Thursday, 5 June 2014

3 x 3 x 3 BlindFold - M2R2 Method

How To Solve A  3 x 3 x 3 BlindFold using M2R2 Method

         There are many methods to solve a Rubiks cube blindfold (without seeing the cube) . But amongst those methods I prefer to follow this M2R2 Method by which i feel more convinient . I will also help you get to the other methods with I know . As I said before , the postion of the cube , how you hold the cube in your hand is much more important before starting with the methodology . The Position is : 


White   - Top (opposite to Yellow)
Yellow - Bottom (opposite to White)
Red      - Front facing you (opposite to Orange)
Blue      - Right side of Red (opposite to Green)
Green    - Left side of Red (opposite to Blue)
Orange  -Remaining side (opposite to Red)


 Here's an example solve, the scramble is

 B' R' B' U' F L' U F2 L F R' D' R' B D F2 L2 D' R2 D'
and the solution is just below .


Target
Algorithm
FR
U R U' M2 U R' U'
UL
L U' L' U M2 U' L U L'
RB
l U' R' U M2 U' R U l'
DB
M U2 M U2
LD
x' U L U' M2 U L' U' x
RU
x' U' R U M2 U' R' U x
UB
M2
DR
U R2 U' M2 U R2 U'
DB
M U2 M U2
FL
U' L' U M2 U' L U
BLD
U' L U R2 U' L' U
FLU
R' U L U' R2 U L' U' R
RBD
(R' U R2 U' R' F' R U R2 U' R' F)
ULB
L' U' L U R2 U' L' U L
UBR
R2
FDL
U' L' U L' U' L U R2 U' L' U L U' L U


This is an easy solve just to show the core idea. It does not include odd parity, breaking into new cycles, and cleaning up misoriented pieces . Though, every once in a while, you might indeed get a solve like this . In this example you can notice that " M2 " & " R2 " which are repeated throughout the algorithm . You better don't get much concern with this example because you have not learnt yet and this is just an example to help you with . Lets begin with our work .

Let me first talk about edges. Notice you should think in terms of stickers. When I say LU, I mean the L part, when I say UL, I mean the U part. It is Recommended that you should memorise each and every algorithm for all the targets which you can see below .


Edges
Target
Algorithm
To solve one edge at a time, we use place DF as "buffer" and swap the edge currently in that place to where it belongs. we use one swap algorithm which swaps DF with UB. To swap DF with another edge, we first bring that edge to UB with setup moves, then apply the swap, then undo the setup moves.

Since it's impossible to just swap two pieces and not change anything else on the cube, we do have to have some side effect. My swap algorithm actually is only an M2 move, so the side effect is a rotation of the M-slice centers and swapping the FU and BD edges, though we just think of solving these two relative to the centers, so they're not really swapped (relative to the centers they stay where they are). It only matters for choosing the algorithms for these two edges, think of the "target" telling you where the edge belongs *before* the algorithm. So for example if you target FU then *after* the algorithm the edge will actually end up at BD.

Obviously it is called as "M2 method" because of the prominent M2 move.The algorithms (see right side) should be very easy to understand.

For the M-slice edges we use the same algorithm for both orientations. we might end up with some flipped M-edges but that's not too bad (as you'll see later). The alternative is to use longer algorithms for half of the cases.
UB
BU
M2
M2
FR
DR
BR
UR
U R U' M2 U R' U'
U R2 U' M2 U R2 U'
U R' U' M2 U R U'
R' U R U' M2 U R' U' R
FL
DL
BL
UL
U' L' U M2 U' L U
U' L2 U M2 U' L2 U
U' L U M2 U' L' U
L U' L' U M2 U' L U L'
RU
RF
RD
RB
x' U' R U M2 U' R' U x
x' U' R2 U M2 U' R2 U x
x' U' R' U M2 U' R U x
l U' R' U M2 U' R U l'
LU
LF
LD
LB
x' U L' U' M2 U L U' x
x' U L2' U' M2 U L2 U' x
x' U L U' M2 U L' U' x
r' U L U' M2 U L' U' r
DB
BD
UF
FU
M U2 M U2
M U2 M U2
U2 M' U2 M'
U2 M' U2 M'


Now the next part to be solved is the corners .


Corners
Target
Algorithm

This is really very much like the edges, only that things are happening in the R-slice instead of the M-slice. In this method , we can solve the corner at DFR by swapping it to UBR with the "algorithm" R2. The side effect is a rotation of the R-slice "centers" (which are edge pieces), and URF and DRB stay where they were relative to the R-slice centers.

Targets outside the R-slice (i.e., in the L-slice) get swapped with DFR after bringing them to UBR with setup moves.

Targets inside the R-slice have special algs, and for UBR we can simply use R2 for every orientation so that it'll likely end up misoriented which we can fix at the end (you'll see it soon). 

