dog Cat
M U2 M U M' U2 M' U' (8) - Duck Duck
M U M U M' U M U M2 (9) - Cat Cat
M U M U2 M U2 M2 U' M' (9) - Goose Duck
U' M U M U2 M' U M' U (9) - Weird M
U' M U M' U M U M' U2 (9) - Duck Goose
U2 M U2 M U M' U2 M' U (9) - Dog Dog
M U M U2 M U M' U2 M' U2 M' (11) - Cat Dog
M U M U' M' U' M U' M' U2 M' (11) - Coffee
M U M' U' M U' M' U' M U2 M' (11) - Side U
M2 U M U' M' U' M U' M' U2 M2 (11) - Goose Goose

U2 M U M U M U2 M' U M' U' M' U2 (13) - Bad M
[U2 M U M U: M, U2]

There are *some* (conjugated) commutators in there...


----------



## Sakarie (Jun 2, 2011)

blah said:


> Here's a list of all non-isomorphic cases and their optimal algs:
> 
> M U2 M' U2 (4) - Good M
> U M U2 M' U (5) - Good T
> ...



These algs are nice, but unfortunately you need just the right cycle for some of them to be the best. I won't use the Bad T, since UF is my buffer, and I'd say [M D M', U2] is faster than y <MU> y'. And I think there are better algs for most cases for all of the 9-movers.


----------



## lucarubik (Jun 2, 2011)

M U M' U M U M' U (8) - Dog Cat
M U2 M U M' U2 M' U' (8) - Duck DuckU' M U M U2 M' U M' U (9) - Weird M
theese i find them cool
where did you get them?
what does isomorphic mean?
wich are those 27 cases?
nice job anyway!


----------



## blah (Jun 2, 2011)

Sakarie said:


> These algs are nice, but unfortunately you need just the right cycle for some of them to be the best. I won't use the Bad T, since UF is my buffer, and I'd say [M D M', U2] is faster than y <MU> y'. And I think there are better algs for most cases for all of the 9-movers.


I don't know what you're talking about. MU algs are mostly sub-1. I'd pick an MU 9-mover over any 8-mover any day of the week.

UF is my buffer as well. Besides, nowhere did I say "HEY EVERYONE LOOK AT THESE AWESOME ALGS COME USE THEM!!!" I just decided to write some code to generate all those MU algs one day and publish them here. Simple as that. What I did was purely academic.


----------



## Sakarie (Jun 2, 2011)

blah said:


> I don't know what you're talking about. MU algs are mostly sub-1. I'd pick an MU 9-mover over any 8-mover any day of the week.
> 
> UF is my buffer as well. Besides, nowhere did I say "HEY EVERYONE LOOK AT THESE AWESOME ALGS COME USE THEM!!!" I just decided to write some code to generate all those MU algs one day and publish them here. Simple as that. What I did was purely academic.


 
I'm sorry, I didn't mean it like that. I weren't trying to degrade your effort, just say that I'll probably not use all of them.

And "what I'm talking about" is that if I have the threecycle UF UB LD, I'd rather do [M D M', U2] than y' M U M U2 M' U M' y.


----------



## amostay2004 (Jun 3, 2011)

Really cool cycles there. Might actually switch to some of them, when I finally find time to practise.


----------

