Dr. Richard Carr's Blindfold Cubing 3阶盲拧原文

kitor

3.1 Memorizing The Cube
We can not assume that a corner has already been solved as was the case with
the 2x2x2 cube because there are fixed centres on the 3x3x3 cube. To make
memorization easier and faster I recommend that you always start o? with a
particular face as U face and a particular face as F face (unless the cube looks
particularly easy from another point of view - e.g. corners already oriented et
cetera) - I use White as Up face and Green as F face.
I already discussed memorizingcorners for the 2x2x2- the same principles apply
here except you have to remember at least 7 corners as the last one is no longer
fixed. I just remember the whole 8 of them as it isn’t too much extra work and
provides extra security.
Therefore, I will begin here by talking about the edges. First the numbering of
the edges. The edges are numbered 1-12 by the following scheme:
the edges belonging to the U face are numbered 1-4 according to UF=1, UB=2,
UR=3, UL=4;
theedgesbelongingtotheDfacearenumbered5-8accordingtoDF=5,DB=6,
DR=7, DL=8;
the other edges are labelled 9-12 according to FR=9, FL=10, BR=11, BL=12.
If you have read the section on 2x2x cubing you will see that I have labelled
them according to priority. Thus the U,D faces have high priority (and within
these ImakeU have higher prioritythanD), the F,Bfaces havemedium priority
(and within these I make F have higher priority than B) and the R,L edges have
low priority (and within these I make R have higher priority than L). Then the
edges are ordered according to prioritywith a lexicographic order (given 2 edges
GH and IJ, GH comes before IJ if G has higher priority than I or if G=I but
H has higher priority than J - so UL comes before DF because U has higher
priority than D (irrespective of F having higher priority than L) and UR comes
before UL because R has higher priority than L).
The edges should be memorized in the order that would give 1-12 in the solved
cube.
Sotheedgepermutation211781210519643hastheUBedge(edge2)inthe
UF position(position 1) and the BR edge (edge 11) inthe UB position(position
2) and the DF edge (edge 5) in the DL position (position 8) for example.
Technically, you only need to remember the position of the first 11 edges (as
the last one is then automatically predetermined). In fact, it is possible to
remember only the first 10 edges (or the first 11 edges and the first 6 corners)
because the permutations must both be odd or both be even (you’ll be OK if
the cube can be solved - i.e. is put together correctly - as the other 2 can then
be worked out). If that doesn’t make any sense don’t worry, it’s not essential
and in fact for peace of mind it’s better to remember all 12 anyway. In any
event you have to remember at least the first 7 orientations (corners) and 11
orientations (edges).
So much for position, now we come to orientation.
An edge has distinct colours and one of these is higher priority than the other
(even using the more primitive priority scheme of high, medium, low - that’s
because the priorities are chosen so that the two colours of high priority are on
opposite faces (so edges and corners can’t have 2 colours of high priority) and
similarly for medium priority and for low priority).
Given an edge in a particular position the edge lies in 2 faces (for instance if
the UF edge is in the BR position it is lying in the B face and the R face). If
the higher priority colour of the 2 edge colours is in the higher priority colour
of the 2 face colours (which we take to be the colour of the centre square) then
we say that the edge has orientation 1 (is incorrectly oriented) otherwise it has
orientation 0 (is correctly oriented). Note that in the solved cube the colour of
an edge matches the colour of the face in which it lies so that higher priority，matches higher priority and each edge is correctly oriented.
In the parenthetical example above the UF edge is correctly oriented if the U
part of the edge is in the B face (as U has higher priority than F and B has
higher priorty than R) and is incorrectly oriented otherwise.
The total number of incorrectly oriented edges is always even (for a cube that
can be solved) so if it isn’t like that then the cube can’t be solved.
Memorize the orientation of the edges in the same order as the position of the
edges. Thus,ifyouhaveorientation100111010100thentheedges
