# Optimal 2 stages last layer solution



## Robert-Y (Feb 21, 2009)

Given that you have to solve the last layer in 2 steps, what would be the best solution in terms of the number of moves required on average for each turning metric system?

I thinking that perhaps (orientation of edges + permutation of corners) and then (orientation of corners + permutation of edges) aka step 6 + 7 of the Petrus method might be a good idea, (although this is just a weird feeling lol, I don't have any logical explanation behind my thought )


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## Lucas Garron (Feb 21, 2009)

I suggest the following two steps:

EPLL, CPLL, EOLL, and COLL all in one step, ignoring AUF
AUF
That's pretty optimal.


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## Robert-Y (Feb 21, 2009)

Ok sorry I meant in 2 stages, you are given the option to do one of the following:

A. 1. COLL + CPLL 2. EOLL + EPLL
B. 1. COLL + EOLL 2. CPLL + EPLL
C. 1. COLL + EPLL 2. CPLL + EOLL
D. 1. CPLL + EOLL 2. COLL + EPLL
E. 1. CPLL + EPLL 2. COLL + EOLL
F. 1. EOLL + EPLL 2. COLL + CPLL

G. 1. COLL 2. CPLL + EOLL + EPLL
H. 1. CPLL 2. COLL + EOLL + EPLL
I. 1. EOLL 2. COLL + CPLL + EPLL
J. 1. EPLL 2. COLL + CPLL + EOLL

K. 1. COLL + CPLL + EOLL 2. EPLL
L. 1. COLL + CPLL + EPLL 2. EOLL
M. 1. COLL + EOLL + EPLL 2. CPLL
N. 1. CPLL + EOLL + EPLL 2. COLL

Which method takes the least number of moves on average?


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## Ron (Mar 9, 2009)

Your list is very limited.


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## StachuK1992 (Mar 9, 2009)

In addition to this: what 2-step algorithm list would be the shortest?


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## Tiw (Mar 10, 2009)

nice thread^^
I like last layer algs xD

OLL/PLL is for fewest moves just bad...10 moves OLL and at least 12 moves PLL sometimes 14 or more.
COLL has a better average, but i think this way just will make sense if you use Petrus method.
In my opinion you're right, the step 6+7 index of Lars Petrus method is the best way to solve the last layer! 
If you are not use Petrus, maybe the VH-system makes a good job to orientate the egdes.
Can make for us a complete list of the S6+7 algs including mirrors an inverses? And of course optimal!


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## cuBerBruce (Mar 10, 2009)

Tiw said:


> Can make for us a complete list of the S6+7 algs including mirrors an inverses? And of course optimal!



Already been done. See here.

I note that I believe mirror cases are not listed separately.
Actually Helmstetter has computed (for face-turn metric) average move counts for many of these possible LL steps. See here. Generally, Helmstetter does not lists mirrors and inverses as separate cases.

I note that "COLL" generally has a different meaning in cubing than the way Robert used it. Robert, I highly recommend not using COLL to mean "corner orientation of the last layer." I think Tiw was using COLL with the normal meaning.


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## Robert-Y (Mar 10, 2009)

What should we call "corner orientation of the last layer" instead?


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## Swordsman Kirby (Mar 11, 2009)

Lucas calls it OCLL, so I just go with that.


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## Tiw (Mar 11, 2009)

This is nice website! http://puzzlingaddiction.com/Cube/ll-algs/
All possible last layer cases, i don't know whether they are optimal.
i found it randomly.


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