Solving OLL by using only one algorithm (with AUF permitted)

[Robert-Y]

Using the help of ksolve, I've just discovered that it's possible to solve OLL using only one algorithm (with AUF permitted). An example of such an algorithm would be sexysledge (R U R' U' R' F R F').

EO (preserves CO):
4flip: SexySledge U SexySledge U SexySledge U2 SexySledge
adj 2flip: SexySledge U SexySledge U2 SexySledge' U' SexySledge
opp 2flip: SexySledge' U SexySledge U' SexySledge U2 SexySledge

CO (preserves EO):
antisune: SexySledge U SexySledge U' SexySledge'
sune: SexySledge U SexySledge' U' SexySledge'
L: SexySledge' U' SexySledge U SexySledge U2 SexySledge'
U: U2 SexySledge U' SexySledge' U SexySledge'
T: U SexySledge U' SexySledge U SexySledge'
Pi: U2 SexySledge' U2 SexySledge
H: U SexySledge' U' SexySledge' U2 SexySledge'

I just this was kinda cool so I decided to share

 

[Stefan]

Here's an easier proof:

Do U R2 B' R D' B2 L F L' B2 D R' B R2 until UF and UFR are oriented. Then do U.
Repeat until OLL is done.

Edit: LOL, after posting this I went ahead to actually try it with my cube... OLL skip.

 

[qqwref]

Cool discovery. Stefan does raise a good point, although that alg is positively awful (I tried it several times, got a messed up cube, then went to alg.garron and it still took me two tries to get it right ). Perhaps with a good alg we could actually teach this as part of a two-alg method.

Are there any PLLs that can be solved by SexySledge alone? <U, Stefan's alg> doesn't get you any, but maybe with Rob's you can get some.

EDIT: I got N and R perm after playing around. At least CP is possible.

 

[Robert-Y]

Here's an easier proof:

Do U R2 B' R D' B2 L F L' B2 D R' B R2 until UF and UFR are oriented. Then do U.
Repeat until OLL is done.

Edit: LOL, after posting this I went ahead to actually try it with my cube... OLL skip.

That's a cool "trick", thanks

Cool discovery. Stefan does raise a good point, although that alg is positively awful (I tried it several times, got a messed up cube, then went to alg.garron and it still took me two tries to get it right ). Perhaps with a good alg we could actually teach this as part of a two-alg method.

Are there any PLLs that can be solved by SexySledge alone? <U, Stefan's alg> doesn't get you any, but maybe with Rob's you can get some.

EDIT: I got N and R perm after playing around. At least CP is possible.

So I guess that means you can do OLLCP with one algorithm, and as we already know, we can do EPLL using only one algorithm (U perm), therefore you can complete the last layer using just two algorithms... (I'm guessing this isn't a new discovery though)

 

[TDM]

EDIT: I got N and R perm after playing around. At least CP is possible.

I've been playing around too and I've also only seen N/R. Is there a way to prove/disprove you can't do EPLL like this?

(maybe it's possible with a different alg?)

 

[Randomno]

Edit: LOL, after posting this I went ahead to actually try it with my cube... OLL skip.

Solve that with: SexySledge SexySledge SexySledge

 

[Stefan]

Stefan does raise a good point, although that alg is positively awful

First one that Cube Explorer spat out . Alternatively, you could combine Y-Perm with Y-perm, b-i-t-c-h-e-s.

Some other possibilities (their inverses/mirrors work as well, of course):
U' R U R' U' R U F R2 U R2 U' R' U R' U' F' R'
U' R U R' U' F' R' U' R U' R' U2 R U2 F R U R'
F U' R2 D R' U R D' R U' R U F' U' R' U R

 

[Stefan]

Literally thinking outside the box (that is LL): Orient UB and UBL by repeating R' U2 F R F' R' U' R U' R, then AUF and repeat for the other four LL pairs (this has order 12, you might have to do it six times in the end to restore F2L). Maybe by adding swapping between LL and F2L one could include PLL as well?

 

[qqwref]

If you don't mind messing up F2L constantly: let Q = F' D F' L2 D F L' D L F' D' L2 D' F

You can use <Q^4, U> to modify corner orientation and permutation, and <Q^9, U> to modify edge orientation and permutation.

Example:

Spoiler

LL scramble: U' F2 U' L2 U R2 U' L2 U R2 F' U F R' F' R U' F'
corners: U Q^4 U2 Q^8 U' Q^-8 U' Q^-4
edges: Q^9 U Q^9 U' Q^18 U' Q^-9 U Q^9

btw, for convenience,
Q^4 = B2 D R D' B2 U2 F2 L2 U L U' L2 F2 U2
Q^9 = U2 F' U F U' L' U2 F' U' F L F' U2

 

[TDM]

(very inefficient) OLLCP:

(SS = sledgehammer btw)

Spoiler

1. CP
adj swap on F: SS
diagswap: SS U' SS

2. CO
Sune: U SS' U' SS'
Antisune: SS U SS
use these like the beginner's method to orient corners

3. EO
UFUB: SS' U SS U' SS U2 SS U2
UFUR: SS U' SS U2 SS U2 SS' U
4flip: SS U SS' U' SS U2 SS U SS' U' SS U2
(thanks RobertY for finding these EO algs)