in positions 1,4,5,6,8 and 10 are incorrectly oriented and the edges in position
2,3,7,9,11and 12 are correctly oriented (not that the UF, UL, DF, DB, DL and
FL edges are incorrectly oriented et cetera although that may also be the case).
Theorientation100101001111doesn’tcorrespondtotheorientationof
a cube that can be solved as 7 edges need orienting and 7 is not even - that is
7 isn’t divisible by 2.
(Aside: a 3x3x3 cube can be solved if and only if the following conditions are
satisfied
* The stickers are on correctly (so that if you took it apart it would be
possible to assemble into a solved cube).
* The sum of the corner orientations is divisible by 3.
* The sum of the edge orientations is divisible by 2.
* The corner and the edge permutations are either both even or both odd.
(A little more technical - if you don’t know what this means don’t worry,
you won’t be able to do the neat trick but at least half of the time you
should be OK.)
(A 2x2x2 cube is solvable if and only if the first 2 conditions here are met.)
Thus it is possible to determine just by looking at the cube whether it can be
solved and, if not, what needs to be done to make it capable of being solved.
Each step is fairly easy to verify (except the last).
As a smugness bonus you can take on cubes that can’t be solved blindfolded,
get as far as possible (up to one edge badly oriented, up to one corner badly
oriented and up to 2 corners needing swapping, which you can assume to involve
only the UFR and UFL corners and the UF edge) then if necessary take out the
UF edge and do the necessary adjustments to each piece and stick it back in.
You need to be careful to get the edge back in the correct way but if someone
is tryinng to set you up it should put egg on their faces.
Aside 2: Ifyouare curious, thisis howto tell ifapermutationis odd oreven. I’ll
just give an example and hope the general technique is clear. It really doesn’t
matter about this for blindfold cubing.
Saygivenapermutation211781210519643asabove.
Start o? with 1 and see what lies in position 1, in this case 2. Then go to that
position (in this case posiition 2) and see what lies there, in this case 11. Go to
that position and see what lies there - in this case 4. Keep going until you get
to 1. This gives what is known as a cycle - in this case we’d write (2 11 4 8 1),finishing at 8 because 1 is in position 8. Next go to the first unused number on
the list (if any) and make a cycle from that. In the present case it is 7. 5 lies
in position 7, 12 lies in position 5, 3 lies in position 12 and 7 lies in position 3.
We get the cycle (7 5 12 3).
The next unused number on the list is 10 and we get a cycle (10 6). Finally we
get a cycle (9).
Theentirepermutationhascycledecomposition(211481)(75123)(106)(9).
The order of the cycles is not important, we could equally well write (10 6)(2
11 4 8 1)(9)(7 5 12 3). Also in a given cycle it doesn’t matter where we start so
(75123)isthesamecycleas(51237),as(12375)andas(37512),but
notas(57312).
A cycle is a transposition if it has length 2.
Some cycles have even length and some have odd length. A cycle is odd if it
has even length. (This is because such a cycle can be written as a product of
an odd number of transpositions in the symmetric group.)
The permutation is even if it has an odd number of odd cycles - otherwise it is
even.Thus211781210519643isanevenpermutationsinceithas2odd
cycles, (10 6) and (7 5 12 3).
If a cube can be solved then the corner and edge permutations must either both
be odd or both be even. (If you are really up for it, their product in the sym-
metric group S12 has to be even.)
Anyway, enough of the asides - they aren’t necessary for blindfold cubing.
Once you have memorized the corner and edge permutations (positions) and
orientations you are ready to don the blindfold.
I recommend memorizing them in the followingorder - edges first then corners -
end with the corner orientation. The exact order of memorizing the edges (ori-
entation then permutation or permutation then orientation) isn’t too crucial.
The hardest to remember is either the corner orientation or the edge permuta-
tion.
You should also try to keep in mind pairs of incorrectly oriented edges that you
might want to flip together. If you do this you may not have to remember a
sequence for the edge orientation - just which pairs to flip.

