A Collection of Algorithms

[Kirjava]

M' U2 F' U' F2 R' F' R2 U' L'

lolwtf

 

[irontwig]

Conjugated (that should be) wellknown 8-move pure OLL

 

[Robert-Y]

F R2 D R' U R D' R2 U' F'

yaaaaaah

lol waffle - I actually learn all the algs I post here that aren't useless. (and some of the useless ones XD)

rob yau found this - F R U' R D R' U2 R D' R2' U' F'

Replace the F and F' in both algs with f and f'

 

[Kirjava]

Wow. That's awesome. I think I know every edge case for that CLL now O_O

 

[Kirjava]

DiagPi4Flip
B' R2 F R F' U R B L U' L'

change U to U', invert and cleanup;

FatNiklas
L U2 L' B' R2 F R F' U' R B L U' L'

invert and repeat a section;

DiagT
L U L' B' R' U' F R' F' R F R' F' R2 B

 

[Escher]

Cmowla would be proud.

 

[Kirjava]

RUR'F' is powerful for finding stuff by hand

R U R' U F' L' U L F U' R U' R'
R U R' U F' L' U' L F U' R U' R'
R U R' U F' L' U2 L F U' R U' R'

 

[Robert-Y]

COLL/CMLL:

DiagAS: R U R' F' (Fat sune) F R U' R'
DiagS: R U R' F' (Fat antisune) F R U' R'

I agree, Thom

EDIT:

DiagAS: R U R' F' (Sune) F R U' R'
DiagS: R U R' F' (Antisune) F R U' R'

EDIT2:

Anti Niklas + UF/UB flip: (U2) R U R' F' (Niklas) F R U' R'
Anti Niklas + UF/UL flip: (U2) R U R' F' (Anti Niklas) F R U' R'
Niklas + UF/UL flip: (U2) L' U' L F (Niklas) F' L' U L
Niklas + UF/UB flip: (U2) L' U' L F (Anti Niklas) F' L' U L

 

[Christopher Mowla]

"2-Gen" OLL parity algorithms (pure form)

Cmowla would be proud.

Of what?
------------------


Now to everyone, I present the first "2-gen" pure edge flip algorithm for big cubes.

Yeah I know it's long, but it's "2-gen"!

(r U2 r U2)
[r, U R U r U2 r' U' R' U']
(r)
(U2 r' U2 r')

=r U2 r U2 r U R U r U2 r' U' R' U' r' U R U r U2 r' U' R' U' r U2 r' U2 r' (35q/29h)

Note 1: The first and last two r's can be made wide.
Note 2: For those who are curious about what happens if you convert all of the single slice r turns to wide, also add in the bold move below to preserve the most.

Rw U2 Rw U2 Rw U R U Rw U2 Rw' U' R' U' Rw' U R U Rw U2 Rw' U' R' U' Rw R U2 Rw' U2 Rw'


Note 3: The following algorithms can be devised for other cases of 2-cycle OLL parity from this one using the technique of shifting from my "Methods" thread:

Diagonal (oriented)
Rw2 U2 r' U R U r U2 r' U' R' U' r2 U R U r U2 r' U' R' U Rw2 (29q, 23h)

Across (oriented)
x r U' R' U' r2 U R U r U2 r' U' R' U' r' U R U r U2 r2 x' (25q, 21h)

Across (un-oriented)
Rw U' R' U' r2 U R U r U2 r' U' R' U' r' U R U r U2 r' Rw' (25q, 22h)


Directly Across:
Rw U2 r' U2 r' U' R' U' r' U R U r U2 r' U' R' U' r2 U R U r2 U2 Rw' (31q, 25h)
Rw U' R U r U2 r' U' R' U' r U R U r U2 r' U' R' U' r2 U2 Rw' (27q, 23h)

Directly and diagonally across (even cubes only!)
U R U r U2 r' U' R' U' r2 U R U r U2 r' U' R' U' r u2 r2 u2(29q, 23h)

(Sorry, no un-oriented adjacent from this!)

Note 4: Obviously Double parity (4-cycle) can be made from this idea as well:

Doubleparity
r' U' R' U' r' U R U r U2 r' U' R' U' r2 U R U r U2 r U2 r' U2 (29q, 24h)


@Stefan, what do you think of the pure edge flip algorithm? I know it's not brief, but I thought you might be interested in it since you have made a 2-gen double parity/Petrus Parity in the past.


Edit: I have added another (shorter) algorithm for the directly across case.

 

[Robert-Y]

X perm for megaminx:

L' (Triple sune) L

 

[bobthegiraffemonkey]

X perm for megaminx:

L' (Triple sune) L

I've used that for a while, and using a single sune is good for OLL. Also, try L' (sune) L, then solve using the same trick from the other angle (using antisune). Not sure of notation, but it should be easy to figure out what I mean:

(Lf' (R U R' U R U2' R') Lf) (Lb (R' U2' R U R' U' R) Lb') (U)

also, don't know how many of these are known:

(R U R' U) (R U R' U) (R U' R' U') (R U' R' U2) (R U R' U') (R U2 R')

(R U2 R' U) (R U2' R' U) (R U2' R') (L' U' L U' L' U2 L) (last part may benefit from z rotation)

(R U R') z (R' U' R' U R2) D (R2' U' R U D')

x' (R2 U R') D (R U2' R') D' (R U R2')

R2 U2' R2' U' R2 U2' R2'

(R U2 R2' U' R2 U' R' U R' U R U2') (R U R' U R U2' R')

R U R' U' R' L F R F' L'

Megaminx is cool.

