## 6412Re: [Speed cubing group] Re: DanK's website?

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• Sep 1, 2003
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On Mon, Sep 01, 2003 at 11:48:01AM -0000, jasmine_ellen wrote:
> I remembered that DanK had something like this on his site about a
> beginner method, an intermediate method and an advanced method. This
> is actually what I was after. Who else has something like this on
> their site?

I'll describe the beginner and intermediate methods that I once used.
They are simplications of the Fridrich last layer system. You need to
first understand how that system works:

http://www.ws.binghamton.edu/fridrich/system.html#last

This general strategy, orienting first, then permuting, is good because
it is very easy to recognise the positions quickly. But instead of
orienting all the pieces at once, you just orient the edges first, and
the corners second.

BEGINNER METHOD

First, orient the 4 edges (ie. make a cross). There are only 4 patterns,
and one algorithm to solve them all! To view this, you need to use a
fixed width font:

--- --- -x- -x-
-x- xxx xx- xxx
--- --- --- -x-

For each pattern, apply the algorithm "R'U'F'U F R" and it will take you
to the next pattern. Eventually you will end up with a cross.

Improvement: notice that if you apply the algorithm when you already
have the cross, you will end up with a line. That means that you can
jump immediately from the 2nd pattern to the 4th pattern by applying the
algorithm backwards! So, this step should take an average of 6 moves.

Next, orient the corners. There are only 6 patterns apart from solved.
Look through this complete list, and find all the patterns (and
algorithms) that have a cross already formed:

http://www.ws.binghamton.edu/fridrich/Mike/orient.html

For the case when 3 corners need to be twisted, I recommend the Sune TM
algorithm from Petrus. See the applet at the top/right of his page:

http://lar5.com/cube/fas6.html

I think it's useful to learn to twist them forwards and backwards:

- R U R'U R U2 R'
- R'U'R U'R'U2 R

To see that done fast, have a look at the quicktime movies at the bottom

http://lar5.com/cube/speed.html

I recommend this algorithm because one of the other orientation cases
can be solved by just applying this algorithm twice. To know which case
I'm talking about, apply this to a solved cube: RU2R'U'RUR'U'RU'R'.

Now, apply the sune (RUR'URU2R') twice:

RUR'URU2R' + RUR'URU2R'

Notice that the moves in the middle cancel out? So you can actually do:

RUR'URU'R'URU2R'

which is an "optimal" solution.

Next, permute the corners (yes, before the edges). Most of the time
there will be a 3 cycle of corners. In this case, look at the 4 sides of
the last layer. On one of the sides, the two last layer corners will be
matching in colour. Hold those two corners on the back side and do:

R'FR' B2 RF'R' B2 R2

Now the corners should be solved. If you don't find any two corners that
match, apply the above algorithm and that should result in a position
where two corners match. Don't worry, this case rarely happens. If you
want, you can learn a special algorithm for that case by picking the
most attractive one from:

http://www.ws.binghamton.edu/fridrich/Mike/permute.html

The "Y" pattern on that page has the desired corner effect.

Next, permute the edges. Again, most of the time, there will be a 3
cycle of edges. You need to learn to cycle the edges forwards and
backwards:

- R2U FB'R2F'BU R2
- R2U'FB'R2F'BU'R2

Sometimes, all 4 edges need to be swapped in opposite pairs. That's an
easy case, so why not learn it:

RLU2R'L' [U] R'L'U2RL

The [U] means rotate the whole cube from the up side, 90 degrees.

There's also a rare case where all 4 edges need to be swapped in
adjacent pairs. The algorithm's difficult so it's not worth learning.

INTERMEDIATE METHOD

First, orient everything like the beginner method. Then permute
everything like the full blown Fridrich method.

How can you learn all the permutations? See my previous email:

http://groups.yahoo.com/group/speedsolvingrubikscube/message/4736

There, I list which algorithms to learn first, and which algorithms to
learn last.