# A Collection of Algorithms

Discussion in 'General Speedcubing Discussion' started by pjk, Mar 22, 2007.

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1. ### KirjavaColourful

6,122
24
Mar 26, 2006
WCA:
2006BARL01
snkenjoi
come on... (rU2)*5 is nine moves without the last U2 that preserves centres.

no idea for LL though.

828
5
Sep 17, 2009
New Orleans, LA
4EverTrying
Too long to not have in a spoiler.
It's helpful to note that (r U2)5 U2 = [r: [U2, r] [r2 U2: r]]

That is,
r
U2 r U2 r'
r2 U2
(r)
U2 r2
r'

Clearly the first and last moves are outer conjugates to complete the centers, the second piece is a commutator, the parenthesized move is the quarter turn. The only not so obvious part (well not to me, but...) is the r2 U2 conjugates.

If you start out with a solved cube and do U2 r U2 r' r2 U2, you will see that when you do (r) next, the 1x(n-2) center block in face B in slice r replaces the 1x(n-2) center block in face D in slice r of the same color. In fact, that's why this 4-cycle even works at all, because with these conjugates, r2 U2, around the quarter turn, we displace only half of the center pieces. This is similar to my main method for forming 2-cycles, regardless if it's wide turn based (the Holy Grail) or single slice turn based (conventional algs) because we do a 3-cycle of three fourths of a slice and do a quarter turn to put back half of the center pieces.

The "Standard Dedge Flip" alg, or any other 2-cycle algorithm I have derived or my methods apply to can be derived this way too.

Since (r U2)5 U2 is 2-gen, the most popular dedge flip alg that can be modeled exactly like it is "Waffle's Alg" (I know that Sarah said Chester posted it before...anyway)

l U2 r' U2 r U2 l' U2
r U2
(r')
U2 r'

(Just conjugate all of that with r' U2 r2 to achieve a transformation of that alg).

The algorithm I posted previously is literally a 2-cycle of wings but with 3x3x3 distortion as well, not a 4-cycle (you probably know this, but it seems you are relating the two different cycles too closely). Proof: See the translation link to the 5x5x5.

If there is a 2-cycle algorithm of length 9 (or even less than 12) that can preserve the centers, much less everything but the LL, I certainly don't know how to approach it. I believe I have shown that I have a good understanding of (r U2)5 U2 to the extent that I linked my representation of it with my methods. Keep in mind also that (r U2)5 U2 is so brief because, by my outline, there were several move cancellations and the commutator was as brief as a commutator can be.

Last edited: Sep 23, 2011
3. ### KirjavaColourful

6,122
24
Mar 26, 2006
WCA:
2006BARL01
snkenjoi
Anyone have something good for this; M' U r2 F2 r F R' F2 r U' R M ?

4. ### CubenoviceForever Slow

As you're Roux I suppose you are not looking for the standard M U R U R' U' M2 U R U' r' as OLL?
But rather something that solves the whole cube...

5. ### KirjavaColourful

6,122
24
Mar 26, 2006
WCA:
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snkenjoi
lol of course not - OLLCP plz

6. ### CubenoviceForever Slow

Still not enough info

Do you want something instead of M' U r2 F2 r F R' F2 r U' R M or something thart solves M' U r2 F2 r F R' F2 r U' R M

7. ### KirjavaColourful

6,122
24
Mar 26, 2006
WCA:
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snkenjoi
They're both the same things.

EDIT:
<+RobertY> x R B' R2' U2 B' R U R' B U2 R2 B R' x'
<+RobertY> F R' F R2 U R' U' F2 U' L F' L' F
<+RobertY> Colourful: there's also R' F R F' U R2 U B U' B2 R' B R'
(M' U') (R2 B2 R' U' r B2 R') (B r2' R)

Last edited: Sep 24, 2011
8. ### tellerREAL Fingertricks!

Dec 15, 2008
West Virginia
WCA:
2010COAT01
TellerWest
OLL 47

S' R U2 R2 U' R2 U' R2 U2 R S

9. ### RpottsMember

1,859
26
Mar 23, 2008
KC
WCA:
2010POTT01
rpotts1
there is no way that is faster than B' (R' U' R U)*2 B or mirrors or y2 R' U' (R' F R F')*2 U R

how fast can you do it?

10. ### tellerREAL Fingertricks!

Dec 15, 2008
West Virginia
WCA:
2010COAT01
TellerWest
I have not finished the grips on this yet, so I cannot say. Wanted to put it out there because it *oozes* RU potential and you know RU can really fly sometimes. The S is probably off-putting, but I hope to set that right...

11. ### tellerREAL Fingertricks!

Dec 15, 2008
West Virginia
WCA:
2010COAT01
TellerWest
Lefty R-Perm:

S R' U R U' S' U' R' U R U x' U' R U R'

12. ### ianographyMember

832
2
Nov 24, 2010
Shanghai, China
WCA:
2009BOUR01
I have yet to see you sub-1 a case with an 'S'. Video pl0x?

13. ### tellerREAL Fingertricks!

Dec 15, 2008
West Virginia
WCA:
2010COAT01
TellerWest
My "S" rotationless F2L edge insert is easily sub 1. Does that count? But no...no promises on the sub-1...who do you think I am, Andrew Ricci?

14. ### KirjavaColourful

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Mar 26, 2006
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snkenjoi
R2 yz R2 x' D R2 xz'y' R2 U2 R2 yz R2 x' D R2 xz'y' R2

noregrip

Last edited: Sep 30, 2011
15. ### KirjavaColourful

6,122
24
Mar 26, 2006
WCA:
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snkenjoi
R2 F2 r U2 R U' r2 F2 r F R

still on the OLLCP journey ~_~

16. ### uberCuberMember

Jun 24, 2010
Tucson, Arizona, USA
WCA:
2011THOM01
Wtf
How fast can you do that?

6,122
24
Mar 26, 2006
WCA:
2006BARL01
snkenjoi
like 1.4

18. ### cubersmithMember

731
0
Dec 6, 2010
Glasgow, Scotland, UK
WCA:
2011SMIT04
QoobN00b
I think <R,U,F> is better than <R,U,L> but 0.8x is good :O

19. ### KirjavaColourful

6,122
24
Mar 26, 2006
WCA:
2006BARL01
snkenjoi
r' U' R' F2 R2 U r' F2 R' F2 r2
R' F R y' R2 U' R y R U2 R' U y' R' U R
R U R' U y' R' U2 R y R U' R2 F R F'
r' U' R' F2 R2 U R' M' F2 R' F2 R2

I hate this case.

May 17, 2009
Ponyville
WCA:
2009WHIT01