 

[JonnyWhoopes]

I don't know if this has been posted anywhere before, but I found an intuitive RUL A-Perm.

R U' L' U' L2 U' R2 U L2 U' R2 U2 L U R'

 

[aronpm]

I don't know if this has been posted anywhere before, but I found an intuitive RUL A-Perm.

R U' L' U' L2 U' R2 U L2 U' R2 U2 L U R'

So you say this is intuitive? This algorithm is a 3 move setup to an A9 commutator. RU'L' setup, and the A9 is U' L2 U' R2 U L2 U' R2 U2.

If this is intuitive, the A perm should be too: the A perm is an A9 commutator too.

BTW: an A9 commutator is a setup to an 8 move commutator, but the setup cancels. For the A perm, (x) R' setup gives the commutator U R'D2R U' R'D2R.

 

[JonnyWhoopes]

So you say this is intuitive? This algorithm is a 3 move setup to an A9 commutator. RU'L' setup, and the A9 is U' L2 U' R2 U L2 U' R2 U2.

If this is intuitive, the A perm should be too: the A perm is an A9 commutator too.

BTW: an A9 commutator is a setup to an 8 move commutator, but the setup cancels. For the A perm, (x) R' setup gives the commutator U R'D2R U' R'D2R.

:confused: I'm slightly confused... are you saying that it is not intuitive? I never said (or implied, at least not intentionally) that the A9 was not intuitive. I simply figured I'd post something I found because I thought it was neat and because it was RUL. I haven't seen many RUL A perms, so I thought I'd contribute.

Would you even have responded if I hadn't mentioned that I thought it intuitive? Perhaps I should have just left that part out and posted it just for the sake of RUL:rolleyes:

::EDIT:: Perhaps we have conflicting definitions of intuitive? ::EDIT::

 

[riffz]

I haven't seen many RUL A perms, so I thought I'd contribute.

R2 D2 R U R' D2 R U' R

--> U2 R2 U L U' R2 U L' U

 

[Christopher Mowla]

Genuine 2-Gen Pure Single Edge Flip Algorithm

r U2 r' U2 r2 U2 r U2 r U r' U r' U2 r2 U2 r' U2 r' U r U' r U2 r2 U2 r U2 r' U2 r' (45q, 31h)

Important note: Do not convert to wide turns, unless you want to scramble your cube!


My Comments
The half turn move count isn't that bad, but for the quarter turn move count, :fp.

If 31 is God's number for this case in <r, U>, then pure 2-gen is basically double the length of optimal algorithms in the move set <r, l, U, F>, which many know to be of length 15h. If I am not mistaken, the minimum for <r, l U> is 18h.

 

[Christopher Mowla]

Here is a briefer semi 2-Gen Single Edge Flip:

Rw U2 r U2 r' U2 r2 U' R U r' U R' U' r U R U2 R' U' r' U2 r2 U2 Rw' (33q, 25h)

There are definitely briefer algorithms in <r, R, U> for other 2-cycle cases. I can post them later, if anyone is interested.


EDIT:

A few more turns can be made wide and still be pure:
Rw U2 r U2 r' U2 Rw2 U' R U r' U R' U' r U R U2 R' U' r' U2 Rw2 U2 Rw'

 

[oll+phase+sync]

Here is my version of intuitiv aPerm:

R'D2R U R'D2R U R'D2R U2 R'D2R

It's a commutator but rarher hard to see , as I believe.

M'D2M U M'D2M U M'D2M U2 M'D2M

That U Perm is the other part of my "memorization zero" beginner method, - but al beginners I tried to teach failed on proper repetition /)

P.S: D2 can be replaced by D/ D' but that is not beginner friendly I believe.

 

[Christopher Mowla]

A Pseudo 2-Gen OLL parity for <U, Rw>.

Rw U2 Rw U2 r2 U Rw U2 Rw U2 Rw' U2 Rw' U' r U Rw U2 Rw U2 Rw' U2 Rw' U Rw' U2 Rw' (37q/ 27h)

This is applicable to odd cubes if you include the central slice for every wide turn (so it's farther from 2-Gen for odd cubes, but for even cubes, it's very close to being genuine).

Important note! For all size cubes, the wide turns mean to turn the entire right half of the cube, no matter which orbit of edges you wish to correct. The only moves, therefore, which will vary from orbit to orbit are the two single slice turns of r.

Although this algorithm may seem long, if all r turns were wide, it would be even longer. I am not sure what the future will bring, but this algorithm type (with a couple of single slice turns while most are wide) may be much more practical to execute (for fun) than a pure 2-gen in <U, Rw>.

EDIT:
I know I often outsmart myself after making "impossibility" claims, but I must admit that I cannot imagine being successful in making a pure edge flip strictly in <U, Rw>. (Not that it is impossible for an algorithm to exist). So, on the surface, this just might be as close as I can ever get. I am surprised the length was not longer than what it turned out to be.

 

[Lucas Garron]

Now to everyone, I present the first "2-gen" pure edge flip algorithm for big cubes.

Interesting, but definitely not the first. I asked for one a few years ago, and I Mitchell Stern found it.

I must admit that I cannot imagine being successful in making a pure edge flip strictly in <U, Rw>. (Not that it is impossible for an algorithm to exist).

Fortunately, that's an easy question to answer.