kitor

3.2 Donning The Blindfold
Don the blindfold.

3.3 Orienting The Corners
The first thing to do is to orient the corners. I described this in the 2x2x2 sec-
tion and it is exactly the same. Those moves will not only preserve the corner
permutation but also the edge permutation and edge orientation.

3.4 Orienting The Edges
After this you should usually orient the edges (you could permute the corners,
but in the event that you are left with 2 to permute, you will either have to
leave them until later or switch some edges and we really want to orient the
edges before permuting any of them). If more than 6 edges are to be oriented,
a di?erent strategy is to unorient the correct edges and then orient them all at
the end.
To do this, I use 2 basic moves. You could use more, but the fewer algorithms
the better for blindfold cubing (it is harder to get confused that way).
The two moves are:
2 2 1 2 1 2
LsFRsU LsFRs B U- RsB LsU- B
which flips the UB and UL edges (the first part does the flipping and the second
part corrects the permutation) and
1 1 1 1 2 2 2
FsUF- U- Fs- LFL- F ULsF RsUF
which flips the UL and UR edges (the first part does the flipping and the second
part corrects the permutation).
Note that the correcting steps are quite similar (in fact, they both permute 3
edges - the first does UR→UB→UL→URand the second UR→UF→UL→ UR).
In fact, you can get away with only using the first of these (as the second can
1
be done using the first followed by U- then the first then U). I only used the
first when solving the Revenge blindfolded.
Of course, you may have to temporarily use di?erent faces as U face, F face et
cetera to bring the pieces into the correct places (UL and UB or UL and UR) -
if you do, remember what you did so you can udno it afterwards. Also, you may
need to use a couple of auxillary moves to get things in the right place. Thus,
if you want to flip the edges in the UF and UL positions either rotate the whole
cube so that they are in the UL and UB positions do the first move and tehn
1
rotate the cube back or do U(the first move)U- . If you want to flip edges DF
2 2 2 2
and UR, then do F U (the first move)U F et cetera.
After havingoriented the corners andedges it’stimetopermute. Ifyoupermute
the corners first it is quicker (there are less of them) so you can get onto the
edge permutations quite soon. If you do the edge permutations first you have
longer to wait to get to the last part of the solution but less to remember when
you get there.
Assuming you remembered them well, you might as well permute the corners
first (as the dges should be fixed in your mind and you get there quickly).3.5 Permuting The Corners
Permute as in the 2x2x2case (you first have to get corner 8 in position if it isn’t
using similarmethods). If you have only2 to swap at the end, use the move P10which will change the first two edges in your mental permutation, but preserve
theorientationso112781210519643wouldbecome211781210519
643forexample.Theedgepermutationcouldn’thavebeen21178121051
9 6 4 3 at the outset if you need to swap 2 corners at the end - unless the cube
can’t be solved).
The technique I give in the 2x2x2 case is really not too advanced. It certainly
isn’t essential to permute the corners in the way I suggest (8 then 7 then 6
et cetera) and it isn’t e?cient but is easy and you can lop o? the end of the
permutation you have to remember at each stage. In general, I would not be
using this technique in the exact way I describe.
Remember if you do use this technique, get corner 8 into position first! You
didn’t have to worry about it for 2x2x2 but you do for 3x3x3.
3.6 Permuting The Edges
Lastly we come to permuting the edges. The basic move is the 3-cycle
2 2 2
R UFsR BsUR
which permutes 3 edges (UF→UB→UR→UF) without altering orientations. If
1
you use U- in place of U (in both places) you get the inverse permutation
(UF→UR→UB→UF).
Similarly you can permute on the other side (but if you want to avoid to you
2 2
could use U (the move)U ) and other such things.
You can apply this move in 8 ways on the U face (the move and its inverse and
j j
you can use U (the move or its inverse)U- forj=-1,2or1fortheother6.
You can also do similar moves in the D face, R face or L face. Don’t do these
moves in the F or B face as they will change the orientation of two of the edges.
You could, but you’d have to be careful to reorient the edges. Remember to
keep updating your mental image of the edge permutation at each step.
There are a number of ways to proceed. One way is to get the edge of the
middle layer in first. You can get them from the U or D layer by using 3-cycles
in the L or R face as appropriate.
If they are already in the middle layer but incorrectly positioned you may still
2 2 2 2 2 2
be able to use such a move. Another crucial move is U R U R U R which
switches the UF edge with the UB edge and the FR edge with the BR edge.
This move does not alter orientations and any variant may be safely used, e.g.
2 2 2 2 2 2
U F U F U FR .
When you’re done with the edges of the middle layer you may have to move
edges between U and D faces.
2 2 2 2
The move Rs F Rs B switches the UF edge with the DF edge and the UB
edge with the DB edge (and preserves orientations). By doing this (possibly
preceded by a 3-cycle in the U and or D faces) you can bring 2 U edges from
the D face to the up face in exchange for 2 D faces from the U face to the D
face (unless you have less than 2 D edges in the U face).

