Interest in a BH method website?

[deadalnix]

no 2-gen algs for the U perms? I can do them much faster than the STM optimal...

Not sure, the MU gen is really fast. And fit better with « BH mind ».

 

[cmhardw]

no 2-gen algs for the U perms? I can do them much faster than the STM optimal...

Not sure, the MU gen is really fast. And fit better with « BH mind ».

I'm thinking that eventually, after the 3x3 version of the method has been speed optimized that there will be two version of the method, one for 3x3 and one for all other sized cubes.

I personally don't use U perms much on 3x3 because you can't use them on 5x5 for edges. Sometimes on 3x3 I will use a 3x3 optimal alg, but at this point I'm so used to thinking of the optimal commutator that those algs come to mind first if I have a U perm say on the R face.

Obviously you can use the 2 gen U perms and other 3x3 optimized algs for 3x3, that was part of my note that we haven't really done any work at all to optimize for 3x3. What it is optimized for is 5x5, 7x7, etc.

Chris

 

[byu]

I finally returned from my trip, and earlier than I expected. The first thing I looked at was this thread, and I am really grateful that the edges are finally up. However, I although I am tempted to look at the page I have told myself I WILL NOT learn BH edges until I have at least become decent with BH corners.

(My definition of "decent" for BH corners:

1) All commutators can be planned out sub-30
2) Can solve 2x2 BLD (or 3x3 Corners BLD) sub-3.
3) I feel like I really understand all the commutators

)

Anyway, thanks Chris. Can you quiz me on three more 8-move commutators?

 

[cmhardw]

However, I although I am tempted to look at the page I have told myself I WILL NOT learn BH edges until I have at least become decent with BH corners.

I see no reason why you can't learn both. In fact most of the case types are the same, and maybe seeing an A9 on edges will make some of the corner A9's make more sense. There are lots of correlations between piece types.

The only completely new case types for edges are B9's and Slice-Planes. Either I or Daniel can explain these in more depth soon on the website, but other than those cases most cases are similar to corner cases.

--EDIT--
Also there are the Wide turn setup cases which are seen in edges but not in corners. Daniel explained those in the BH Resource Center thread if you want to read more about them.

Anyway, thanks Chris. Can you quiz me on three more 8-move commutators?

Sure.

(URB LFU RFD)
(URB RDB RFD)
(URB BDL FDR)

Chris

 

[byu]

Chris's Pure Commutator quiz

1) 10.9
2) 14.0
3) 10.7

I got them all sub-15! The second one I kind of messed up, so I re tried, so I guess you can call that a DNF. Time to work on A9s

 

[cmhardw]

Chris's Pure Commutator quiz

1) 10.9
2) 14.0
3) 10.7

I got them all sub-15! The second one I kind of messed up, so I re tried, so I guess you can call that a DNF. Time to work on A9s

Great job! I was trying to again give you more difficult cases!

Ok A9's. I'll start easy and they'll get more and more challenging.

(URB FRU DRF)
(URB RFD BLU)
(URB RUF BDL)

Chris

 

[byu]

Complete FAIL at all of these, Chris. I can't seem to figure out A9s, I can't see any cancellations even if I'm looking? Can you give me a "walkthrough" of these commutators and explain how you find the cancellation? Thanks.

 

[Pedro]

(URB FRU DRF)
can be done as an A perm on the right layer

 

[cmhardw]

Complete FAIL at all of these, Chris. I can't seem to figure out A9s, I can't see any cancellations even if I'm looking? Can you give me a "walkthrough" of these commutators and explain how you find the cancellation? Thanks.

They key to doing the A9's is to find the setup move into an 8 move commutator. Don't care at all about finding the setup move or one of the setup moves that cause a cancellation. Just, can you find any setup move at all that creates an 8 move commutator?

Once you get used to doing that, consider the options of all setup moves you have to create an 8 move commutator. At that point you'll start to see which one creates a cancellation. Daniel and I were talking about how to explain seeing the A9's and he came up with a really eloquent way to see them. I'll let him post it when he has the time.

But for now, as a warmup, can you find any 10 move algorithm at all that solves each of those three cases? Give me a 10 move alg for each one, and I'll show you how to find the setup that causes the cancellation.

Chris

 

[byu]

Chris- for the first nine move case:

D' R' U L' U' R U L U' D

There's my ten mover. I'm tired now, I'll see if I have energy for 2 and 3

EDIT: Second one in 10 move form done.

L2 F' U F D F' U' F D' L2

EDIT 2: Third one In ten

B' L2 F' L F L2 F' L' F B

 

[Rubixcubematt]

i think i know the second and third one!

Spoiler

L2 D' L' U2 L D L' U2 L'

F' U2 F' D F U2 F' D' F2

 

[cmhardw]

Chris- for the first nine move case:

D' R' U L' U' R U L U' D

There's my ten mover. I'm tired now, I'll see if I have energy for 2 and 3

EDIT: Second one in 10 move form done.

L2 F' U F D F' U' F D' L2

EDIT 2: Third one In ten

B' L2 F' L F L2 F' L' F B

Brian only the second algorithm works for me. The 1st and third don't seem to solve the cycles.

Try the first and the third one again. Now for the second one, come up with a different 10 move algorithm that solves the same cycle. Meaning I want you to solve it again, but use a different setup turn than the one you used.

What I am asking you to do is to learn to see *all* possible setups into an 8 move commutator. Then you will choose the one that gives the canellation.

Chris

 

[dbeyer]

A commutator that uses 9 moves is rather interesting. You find cancellations with the setups and the insertion or the interchanging.

