Difference between revisions of "Beyer-Hardwick Method"

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Thanks to LexCubing it's no longer a stub. This is not a tutorial so if you want a better understanding and how to do them go look up Byu's unfinished BS but hey corners are done. I'll be making a tutorial someday so stay tune but you don't need to be optimal to 3-style just know how Pure Comms work and setup to them and everything will be okay.
 

Revision as of 13:20, 23 May 2017

Beyer-Hardwick Method. An advanced blindsolving method based on the use of 3-cycle algorithms. The fundamental idea behind the BH method is to use pre-memorized, move optimal, commutator 3-cycles for all possible 3-cycles starting from a fixed buffer location. For pieces where orientation is defined, the position and orientation of pieces are solved simultaneously. The use of commutators allows the BH method to be used for solving any sized cube blindfolded.

BH Corners

These are the different types of commutators you will "see" while learning BH.

Pure Commutators (8 moves) - are the purest and smallest form of commutators and all other commutators are just setups into them hence called Pure Commutators (except Cyclic Shifts and Per Specials). They follow this formula: ABA'B' or [A, B] for short.

A is always a 3 move insert B is the interchange move and always 1 move and opposite from the middle move of A. Ex [R U R', D] U is the middle move of the A move that means the B move must be some form of D move

To recognize 1 corner is in 1 layer and the remaining 2 are in a different layer. The 2 corners in one layer must be interchangeable and there must be a 3 move insert between 1 corner in 1 layer and 1 corner in the different layer.

There are only 3 A moves: R U R' R U' R' R U2 R' All Pure Comms are composed from these 3 A moves meaning there's only 18 algs and everything else is just mirror/inverse/rotation from the 18 algs.

A9 (9 moves) - are conjugated Pure Comms with a cancellation resulting in 9 moves instead of 10. They follow this formula: SABA'B'S' or [S: [A, B] ]where S is the setup move.

Ex. [R: RUR', D] becomes R R U R' D R U' R' D' R' or simply R2 U R' D R U' R' D' R'.

All setup moves or S moves must cancel with A. There are no B9s or a corner commutator with a S move that cancels with the B move. If you find 1 then that just means it's a Pure Comm. Edge commutators though have B9s.

To recognize them they're the same as Pure Comms but they don't have a 3 move insert. But that's not always the case so just use elimination to figure it out. The first rule always applies so if you see that then it's a A9.

Orthogonals (10 moves) - are conjugated Pure Comms with no cancellations resulting in 10 moves instead of 9. They follow the same formula [S: [A, B]] as well but the S move doesn't cancel with A nor B.

To recognize them you must know 2 terms:

Opposites - when 2 corners can't go to each other's places with 1 quarter turn. Ex. UBL is opposite to DBR Note: We're only talking permutation-wise. Meaning UBL being opposite to BDR is as the same as saying UBL is opposite to DBR.

AnI or nI (Adj Non-interchangeable or Non-interchangeable - nI is a better term since saying AnI sometimes doesn't make sense. Put it simply a sticker is not interchangeable with another if you can't do it 1 move.

To recognize all 3 corners are opposites and nI to each other. (See what I mean? Saying AnI here doesn't make sense when alll the corners are opposite)

To do them just do ANY quarter turn S move and it will setup into a Pure Comm and undo the S move.

Cyclic Shifts (11 moves) - they don't come from Pure Comms and follow a different formula: [A: B] [C: B] or A B A' C B C'

A is always 2 moves which are comprised of 2 adjacent layers (Ex. F and R) and one is going clockwise and another going counterclockwise

B is always a half turn and is not a opposite layer to either A or C Ex. A is R F so B must not be any form of B or L move

C is the reverse of A (not inverse) Ex. A is R F so C must be F R

Ex. [R F: U2] [F R: U2]

To recognize all 3 corners are on the same layer and are nI.

To do them figure out the middle piece of the cycle. Ex. UBL -> LFU -> BRU The middle piece is UBL and must go to LFU. Do [R F: U2] to swap them and now the next piece must go to BRU so do [F R: U2] to swap them and then you're done.

If you don't understand any of these it's all right since all Cyclic Shifts are the same meaning just by learning the one alg above you just need to mirror/inverse/rotate to solve any Cyclic Shift.

Column Cases (11 moves) - they're just 11 movers that can be done in 2 ways: a setup into an A9 with no cancellation or a setup into a Cyclic Shift with a cancellation.

To recognize there are 2 corners interchangeable by a half turn and the remaining corner is nI to them.

Per Specials (12 moves) - a special type of commutators that follow the same [A, B] formula but the A part is a 5 move insert and B is just a half turn. There's 6 of them and they're all the same meaning you just need to learn 1 alg and just mirror/inverse/rotate it.

Ex. [L U2 R' U2 L, U2]

To recognize all 3 corners are opposite and mutually interchangeable. Ex. UBL -> DFL -> DBR

BH Edges

- these are the type of edges you'll "see" while learning BH.

Half Slice-Plane (4 moves) - they're the Per Specials of edge commutators by being recognized similarly to Per Specials and has a unique property. Per Specials need a 5 move insert while Half Slice-Plane to be optimal must interchange twice on the same outer layer making the commutator really small only needing 4 moves to do it.

It is recognized by having all the edges on the same slice and are mutually interchangeable.

To do them you must know what they're composed of: [A, B]

A is some sort of half turn of a outer layer where most of the edges are in B is some sort 1/4 turn of a slice where all the edges reside and setups into the A layer for the interchange

Ex. UF ->DF -> UB

To do them figure out what's the middle piece of the cycle. UF is the middle piece and must go to DF. They must interchange on the A layer, so what's A? In the U layer 2/3 edges resides so A is a U2. How to we interchange it with DF with a U2?

That's where B comes in, B is the 1/4 of the slice where all edges reside so M is B. How do we know if we do M or M'? Well use logic, if we do M the UF and DF stickers will go to the D layer but we want it to go to the U layer so we do M'.

Final answer is [A=U2, B=M']


Slice-Plane (SP5, SP7) (5, 7 moves) - Half Slice-Planes really are special as not all commutators come from Pure Comms instead some come from Half Slice-Planes.

Slice-Planes are conjugated Half Slice-Planes. They follow the formula: [S: [A,B]] where S is a one set up and [A, B] is the 1/2 Slice-Plane.

To recognize them is just to know all 1 move setups to a certain Slice-Plane:

5 movers are conjugated 1/2 Slice-Planes with a cancellation. There are no optimal cancelleation with S moves with M turns or U2s so All S moved must be a U or U'

SP7s are conjugated SP5s without cancellations. Since there must be no U2 for Slice-Planes you can't use U or U' S moves instead you must do M, M', or M2 S moves.

Pure Commutators (8 moves) - All other commutators come from these. They follow the formula: [A, B].

To recognize there's an interchange on the slices or layers and there is a either a layer insert or slice insert. Ex. M interchanges: UF -> DB (M2) Layer Interchange: UR -> FR (R or R') M insert: U M2 U' or [U: M2] Layer insert: U R U' or [U: R]

They're exactly Pure Corner Comms so just do [A, B].

A9/B9 (9 moves) - Exactly like A9 corner commutators except B9 exists meaning there's a optimal solution where the S cancels with B. To recognize there's no 3 move insert like A9 corner comms. There are no M S moves that cancels with B if B is also a M move.

Orthogonals (10 moves) - To recognize all edges can't be interchange with each other in 1 move. To do them just do some sort of turn and it will setup to a Pure Comm. Formula: [S: [A, B]].

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