Of course, feel free to use other algs, especially for FUR and BDR you might like A-perm plus R2 better.
UBR
BRU
RUB
R2
U' L' U L U' L' U R2 U' L U L' U' L U
U' L U L' U' L U R2 U' L' U L U' L' U
BLD
ULB
DLF
FLU
U' L U R2 U' L' U
L' U' L U R2 U' L' U L
U' L2 U R2 U' L2 U
R' U L U' R2 U L' U' R
LBU
LUF
LFD
LDB
U' L' U R2 U' L U
L' U' L' U R2 U' L U L
L2' U' L' U R2 U' L U L2'
L U' L' U R2 U' L U L'
BUL
DBL
FDL
UFL
y R U R2 U' R' F2 R U R2 U' R' y'
U' L2 U L' U' L U R2 U' L' U L U' L2 U
U' L' U L' U' L U R2 U' L' U L U' L U
L U' L' U L' U' L U R2 U' L' U L U' L U L'
RBD
BDR
DRB
(R' U R2 U' R' F' R U R2 U' R' F)
(R U R' D r2 U') (R U r2' U') (D' R)
(R2 U' R' F') (r U R2' U') (r' F) (R' U)
RFU
URF
FUR
(F' R U R2 U' R' F R U R2' U' R)
U' (R F' r U R2 U') (r' F R U R2')
(R2' U' r x) (l2' U L U') (R' U) (L' U' L') (R' U)

Now comes the final part . we will see how to deal with the special cases: odd parity, cleaning up misoriented pieces, dealing with more than one edge or corner cycle. This helps you in dealing with bad position in the cube which may occur after performing M2 method (after correcting possible edges) or after performing R2 method (after correcting possible corners) .


Special cases
Goal
Algorithm
If there's another cycle when we are done with one, we break into the new one , choosing a target with a fast algorithm (usually M2 or R2).

After solving the edges, we might end up with some M-slice edges flipped and some non-M-slice edges flipped because they were like that at the start of the solve. we flip them all together, usually with one of the algorithms on the right side after a setup move. Similarly corners, though mostly DFR and UBR are misoriented.

In case of odd parity, the M and R crosses need to be rotated back and the parity algorithm does just that.

we have one big clean-up step at the end, fixing misoriented edges and corners and the parity all at once. 


Orient
edges
(M' U)*4
M' U M' U M' U2 M U M U M U2
(M' U M' U M' U M' U')*2
(U L U' L') (M' U)*4 (L U L' U')


Orient
corners
(R' U R2' U' R2 U' R' U) (R U R' U') (R2 U' R2 U)
(R U R2' U' R2 U' R' U) (R U R' U') (R2 U' R2 U R2)
(L' U' L U' L' U2 L) (R U R' U R U2 R')
(R U2 R' U' R U' R') (L' U2 L U L' U L)
Odd
parity

(R2' U' R2) (R' U) (L' U2') (R U' R' U2 R) (L U') (R2' U)
Combi-
nations
(R2 y') (R' U' l' L U' L U) (L' r' U) (l U') (F R U)
(L2 y') (R' U' l' L U' L U) (L' r' U) (l U') (F R U)



The Algorithms for different target stickers are to be memorised . The way of memorising the algorithm , I leave it in your part because I can only say What to learn but i cannot say how to learn .

I have also listed few more Example Scrambles just to help you and make you fimiliar with this Method . 

Example Scrambles:

Solve 1 
Solve 2 
Scramble:
L U L' B' D2 U R' F2 B' D' U B' R2 U' D' F R D' F' U R B2 D B' D'
Scramble:
R B2 L' R2 D2 F2 R2 F2 R U2 F U' F2 D' B' D2 U' R' B2 D' F'
DB: M U2 M U2
UB: M2
DL: U' L2 U M2 U' L2 U
UR: R' U R U' M2 U R' U' R
LF: x' U L2' U' M2 U L2 U' x
DB: M U2 M U2
BR: U R' U' M2 U R U'
RF: x' U' R2 U M2 U' R2 U x
BU: M2
DB: M U2 M U2
UB: M2
DL: U' L2 U M2 U' L2 U
RU: x' U' R U M2 U' R' U x
FL: U' L' U M2 U' L U
BD: M U2 M U2
BR: U R' U' M2 U R U'
RF: x' U' R2 U M2 U' R2 U x
BU: M2
Orient edges:
L F (M' U M' U M' U2 M U M U M U2) F' L'
Orient edges:
R F (M' U)*4 F' R'
LUF: L' U' L' U R2 U' L U L
UBR: R2
DLF: U' L2 U R2 U' L2 U
BDR: (R U R' D r2 U') (R U r2' U') (D' R)
RBD: (R' U R2 U' R' F' R U R2 U' R' F)
BRU: U' L' U L U' L' U R2 U' L U L' U' L U
BLD: U' L U R2 U' L' U
LBU: U' L' U R2 U' L U
DBL: U' L2 U L' U' L U R2 U' L' U L U' L2 U
LUF: L' U' L' U R2 U' L U L
UBR: R2
DLF: U' L2 U R2 U' L2 U
BDR: (R U R' D r2 U') (R U r2' U') (D' R)
RBD: (R' U R2 U' R' F' R U R2 U' R' F)
BRU: U' L' U L U' L' U R2 U' L U L' U' L U
BLD: U' L U R2 U' L' U
LBU: U' L' U R2 U' L U
DBL: U' L2 U L' U' L U R2 U' L' U L U' L2 U
Orient corners and fix parity:
(L2 y') (R' U' l' L U' L U) (L' r' U) (l U') (F R U)
Orient corners and fix parity:
(L2 y') (R' U' l' L U' L U) (L' r' U) (l U') (F R U)


Thus we , now , have learnt how to solve a Rubiks Cube BlindFold using the M2R2 Method . Thanks for joining me Friends ...