You want your setup move to be a quarter turn that creates interchangeability with one other piece. You will notice, that another quarter turn in the same direction will make that cubie interchangeable with the third cubie.

You are looking for two consecutive quarter turns of a face that make one piece interchangeable with the other two.

URB -> DFL -> FDR.

You will notice that
L, and L2 created interchangeability between the DFL and the FDR, then the DFL and the URB.

L [D2, LU2L']
S [A, B]

L D2 LU2L' D2 LU2L2

Another good example is a quarter turn setup move that preserves existing interchangeability between two pieces. Then the double turn allows for the insertion of the lone cubie.

Such as URB -> RDB -> DLB
URB and RDB are interchangeable on the B slice.
DLB and RDB are interchangeable on the B slice as well.

URB and and DLB are interchangeable opposites: this is a good thing. It shows you part of the commutator.

Possibilities for the setups are
D or R'.

D [L', DR2D'] => D L' DR2D' L DR2D2
R' [R'D2R, U] => R2D2R U R'D2R U' R

D and R' both move the RDB.
D moves DLB along with the RDB, preserving interchangeability.
R' moves the URB along with the RDB, preserving interchangeability.

Either D2 or R2 preserver interchangeability of the DLB and URB, while moving the RDB with one of the other corners respectively.


Later,
DB

 

[trying-to-speedcube...]

A commutator that uses 9 moves is rather interesting. You find cancellations with the setups and the insertion or the interchanging.

Huh?

The cancellation is always in the insertion, not in the interchanging move... Right?

P.S. my 8-movers are pretty good, most of them are sub-10 now My A9s need some more work to do. What Brian's doing is very smart, just asking other people to test him

Test me too !

 

[cmhardw]

The cancellation is always in the insertion, not in the interchanging move... Right?

For corners only that is correct. All cases that are 9 moves long are A9's, meaning the cancellation is between the setup turn and the A (insertion) part of the commutator. This is not always the case for edges, where you do get cancellations with the interchanging part of the commutator, the B part. We call these, for consistency, B9's. Colloquially we call B9's "Ferris Wheel" cases, because the interchanging side does a full 360 degree turn if you choose your turn direction to match the interchanging and setup move direction.

Test me too !

(URB FUL BLD)
(URB DFL FDR)
(URB BRD BDL)

That is a mix of A9's and 8 movers, but I won't say which are which.

Chris

 

[trying-to-speedcube...]

26.74: I was trying to shoot to BLD, instead of FUL...
DNF: really couldn't find a cancelling setup, so gave up.
6.74: really easy

1: F R' F' L2 F R F' L2
2: L2 U' L' D2 L U L' D2 L' (found it now)
3: R D L D' R' D L' D'

 

[byu]

I can execute A9s pretty quickly now, as well as orthogonals. My only problem is I can only find cancellations a little over half the time. So, I know how to execute A9s, but they are not all optimal. I hope to improve this soon.

Questions:

1. Chris- can you explain Per Specials to me again? The previous explanation didn't make mud sense. Thanks.

2. Of the 30 ten-movers, how many are orthogonals and how many are cyclic shifts?

 

[tim]

2. Of the 30 ten-movers, how many are orthogonals and how many are cyclic shifts?

Daniel answered that in your own thread:

Look check this out:
There are 30 cases that are 10 moves.
There are two case types:
18 cyclic shifts
12 orthogonals.

 

[byu]

I think I fully understand A9s and how to find cancellations (thanks to an extensive AIM chat with Daniel). Can someone quiz me on three commutators that are either pure or A9s, but don't tell me which?

 

[AvGalen]

I am interested in BH for FMC. I really suck at corner insertions and knowing/studying this would greatly improve that.

I am pretty good at edge-insertions, but last week I found a very weird start in about 10 minutes. I needed almost the entire rest of the hour to find good edge-insertions. I couldn't find short ones at all, 9 moves was the shortest I could find. In the end I ended up creating 3 * 10 move insertions that cancelled really nicely, but I am wondering if there were easier/shorter insertions that I missed. This is what I am talking about:
Scramble: L2 D2 F2 U B2 D' F2 D' R2 U' L2 R2 U2 R' B L F' R D' U
Explanation:
Corners first: D2 B2 R D' B' U * B' D2 R B R2
Insert 3 edges at *: R L' D' F2 ** D R' L B' D2 B
Insert 3 edges at **: F' B R U' R' *** F B' D R D'
Insert 3 edges at ***: R' L U' B' U R L' B' D B

It took me about 30 minutes to test all 3 cycles at all the 12 original positions (start and after each of the corners first moves)
Then it took me about 15 minutes to test the other 2 cycles at the newly created positions (about 20 test) and finally a couple of minutes for the remaining cycle at the latest newly created positions (about 10 tests)

Don't get me wrong, I am really pleased with getting a 29 move solution that has 3 10 move insertions, but I am wondering:
1) If I missed short cycles
2) What the distribution for edge-cycles is (a * 6 moves, b * 7 moves, c * 8 moves, etc) where a+b+c+.. seems to be 440
3) A big difference between the corners and edge cycles is the amount of different ways to do the same optimal cycle. Some 8 move corner-cycles can only be done in 1 way, others can be done in 2 ways, but none can be done in 3 ways. For edges it seems that there are often many ways to do an 8 move edge-cycle. Is anything known about this?

I guess I just want to know if I am right in assuming that
a) short corner-cycles are more common than short edge-cycles and
b) Edge-cycles have a better probability for cancellations because there are more to choose from