If you have exactly one D edge in the U face then bring another one up first
(you can do this as follows: say the D edge is in the UF position for example
- if the U edge in the D face is not in the DR position put it there by rotating
2 2 2 2 2 2
the D face then use B R B R B R and then undo the rotating of the D face.
Remember where everything went!
Then you’ll have 2 D edges in the U face in the UB and UF positions and you
2 2 2 2
can use Rs F Rs B to get all the U edges in the U position.
Use 3-cycles in the U face to get the DR and DL edges (edges 7 and 8) into the
correct positions.
If edge 5 is not in the correct position you need to switch edges 5 and 6, so use
2 2 2 2
Rs U Rs D . (This will also switch the edges in positions 1 and 2).
Use 3-cycles to position the U edges (you can do this in at worst 2 steps; get any
edge into position with the first 3 cycle and then, if you need to use a 3-cycle
to get any other edge in position - if your cube can be solved they will now all
be in position, unless you messed up somewhere).

3.7 Putting The Cube Down
Put the cube down.

3.8 Removing The Blindfold
Remove the blindfold.
Your cube should now be solved, if you didn’t mess up.
When you can consistently do the 3x3x3 cube you will be ready to start the
Revenge. (NB It gets a lot harder now.)

kitor

有没有高手翻译一下。谢谢。

[此贴子已经被作者于2006-11-26 23:02:58编辑过]

彳亍

初看了一下，有些眼晕  ：）

还是建议看老大的教程。 方法差不多。

彳亍

2~5的文字版都有吗？

只见过pdf的

[此贴子已经被作者于2006-12-9 0:04:15编辑过]

kitor

我也是pdf的，只不过我把它的文字提取出来而已。

kitor

Blindfold Cubing
Dr. Richard Carr
February 23, 2002
The followingisan introductionto blindfoldcubing. It does not alwaysshow
the most e?cient methods. It will be built up in chapters - as of the present it
is somewhat incomplete.
1 1x1x1 Cubes
1.1 Memorizing The Cube
There really is nothing to do.
1.2 Donning The Blindfold
Don the blindfold.
1.3 Permuting And Orienting All The Pieces In One Go!
There really is nothing to do.
1.4 Putting The Cube Down
Say “bad cube” or prepare a lethal injection and give it to the cube. No that’s
all very cruel. Seriously, just put the cube down (place it down).
1.5 Removing The Blindfold
Remove the blindfold.
Unless you are really incompetent the cube should be solved.
Stop being silly and progress to:

[此贴子已经被作者于2006-12-10 13:35:28编辑过]

kitor

2 2x2x2 Cubes
Solving the 2x2x2 cube blindfolded is important in solving bigger cubes blind-
folded. If you can do this then it will help in solvingthe corners of bigger cubes.
If you can’t then you haven’t much hope on bigger cubes.
2.1 Memorizing The Cube
With the 2x2x2 having no fixed centres we are free to make sure at least one
corner is solved before we even start. To begin the memorization place the cube
so that the DBL corner is in the correct place and is correctly oriented.
On my cube I use the White side as Up face, the Green side as Front face and
the other faces are Down - Blue, Back - Yellow, Right - Red, Left - Orange. So
for me, that means positioning the cube so that the Blue-Yellow-Orange piece
is in the DBL position with Blue on the D face.
Now we are ready to start memorizing the cube:
each corner has a number associated to it as follows: start with 1, add 1 if the
corner has the Left (Orange) colour on it, 2 if it has the Back (Yellow) colour
on it and 4 if it has the Down (Blue) colour on it.
Thus the Up-Back-Left (White-Yellow-Orange) piece has the number 1+1+2=4
associated to it.
The Down-Front-Right (Blue-Green-Red) piece has the number 1+4=5 associ-
ated to it.
Memorize the number of each cube in turn in the following order:
* the corner in the UFR position (this may not be the UFR corner)
* the corner in the UFL position
* the corner in the UBR position
* the corner in the UBL position
* the corner in the DFR position
* the corner in the DFL position  * the corner in the DBR position
You don’t need to memorize the corner in the DBL position as it is the DBL
piece. Technically, you don’t need to memorize the corner in the DBR position
either as, when you get to that stage, it is the only possible piece left. Having
said that, in bigger cubes we will memorize all 8 pieces. (Although we need only
really do 7.)
This gives a sequence of7 digitsfrom 1-7in some order, whichwe call the corner
permutation.
Forinstance,ifitis2571463then
* the UFL corner is in the UFR position,
* the DFR corner is in the UFL position,
* the DBR corner is in the UBR position,
* the UFR corner is in the UBLposition,
* the UBL corner is in the DFR position,
* the DFL corner is in the DFL position,
* the UBR corner is in the DBR position,
* the DBL corner is in the DBL position.
Inthesolvedcubethecornerpemutationwillbe1234567(8).
We also need to remember the orientation of each corner: the orientation of a
corner will be a number 0, 1 or 2 defined as the number of times you would have
to physically twist the corner clockwise to get the U (or D) part of the corner
into the U (or D) face.
The following table shows the orientation of corners:

