## Re: Corner Perm.

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• ... In case you cared to know for sure, you re correct. I had written this into a program a bit ago and this is from the output - # of edge orientation states
Message 1 of 11 , Apr 5, 2004
--- Ron van Bruchem wrote:
> ... Another thing is this: without looking at the cross, just orient
> all edges. This is much easier than for blindfold because you can
> do F to flip 4 edges. I think the maximum depth for edge
> orientation is 7 moves...

In case you cared to know for sure, you're correct. I had written
this into a program a bit ago and this is from the output - # of edge
orientation states at each depth:
depth 0: 1 0.05%(solved)
depth 1: 2 0.10%
depth 2: 21 1.03%
depth 3: 178 8.69%
depth 4: 592 28.91%
depth 5: 914 44.63%
depth 6: 327 15.97%
depth 7: 13 0.63%
Total : 2048

After that, corners can be oriented in at most 7 more moves, though
I'm sure us human solvers won't always see the optimal solution when
it's 5-7 moves away.

- Grant
• ... Can you tell us what these 13 states are? ... though ... when ... Hmm, maybe a simple greedy algorithm could work... but I haven t tried it yet, this is
Message 2 of 11 , Apr 6, 2004
> depth 7: 13 0.63%

Can you tell us what these 13 states are?

> After that, corners can be oriented in at most 7 more moves,
though
> I'm sure us human solvers won't always see the optimal solution
when
> it's 5-7 moves away.

Hmm, maybe a simple greedy algorithm could work... but I haven't
tried it yet, this is just an idea that came to my mind as a

Cheers!
Stefan
• How fast can you execute this? Some time ago I found that you can get the same using a double Sune , i.e. (L U L U L U2 L) (R U R U R U2 R ) This will
Message 3 of 11 , Apr 6, 2004
How fast can you execute this? Some time ago I found that you can
get the same using a "double Sune", i.e.

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

This will twist the UFR and URB, so rotate the cube to achieve
exactly what your alg does. Due to the nature of the above alg you
can easily mirror it just by doing the second part first, i.e. try

1. (L' U' L U' L' U2 L) (R U R' U R U2 R')
2. z'
3. (R U R' U R U2 R') (L' U' L U' L' U2 L)
4. z

Cheers!
Stefan

--- In blindfoldsolving-rubiks-cube@yahoogroups.com, "Michael
Atkinson" <unipsycho6@y...> wrote:
> One algorithm that I often use is from Richard Carr's document:
>
> R'D'LDRD'L'DUL'UR2U'LUR2U2
>
> You hold it so there's a corner with orientation 2 in position
UFR,
> and a corner with orientation 1 directly below that. It's my main
> corner orientation algorithm.
• I agree, all these algs are fast... but I think, ... the fastest way is just looking and planning ahead w/ nonstop, as ron says: just simply looking ahead
Message 4 of 11 , Apr 6, 2004

I agree, all these algs are fast...  but I think, ...  the fastest way is just looking and planning ahead w/ nonstop, as ron says: "just simply looking ahead makes a huge difference"
-bm
Stefan Pochmann <pochmann@...> wrote:
How fast can you execute this? Some time ago I found that you can
get the same using a "double Sune", i.e.

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

This will twist the UFR and URB, so rotate the cube to achieve
exactly what your alg does. Due to the nature of the above alg you
can easily mirror it just by doing the second part first, i.e. try

1. (L' U' L U' L' U2 L) (R U R' U R U2 R')
2. z'
3. (R U R' U R U2 R') (L' U' L U' L' U2 L)
4. z

Cheers!
Stefan

--- In blindfoldsolving-rubiks-cube@yahoogroups.com, "Michael
Atkinson" <unipsycho6@y...> wrote:
> One algorithm that I often use is from Richard Carr's document:
>
> R'D'LDRD'L'DUL'UR2U'LUR2U2
>
> You hold it so there's a corner with orientation 2 in position
UFR,
> and a corner with orientation 1 directly below that. It's my main
> corner orientation algorithm.

:)
--Brent

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• ... Hmm... I sent a response to this yesterday, and it doesn t appear to have gone through - I ll repost. Not surprisingly, the 13 states are superflip along
Message 5 of 11 , Apr 8, 2004
--- Stefan Pochmann wrote:
> > depth 7: 13 0.63%
>
> Can you tell us what these 13 states are?

Hmm... I sent a response to this yesterday, and it doesn't appear to
have gone through - I'll repost.

Not surprisingly, the 13 states are superflip along with 12 states
with 10 edges flipped. Here's a summary:
1) Superflip (all edges flipped)
2-5) UF or DF and BL or BR
6-9) UB or DB and FL or FR
10-13) Two edges across F or B from each other (e.g. FR and FL or UB
and DB)

Here's a list of the edges flipped (and not flipped) in each of the
13 states:
1) UF UB UR UL DF DB DR DL FR FL BR BL (All Flipped)
2) UF UB UR UL DF DR DL FR FL BR (Not DB BL)
3) UF UB UR UL DF DR DL FR FL BL (Not DB BR)
4) UF UB UR UL DB DR DL FR BR BL (Not DF FL)
5) UF UB UR UL DB DR DL FL BR BL (Not DF FR)
6) UF UR UL DF DB DR DL FR FL BR (Not UB BL)
7) UF UR UL DF DB DR DL FR FL BL (Not UB BR)
8) UB UR UL DF DB DR DL FR BR BL (Not UF FL)
9) UB UR UL DF DB DR DL FL BR BL (Not UF FR)
10) UF UB UR UL DF DB DR DL FR FL (Not BR BL)
11) UF UB UR UL DF DB DR DL BR BL (Not FR FL)
12) UF UR UL DF DR DL FR FL BR BL (Not UB DB)
13) UB UR UL DB DR DL FR FL BR BL (Not UF DF)

- Grant
• ... I didn t say that right; the summaries of 2-13 indicate which edges are not flipped in each state. - Grant
Message 6 of 11 , Apr 8, 2004
--- Grant Tregay wrote:
> Here's a summary:
> 1) Superflip (all edges flipped)
> 2-5) UF or DF and BL or BR
> 6-9) UB or DB and FL or FR
> 10-13) Two edges across F or B from each other (e.g. FR and FL or
> UB and DB)

I didn't say that right; the summaries of 2-13 indicate which edges
are not flipped in each state.

- Grant
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