Here is my technique for doing the cube blindfolded starting with the
2x2x2 cube. (My record for memorizing the 2-cube for solving purposes is 12 seconds to give you
an idea of efficiency.)
It needs a good memory for numbers - my memory for the J. Fridrich moves
is only good for half of them so far but my number memory is good).
1. Orient the cube so that the DBL corner is in the correct position and
oriented correctly (of course, this is automatic unless you have a
specific corner in mind - I always have white as up face and green as
front face when blindfold solving the 2-cube so I have the
blue-yellow-orange cube as DBL with blue on the bottom.)
2-3. (It doesn't really matter which order you do these in.)
Figure out the permutation of the first 7 corners - technically, you only
need to remember the first 6 as since you have corner 8 in position that
automatically gives corner 7).
For this purpose, my corners are labelled as follows:
Up Face, Front Face, Right Face, count as 0,
Down Face counts as 1, Back Face as 2, Left face as 4. (Then add 1.) So it
is like binary.
For instance the white-green-red corner is corner 1.
I then remember the sequence, e.g. 2 5 3 6 1 7 4 (I do actually take the 4
on board although it is not strictly necessary - see above).
For the orientations, I remember the positions of the corners that need
one twist and the positions of the corners that need 2 twists. There will
always be at least one other corner (than corner 8) that doesn't need
twisting.
That's all.
I don't blindfold cube for speed. I work out the solution after the
blindfold part.
Part of this involves continuously having to change the permutation in
your mind whern you get to that point.
Here is my technique.
First of all, orient the corners - after you do this you can forget about
them if you only use orientation preserving moves.
For this purpose, I use 2 of the J. Fridrich sequences:
(e.g. to twist UFR twice and DFR once)
R'D'LDRD'L'D followed by
UL'UR2U'LUR2U2.
Now for the permutation algorithms: I basically
don't want to even possibly mess up so I only use the one algorithm which
is the corner 3-cycle. Using corner 3-cycles only with corners in the U
face or D face preserves orientation. (If you need to swap corners between
these faces you may need to do a move like F2 or R2 etc. first and then
cycle them out.)
OK, so by doing this you can get at least 6 corners in the right position
and you can ensure that if 2 are bad then they both lie in the U face or
the D face and that they are adjacent.
If there are 2 to switch the original permutation of corners was odd. This
can be overcome by turning the U (or D) face once to get one of those
corners in position leaving a 3-cycle to complete the work.
Further advice on solving the cube blindfolded can be seen on my webpage:
www.math.columbia.edu/~carr/BC.html
(actually, this is for the 3x3x3 cube; it's a bit boring perhaps, as for a
number of the earlier cubes I went into great detail about how I solved
each one. Later I just recorded the position of the cube(s) - since you
can't write down the details in advance, it is possible that I may have a
couple of errors in it, but it is correct to the best of my memory.)
Anyway, you can get techniques on solving the 3-cube blindfolded there
too. I'll discuss this as it may be of some interest. The idea is much the
same except you can't ensure that any corner is in place to start:
there are 4 things to memorize
corner permutation
edge permutation
edge orientation
corner orientation
The hardest is probably corner orientation because you have to remember
not only the positions of the corners to twist but also how many times.
Next comes edge permutation as it is 12 things to remember (although you
could remember just 11). The other bits are fairly easy.
The technique I use is currently just to keep white up and green front
(but I have on occasion done others) as then I know the numbers for the
edges and corners and can memorize faster. Corners are labelled as before
and edges are labelled 1-12 thus (UF, UB, UR, UL, DF, DB, DR, DL, FR, FL,
BR, BL - thus the faces are prioritized U, D, F, B, R, L and labelling
follows this - this is also helpful for remembering orientations).
Edge orientation is 0 (correct) is the edge has its high priority colour
in the higher priority face and 1 (incorrect) otherwise. e.g. If the
white-green edge is in the FR position it has orientation 0 if the white
part is in the front face and 1 if the green part is in the front face -
since white (being the colour of the up face) has higher priority than
green (being the colour of the front face) and the front face has priority
over the right face).
The technique is then to orient stuff before permuting.
Use 3-cycles to permute - there may be a signature problem with the
permutations (i.e. you may have to switch just 2 corners at some point
say). In this case, I usually try to get the corners adjacent and switch
them with 2 edges in a T-formation.
C E C
E
This may be done after permuting various other edges.
3-cycling edges in the U,D,R,L faces preserves orientation of edges but in
the F,B faces it changes the orienation of 2 edges so I don't 3-cycle in
those faces.
I use a couple of other moves sometimes too.
e.g. (F2R2)3 does a double transposition switching edges UF with DF and UR
with DR (and preserving orientations). Also Rs2F2Rs2B2 switches edges UF
with DF and UB with DB etc.
I don't always do this but if you try to place the edges in the middle
layer (9-12) or in one of the other layers, if you prefer then you can cut
out a part of the permutation you need to remember.
A move I rarely do but may, if I remember it is
(F2R2)3R(U2R2)3R' which 3-cycles edges
in positions DF->UB->UF.
You can simplify it by cancelling some Rs
e.g. (F2R2)2R(U2R2)2U2R'.
I haven't mentioned orienting the edges yet:
I use 2 moves here (again from the J. Fridrich set)
First is
LsFRsU2LsFRs followed by
B2U'RsB2LsU'B2
(which flips UB and UL edges).
Second is
FsUF'U'Fs'LFL' followed by
F2ULsF2RsUF2
(which flips UR and UL edges).
My record for memorizing the 3-cube is 167 seconds.
For multiple cubes it gets a bit harder - I only have 2 3x3x3 cubes so I
can't go for the record but I can do 2 cubes. The hardest thing is trying
not to get confused over which stuff belongs to which cube. I always take
the cube with the harder orientations first as this is the hardest bit to
remember (for me). Since that bit is done first, it takes out the hard
part at the start.
I haven't tried a 4x4x4 blindfolded (my old one broke so I can't, unless I
use a subset of a 5x5x5 which might be confusing) but I have a fair bit of
theory behind it and think it is quite possible.
My technique here would be:
orient corners,
solve the centres without disturbing edges or corners (I used to do this
at the end when solving big cubes),
permute corners
3-cycle edge components without altering anything else to solve edges
solve like a 3x3x3 cube blindfolded
if needs be flip one edge using C Hardwick method.
Hope this is of some use,
Dr. C.