Re: [blindfoldsolving-rubiks-cube] Corner Perm.

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• Hi friends, So which do we have? Corner permutations: R FR B2RF R B2R2 (basic + inverse) (L2 U) (B2 U )*2 (L2 U) (B2 U B2 U ) [RB R B]x3 (13)(27) UL2UR2
Message 1 of 11 , Apr 3, 2004
Hi friends,

So which do we have?

Corner permutations:
R'FR'B2RF'R'B2R2 (basic + inverse)
(L2 U) (B2 U')*2 (L2 U) (B2 U B2 U')
[RB'R'B]x3 (13)(27)
UL2UR2 U'L2UR2 U2 (Ron)
U'R2UR2UF2 U'R2U'R2UF2 (Ron)

Edge permutations:
RU'RURURU'R'U'R2 (+ inverse, mirrored F/B, inverted mirrored F/B. These
algorithms are really great!!)
MD2M'D2 (in any direction)
M'UMU2M'UM (in any direction, useful if you can do an easy F/B setup move
that flips edges!!)

Edge orientations:
ERERERER'ERERERER' (in any direction)
(M'U)*4 (UL, UB, DF, and DB)
(M'U')*4 (UR, UB, DF, and DB)
(M'U)*4 (MU)*4
(MD')*4 (M'D')*4
R2 D' (R2M2) (M'U)*4 (R2M2) D R2
F D F D' (EF')*4 D F' D' F'
M' U M' U M' U2 M U M U M U2
(DwDRwR)*3 (octaflip)

Corner orientations:
R'DRFDF' Ux FD'F'R'D'R Ux'
(R'U2RUR'UR) U2 (L2U'F'BL2FB'U'L2)
(R'U2RUR'U'RUR'UR) (F2U'LR'F2RL'U'F2)
(LU2L'U'LU'L') (R'U2RUR'UR)
(F2 L F2 L') (U2 R U' R' F2 R' F2) (R U')
(F' D2 F R' U2 R) * 2

Basically you can do any two generator corner orientation (like RU2R'U'RU'R'
or RU2R2U'R2U'R2U2R), then check which edges are cycled, then undo the edge
cycle (see Edge permutations).
For the corner orientations there are many neat tricks in case the total
orientation of LL is not 0.

What could we add to this list?

One idea I got from blindfold solving to transfer to speedcubing is this:
suppose you could do the orientations (edges/corners) both in one step, and
the permutations (edges/corners) both in two steps. Then in 15 seconds
preinspection you could memorize the orientations. After that you do the
permutations. Total of 6 steps. That is better than the cross/F2L/OLL/PLL
system with 7 steps.
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. OK, now
preinspect the cube to solve the cross using moves in the group
(U,D,R,L,F2,B2). This would leave you a very easy F2L using only U, R and L
moves. And it would leave you a LL with oriented edges. Try this a few times
and then take an average not including the first step of orienting the
edges. Mine was better than my normal average.
Now if you could orient the edges very fast, and still be able to afterwards
solve the cross fluently, then you could maybe even improve your times.
This system can also be useful for one-handed cubing (many easy moves!!!)
and for beginners who have trouble with OLL or F2L (only 8 corners case for
OLL, no rotations or really hard cases for F2L).

Have fun,

Ron
• 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,
Message 2 of 11 , Apr 4, 2004
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.

--- In blindfoldsolving-rubiks-cube@yahoogroups.com, "Ron van
Bruchem" <rvb@c...> wrote:
> Hi friends,
>
> So which do we have?
>
> Corner permutations:
> R'FR'B2RF'R'B2R2 (basic + inverse)
> (L2 U) (B2 U')*2 (L2 U) (B2 U B2 U')
> [RB'R'B]x3 (13)(27)
> UL2UR2 U'L2UR2 U2 (Ron)
> U'R2UR2UF2 U'R2U'R2UF2 (Ron)
>
> Edge permutations:
> RU'RURURU'R'U'R2 (+ inverse, mirrored F/B, inverted mirrored F/B.
These
> algorithms are really great!!)
> MD2M'D2 (in any direction)
> M'UMU2M'UM (in any direction, useful if you can do an easy F/B
setup move
> that flips edges!!)
>
> Edge orientations:
> ERERERER'ERERERER' (in any direction)
> (M'U)*4 (UL, UB, DF, and DB)
> (M'U')*4 (UR, UB, DF, and DB)
> (M'U)*4 (MU)*4
> (MD')*4 (M'D')*4
> R2 D' (R2M2) (M'U)*4 (R2M2) D R2
> F D F D' (EF')*4 D F' D' F'
> M' U M' U M' U2 M U M U M U2
> (DwDRwR)*3 (octaflip)
>
> Corner orientations:
> R'DRFDF' Ux FD'F'R'D'R Ux'
> (R'U2RUR'UR) U2 (L2U'F'BL2FB'U'L2)
> (R'U2RUR'U'RUR'UR) (F2U'LR'F2RL'U'F2)
> (LU2L'U'LU'L') (R'U2RUR'UR)
> (F2 L F2 L') (U2 R U' R' F2 R' F2) (R U')
> (F' D2 F R' U2 R) * 2
>
> Basically you can do any two generator corner orientation (like
RU2R'U'RU'R'
> or RU2R2U'R2U'R2U2R), then check which edges are cycled, then undo
the edge
> cycle (see Edge permutations).
> For the corner orientations there are many neat tricks in case the
total
> orientation of LL is not 0.
>
> What could we add to this list?
>
> One idea I got from blindfold solving to transfer to speedcubing is
this:
> suppose you could do the orientations (edges/corners) both in one
step, and
> the permutations (edges/corners) both in two steps. Then in 15
seconds
> preinspection you could memorize the orientations. After that you
do the
> permutations. Total of 6 steps. That is better than the
cross/F2L/OLL/PLL
> system with 7 steps.
> 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. OK, now
> preinspect the cube to solve the cross using moves in the group
> (U,D,R,L,F2,B2). This would leave you a very easy F2L using only U,
R and L
> moves. And it would leave you a LL with oriented edges. Try this a
few times
> and then take an average not including the first step of orienting
the
> edges. Mine was better than my normal average.
> Now if you could orient the edges very fast, and still be able to
afterwards
> solve the cross fluently, then you could maybe even improve your
times.
> This system can also be useful for one-handed cubing (many easy
moves!!!)
> and for beginners who have trouble with OLL or F2L (only 8 corners
case for
> OLL, no rotations or really hard cases for F2L).
>
> Have fun,
>
> Ron
• ... 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 3 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 4 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 5 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 6 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

Do you Yahoo!?
Yahoo! Small Business \$15K Web Design Giveaway - Enter today

• ... 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 7 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 8 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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