And, although technically off-topic,
Here's a similar approach to generate wing edge only scrambles for the nxnxn. But this one requires
a little programming.
A =
any scramble
B = Inverse(just the face-turn portion of
A)
C = A supercube algorithm which does the inverse effect on the centers as
B =
the same effect on the centers as A.
Then do: [
A,
B C]
[R 2R' 2B' R' L' 2L' 2U2 U 2R 2B 2L R' U' F 2B' R' F' 2L 2F 2U R, (R' F R F' U R U' L R R') (R' U' R' U2' R U B2 D2 F2 L' U2 F2 D' B2 D')]
Note that in my previous post, I used a
14 move supercube algorithm. Most of the 3x3x3 supercube cases where
all centers are rotated (in
some direction)
require more than 14 moves. (If anyone can find a position like that which requires fewer than 14 moves, that would be of great service!)
So to reduce the programming to just a few string manipulation subroutines,
Assume that you will set
C = L2 D U B F D' U' R2 B F D U B' F'
for all potential scrambles.
Sequence
C rotates the composite centers as follows:
F = + 90, B = + 90, L = 180, R = 180, U = + 90, D = + 90
So if you were to extract (this includes remove them from wide turns!) all face turns from sequence
A:
- All of the Fs, F's, and F2s, they should cancel to become F
- All of the Bs, B's, and B2s, they should cancel to become B
- All of the Ls, L's, and L2s, they should cancel to become L2
- All of the Rs, R's, and R2s, they should cancel to become R2
- All of the Us, U's, and U2s, they should cancel to become U
- All of the Ds, D's, and D2s, they should cancel to become D
So, in summary, we put a condition on the bulleted lists at the beginning of this post to be:
A =
any scramble (such that, its face turns match the above bulleted list constraint)
B = Inverse(just the face-turn portion of
A)
C = L2 D U B F D' U' R2 B F D U B' F'
Then do: [
A,
B C]
AND
To make is so that you don't have to create a custom scrambler . . . that you can use
any existing scrambler, you can append the necessary face turns to
A such that the "sum" of all Face turns (where, again, we consider all the turns of each face, separately) matches the above bulleted constraint. (So there will be a maximum of 6 additional turns to any algorithm that you can get from anywhere to scramble an nxnxn.)
EDIT 1:
I added an example below of when you need to append moves to
A to accommodate the specific
C = L2 D U B F D' U' R2 B F D U B' F'.
Suppose we start with
A = Lw' Uw D Bw R B2 Dw' D R2 D2 Dw2 Uw2 Fw Uw Fw2
L' = L'
R R2 = R'
U U2 U = e
D D' D D2 D2 = D
F F2 = F'
B B2 = B'
But we need:
{...} = L2
{...} = R2
{...} = U
{...} = D
{...} = F
{...} = B
So append (L' R' U F2 B2) to
A.
Then
B = (B2 F2 U' R L) F2 U' F' U2 D2 D2 R2 D' D B2 R' B' D' U' L
And of course we chose
C = L2 D U B F D' U' R2 B F D U B' F'
So [
A,
B C] =
[Lw' Uw D Bw R B2 Dw' D R2 D2 Dw2 Uw2 Fw Uw Fw2 (L' R' U F2 B2), (B2 F2 U' R L F2 U' F' U2 D2 D2 R2 D' D B2 R' B' D' U' L) (L2 D U B F D' U' R2 B F D U B' F')]
EDIT 2:
And you can reduce
B to the inverse of the sequence that you need to append to
A to accommodate a specifically chosen
C. You can do this if
A is of the form:
F' (some inner slice turns) F
B2 (some inner slice turns) B2
.
.
.
U (some inner slice turns) U'
That requires a little
more programming, but not much! The variety of wing edge scrambles you can generate is
far less than not restricting
A to this form, but it will naturally make the overall scramble length less (by effectively making
B 6 moves or less 100% of the time). But on the other hand, it's just shorter in STM, not HTM.
EDIT 3:
Here's a 7x7x7 example. (Not of the STM move count reduction just stated. But of the same procedure in
EDIT 1.
[
Link]
[
3d b l2 F D2 3r' 3f' B l 3u' r2 3b2 B' L d B l2 L u2 3d2 F2 3b2 r 3d' l2 3l 3b' 3f2 L' u2 D2 l2 3l2 F B2 3f d2 3f' U2 l' 3b 3r2 u' L' 3d2 u' 3r2 3b2 3l2 3d2 l' b' l B R2 F f2 R 3u r 3r' D l' 3u' B2 D' 3r2 b2 u B' 3f' 3l 3u F u' D L r2 B 3u2 f' l' U' 3f' r 3u l d U' 3b U2 F2 3u u2 U2 3b' u' f U2 D2 B'
,
B D2 U2 F' U B U2 U2 U' F2 U2 B' U D' L' U' R' F U L F U2 B' R2 L' D' U F' U' L' F B U' B2 R2 D B2 U L D' R R' U' R' F2 F' R2 B' L' B L D2 L2 B2 R2 U D2 L U R2 B' L U2 F D2 F' B2 F' L2 L2 D2 U2 L F2 B L' L2 D R' B2 F2 D2 U2 L' L2 B' D' L' B B2 R2 U L' B' F R D2 F' L2 B' D'
L2 D U B F D' U' R2 B F D U B' F'
]
It's a total of 406 HTM (when expanded and simplified). But this is with using a 98 HTM
A, where we have to append U2 D2 B' to compensate for our chosen
C = L2 D U B F D' U' R2 B F D U B' F'.
But clearly, we can reduce
B C in [
A,
B C] to being a 3x3x3 algorithm which does not rotate centers, but does the inverse effect on the corners and (composite) edges of the nxnxn. So for large n, it would be
smart to link the software with a near-optimal 3x3x3 supercube solver which takes into account center facelet twists (
Cube Explorer) to reduce
B C to 25 moves or so. (Whatever is time-feasible.) So that
B C stays fixed at 25
for any cube size, no matter how large (and thus only
A gets longer with larger n).
Then the maximum [
A,
B C]
for the nxnxn will be (
before cancelling moves after expanding) twice the number of moves of
A + 2*6 (if we have to add 6 moves to
A to compensate for our chosen
C) + 2*25 (if 25 is the maximum length of all 3x3x3 supercube positions which do not rotate any of the fixed centers, for example).
So in with this 7x7x7 example,
Within 1 second, cube explorer reduced
B C to 22 moves. So we now have:
[3d b l2 F D2 3r' 3f' B l 3u' r2 3b2 B' L d B l2 L u2 3d2 F2 3b2 r 3d' l2 3l 3b' 3f2 L' u2 D2 l2 3l2 F B2 3f d2 3f' U2 l' 3b 3r2 u' L' 3d2 u' 3r2 3b2 3l2 3d2 l' b' l B R2 F f2 R 3u r 3r' D l' 3u' B2 D' 3r2 b2 u B' 3f' 3l 3u F u' D L r2 B 3u2 f' l' U' 3f' r 3u l d U' 3b U2 F2 3u u2 U2 3b' u' f U2 D2 B', F2 R2 U2 B2 D2 L B2 L' U F2 D R2 D2 F' R D2 R2 U' F D U2 R]
(which is 246 moves instead of 406) . . . and this is still with
A = 98 HTM. So if we half that, then we would have a 148 HTM wing edge only scramble for
both wing edge orbits of the 7x7x7 (
using outer block turns only).
But
again, we can restrict
A to being in the form mentioned in
EDIT 2 and effectively reduce
B C to a maximum of 6 + 14 = 20 moves
for the nxnxn. But
A would consist of many inner slice turn moves!
