brian's own blindfold rules

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brian's own blindfold rules

Post by supercha8 on Fri Mar 14, 2008 5:31 pm

Blindfolding 3x3

Introduction
This blog I created will teach you how to Blindfold solve a Rubik’s Cube 3x3x3. The method I am going to describe here is the “Two-Cycle Method”, but I am going to describe my way of memorization. You can get to as fast as 5 minutes with this method.

First of all, remember that the Rubik’s Cube has only 20 movable pieces, 8 Corners and 12 Edges. So it is like you have to remember 20 stuffs.

We blindfold the Rubik’s cube 3x3x3 in four steps: Orient Corners, Orient Edges, Permute Corners and Permute Edges, Respectively.

We memorize the Rubik’s Cube in this order: Edge Permutations, Corner Permutations, Edge Orientations, and Corner Orientation. I will tell you later why but anyway, you can memorize in any order you want, it depends on you

You can say that Blindfolding is hard, but actually it is not. You can think that turning each side can ruin your illustration, and you are correct, but we have formulae or algorithms and sets that we can use to avoid this problem.

Here are the following formulae that I am using:
Let me give you some Arithmetic:
B+B=0
A+A=0
A+B=B
B+A=A
0+A=B
0+B=A
Let me give you a group:
Eo={(U,U’)(D,D’)(F,F’)(B,B’)(2L,2R)}
The Eo group is not a formula but a group
Orientation
Edge Orientation:
SS :{( M U M U M) 2U (M’ U M’ U M’) 2U} --- It flips the UB (Upper
Back) edge and the UF (Upper Front) edge.

SS :{( M U) 4 (M’U) 4} ---It flips four edges: {(UF) (UB) (UL) (UR)}

Corner Orientation:
Commutator 1= SS :{[( R’ D’) (R D)] 2 U [(D’ R’) (D R)] 2 U’} ---It twists the UFR corner Counter-Clockwise and the UBR corner Clockwise
Commutator -1=SS:{[(D’ R’) (D R)] 2 U [( R’ D’) (R D)] 2} ---It twist the UFR corner Clockwise and UBR counterclockwise.

Permutation
SS :{( R U R’) (U’R’) F 2R (U’R’) U’ (R U R’) F’} ---It swaps UR with UL and swaps UFR with UBR. It looks like a T, so it is called the “T-Permutation”.

Okay, let us go to the memorization phase

Follow this scramble, White face on top and Green face on front:
D L2 F2 D L U' R2 D2 R L B F2 L2 U' R' D' R2 B2 U2 B' U' F B2 D F
Memorization Phase:
Let me tell you how I name each pieces of a Rubik’s Cube 3x3x3
Corners
UFL 1
UFR 2
UBR 3
UBL 4
DFL 5
DFR 6
UBR 7
UBL 8
Edges
UL A
UF B
UR C
UB D
FL E
FR F
BR G
BL H
DF I
DR J
DB K
DL L


You can notice I named the corners and edges position in a counter-clockwise manner.
We are going to hold the cube in a way where the white center is on top and Green center on front

Permutation Memorization:
Edge Permutation:
We use T-permutation to swap edges C and A and corners 2 and 3, don’t mind about the corners yet. So we start at position C. The corner in position C must go to position J, so we remember “J”. When we do the T-permutation, the edge in C will go to J and J to C. So, now it is time to permute the corner in J, the J goes to H, so we shall remember “JH”. The H then to K then K to A. So we remember “JHKA”. The A goes to I, I to B, B to L, L to B, B to D, D to E, E to F and F back to C. When you go back to C, you stop, and check if are there any more unpermuted edges, as you can see, there is none more. So we remember the string “JHKAILBDEF”. We don’t need to remember C, because when you permute to F, the edge in C will permute to F and edge in F will permute to C.


Corner Permutation
Corners
UFL 1
UFR 2
UBR 3
UBL 4
DFL 5
DFR 6
UBR 7
UBL 8

We use the T-permutation to swap corners 3 and 2 and edges A and C, so we will start the corner that is on position 3. We permute the corners like in “chains”. Don’t mind the edges yet.
Look at position 3 of your scrambled cube, that corner on position 3 belongs to position 2. So we shall remember the number “2”. When the corner in position 3 swaps with the corner in position 2, the corner in position 2 will go to position 3 and the corner that WAS in position 3 will be permuted to position 2, so it is in chain. So now look at the corner in position 2, as you can see that it needs to go to position 4. So we remember “24”. The the corner in position 4 will go to position 3. Now look at position 4, it goes to 1. So we remember “241”. Then the corner in position 1 shall go to 5, then 5 to 6 and 6 BACK to 3. So we remember “2416”. We don’t need to remember 3 because when you permute to 6, the corner in 6 will automatically go to 3. You memorize the corner permutation until you go back to position 3.
But we still have two corners left, which is 5 and 8, so we have to start another chain. Let us do this, first we temporarily “unpermute” the corner on position 3 to position 5. So the corner in position 3 will go to position 5. So, as you can see, the corner in must go to 8 and 8 back to 5 and 5 back to 3. So we remember “585” plus the chain above so we have a “2416585”. It is like we just “set aside” the corner 3.
But wait, remember, when we are swapping two corners, we also swap two edges. So when we do the T-permutation once, we swap the edges and if we do T-permutation again, we swap them back. So it means, if we do odd number of T-permutations, the edges are not the same with our memorization and if we do T-permutation an odd number of times, the edges are the same with our memorization above. As you can see with the memorization above, the “2416585”, is 7 digits, and 7 is an odd number. So it means, the edges are not the same with our memorization because we know that the first edge belongs to J. This is what we call “parity”, parity means equality. To fix this, we just do another T-permutation, so that the edges will go back to its correct position. Don’t worry about the corners 3 and 2, they will be solve when you swap the last two edges, because when you swap the last two edges you also swap the last two corners. According to group theory, the rubik’s Cube disjoint cycles, when crossed, the number of crosses is odd, so it means we do an odd number of T-permutations.

