Beyer-Hardwick Method
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
I put to much info on this. I should have made a tutorial instead but the info here is not tutorial wothy yet.
-LSLL
BH edges
Types of commutators you'll "see" while learning BH.
Half Slice-Plane Commutators (4 moves) - These commutators are recognized by being on same slice and are mutually interchangeable. To do them you must interchange twice on the same outer layer. Unlike traditional [A, B] commutators, A is the insert move and B is the interchange move. But for Half-Slice Planes A is the interchange move and B is a just a setup to an interchange for A.
Slice-Planes (SP5, SP7, SP9) (5, 7, 9 moves) - Alongside Pure Comms most of the commutators come from Half Slice-Planes meaning Slice-Planes are conjugated Half Slice-Planes.
To recognize them 2 edges are of the same group (UF and UB are outer stickers while stickers like RF are inner stickers). To do them you must do a 1 move setup to either a Half Slice-Plane(SP5) or a SP5(SP7). SP5s' setup moves cancels with the Half Slice-Plane making the move count to 5 instead of 6.
SP9s are Chris's BS. They're SP5s made longer for no reason. Correct me if I'm but if do a SP9 I can do a SP5 instead. Wtf Chris?
Pure Commutators (8 moves) - alongside with Half Slice-Planes all other commutators come from them. They are recognized by having 2 edges in one layer/slice and are interchangeable and the other corner in another just like how Pure Corner Comms are recognized (instead corners are on different layers) and there's a 3 move insert.
A9/B9 (9 moves) - like A9 Corners they're recognized by using elimination and/or having no 3 move insert that looks like a Pure Comm. Only difference now that there are cases that can only be solved optimally by having the setup move cancel with B.
Orthogonals (10 moves) - are recognized by having all the edges not interchangeable with each other in 2 moves. To do them you must do some sort of setup move and it turn into a Pure Comm, do it and undo the setup move. You actually need to choose the right S move for this.
-LSLL
External links
- BH method for corners - Hardwick
- BH method for 3x3 edges - Hardwick
- BH method for 3x3 edges - Skarrie
- BH method for corners - Riffz
- BH method for corners - Jalocha
- edge cycles - lucarubik
- corner cycles - lucarubik
- Speedsolving.com: Thoughts about the BH method* [http://www.speedsolving.com/forum
- Speedsolving.com: Brian Yu's tutorial for BH corners
- Speedsolving.com: Chris Hardwick's explanation of BH 3x3 edges
- Speedsolving.com: Beginner BH ideas for big cube edges
- Speedsolving.com: Intermediate/Advanced BH ideas for big cube edges
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