[此贴子已经被作者于2006-12-10 13:36:20编辑过]

kitor

Position Face In Which U or D part of corner lies Orientation
UFR U 0
UFR F 1
UFR R 2
UFL U 0
UFL L 1
UFL F 2
UBR U 0
UBR R 1
UBR B 2
UBL U 0
UBL B 1
UBL L 2
DFR D 0
DFR R 1
DFR F 2
DFL D 0
DFL F 1
DFL L 2
DBR D 0
DBR B 1
DBR R 2
DBL D 0
DBL L 1
DBL B 2
In our setup (for the 2x2x2), the DBLcorner will automaticallyhaveorientation
0, but this will not always be the case for larger cubes.
Memorize the orientations of the cube in the same order as you memorized the
positions.
This gives a sequence of 8 numbers, each 0, 1 or 2, the last of which will be 0,
so you don’t need to remember it.
The sum of the orientations over the various corners will be divisible by 3. (*)
Thus 0 1 2 1 1 1 0 0 is a valid orientation since 0+1+2+1+1+1+0+0=6 is
divisible by 3.
Ontheotherhand,01111100isnotavalidorientationsince0+1+1+1+1+1+0+0=5
is not divisible by 3. In this case you can’t solve your cube without taking it
apart.
Inthesolvedcubethesequencewillbe0000000(0).
The fact (*) allows us to only memorize the first 6 numbers if we want (since
the last one is 0, so we could work out the 7th).
So now you have two sequences of numbers remembered. The first is the per-
mutation sequence and has length 8, although you can get away with 7 or even
6. The second is the orienation sequence and also has length 8, but again you
can get away with 7 or even 6.
Now we are ready to don the blindfold. (N.B. the sequences above have to be worked out visually - nothing is to be written down in blindfold cubing, nor
may moves be made to the cube before donning the blindfold.)

[此贴子已经被作者于2006-12-10 13:29:58编辑过]

kitor

2.2 Donning The Blindfold
Don the blindfold.
2.3 Orienting The Corners
This stage is the same for cubes of any size and it should be done first. The
objective here is to find pairs of corners whose orientations are 1 and 2 or to
find triplets of corners whose orientations are all 1 or are all 2. The stage is
ended when every corner has orientation 0.
Supposing we have a corner that needs orienting then there will be at least 2
(by fact (*)). There are two possible situtations: there is at least one corner of
orientation 1 and at least one corner of orientation 2 or not.
In the first case, we will orient a corner of orientation 1 and a corner of orien-
tation 2.
To do this we will require the corners to be adjacent. If they are not, then we
can do a move M to ensure they are.
Forinstance, ifthecorners are inpositionsUBR andDFLthen the moveM=UD
will move them to positions UFR and DFR respectively.
Orient the entire cube so that the piece with orientation 2 is in the UFR posi-
tion and the piece with orientation 1 is in the DFR position (+) (and remember
how you did that - one way it to keep track of the DBL piece - position and
1 1 1 1 1 2 1 2 2
orientation) and do the move R- D- LDRD- L- DUL- UR U- LUR U .
Then undo the orientation of the entire cube (i.e. undo what you did in (+))
1 1 1
and do M- (in the example above D- U- .
This will orient the two corners.
Repeating this we can get to the stage where either all the corners are correctly
oriented or else all the incorrectly oriented corners have the same orientation
(either 1 or 2). In the latter case there will either be 3 or 6 such corners by (*).
As before use a move Nto get two of these corners into the UFR and DFR
1
positions. Use the main move and then perform N- . If the corners had orien-
tation 2, the main move will have correctly oriented the corner that Nmoved
to the UFR position and the the corner moved to the DFR position by Nwill
now have orientation 1.
If the corners had orientation 1, the main move will have correctly oriented the
corner that Nmoved to the DFR position and the the corner moved to the UFR
position by Nwill now have orientation 2.
Then you will have a corner of orientation 1 and a corner of orientation 2 which
you can fix by the method described above. This process will need to be done
twice if you had 6 corners all oriented 1 or all oriented 2.
At this point you should be done orienting corners.
From now on we use moves that do not alter the orientation so you can throw
away that sequence and concentrate on the permutation.

[此贴子已经被作者于2006-12-10 13:37:15编辑过]