Orientation Memorization:
Edge Orientation
Okay, let me teach you first how to Identify if an edge is oriented or not.

Let me give you a set:
Eo={(U,U’)(D,D’)(F,F’)(B,B’)(2L,2R)(2U,2D)(2F,2B)}
An Edge is oriented if it can reach its destination when and if you use any of the dominant or range any of the ordered pair of the Eo group. I mean, that certain edge can reach its solution if you use any of the maneuver or any combination of maneuvers on the Eo group. You can notice the only moves that is not there is {(R, R’)(L, L’)}.

Let me demonstrate to you how:
Look at your cube; let us identify each edge one by one.
Edge A:
Imagine permuting the edge using any moves in the Eo set, you imaginatively permute the edge to position I by using {U’ 2F}, when you do that, you can notice that the edge is not flipped. You cannot imaginatively use permute it using {L F’}, because the “L” move is not in the Eo set. So the Edge A is inoriented
Edge B:
Imagine again, you use 2U move to permute it in your imagination and you can see that it is not flipped when you use 2U in your imagination. So that edge is oriented and 2U is in the Eo group.
Edge C:
Do a 2L move, 2L is within the Eo group, so it is oriented
Edge D:
SS:{2U F}, 2U and F is in the Eo group, so it is oriented.
Edge E:
SS:{null}, but you can see it is flipped, so it is inoriented.
Edge F:
SS :{ F U’}, oriented
Edge G is inoriented

Edge H
SS:{B}, oriented
Edge J:
SS:{D B’}, oriented
EdgesI, K and L are inoriented because no matter what D moves you do, it is flipped.

So now you have identified, now remember them in any order you want. Remember the inoriented edges which is “AEGIKL”
Just remember that you can use any move except {(R, R’) (L, L’)} to test if an edge is oriented. If it cannot reach its solution by just using any moves with in the Eo group, then it is immediately considered inoriented.

PS: There are cases when there are more inoriented edges than oriented ones. So you just have to do is to remember the oriented edges instead of inoriented ones. But if there are less inoriented edges than oriented ones, then you just have to remember the inoriented edges. It is Just a common sense.

Corner Orientation
Okay, the reason we memorize the corner orientation last is because the first step in solving process is the corner orientation. So it means you only have to put the Corner Orientation Memorization in a short term memory. I hope you now get it.
This phase can be a bit tricky at first.

A corner can be considered oriented when one of its three colors face the same direction or opposite the direction of its top or bottom center color. Example, the top of your cube right now is white and bottom is yellow. So it means all the yellow and white of all the corners should be facing either up or down, whatever which is logically possible. Let me show you in this scramble.

Corner 1: It is inoriented, because the yellow color is not facing up.
Corner 2: Is inoriented, because the white color is not facing the same direction as the white center.
Corner 3: It is oriented because the white is facing the same direction as the white center.
Corner 4 is inoriented.
Corner 5: Oriented
Corners 6-8 are inoriented.
It is so obvious if a corner is oriented or not, but there is one problem, a corner can be either inoriented or twisted counter-clockwise or clockwise.
Let me show you how to identify if a corner needs to be twisted clockwise or counter clockwise.
Inoriented corners are: 124678
Let A= twist clockwise
Let B= twise counter-clockwise

Corner 1 should be twisted clockwise, so assign it with A
Corner 2 should be twisted clockwise, so assign it with A
Corner 4 should be twisted counter-clockwise, so assign it with B
Corner 6 should be twisted counter-clockwise, so assign it with B
Corner 7 assign it with B
Corner 8 assign it with A

Now, how to memorize it, notice that the commutator 1 twist corner 3 clockwise(A) and corner 2 counterclockwise(B). So corners with different letters as one pair. Remember the corners 1 and 4 as one pair, 2 and 6 as one pair, 7 and 8 as one pair. So you only have to memorize 3. Memorize the pair, 1 and 4 as “1”. Corners 2 and 6 as “1” also, Corners 7 and 8 as “-1”. I will tell you later why at the solving phase. 1= commutator 1, -1=commutator -1.
All the memorization depends on you.

Solving Phase:
Orient Corners:
We will use the commutators. We orient corners on position 2 and 3, so we will put the corners that needs to be oriented to position 2 or 3 using what we call “setup moves”.

First, what is setup moves? Setup moves are moves that you use to setup an edge or corner to a correct position.

Let’s first orient the corners 1 and 4. The corner 1 is A, so do a 2U move to put corner 1 to position 3, at the same time, the corner 4, which is B will go to position 2. So let’s use the commutator 1 to twists. So we add B to B, so that corner 1 then equals to 0(look the arithmetics above), and A+A, so that the corner 4 equals to 0. If a corner equals to 0, then it is oriented. Now I hope you know why I told you to memorize 1 and 4 as 1, because you only need to use the commutator 1 to orient them. After doing the commutator 1, do a 2U move to return the corners to the original its original position. You notice that you oriented corners 1 and 4 without affecting the orientation or permutation of any other pieces.

supercha8
2x2x2
2x2x2

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Re: brian's own blindfold rules

Post by Brian Nicole Uy on Fri Mar 14, 2008 5:41 pm

I haven't finished that yet supercha8, don't post it yet:) I will finish it and email it to Lester so he can put it in the Speedcubing solutions

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Brian Nicole Uy
2x2x2
2x2x2

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