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Random Cubing Discussion

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Interesting how the thread IDs 2 and 1 are both inaccessible. I wonder what's on there.

EDIT: how did that happen

Is Robert Yau a mod? How was my post edited by him?

OK IM DUMB HOW DID I NOT NOTICE

GOSH
 
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Are there any adjacent states that are both optimally solved in 20 turns (HTM)? So for example, I have a state that is optimally solved in 20 moves HTM, I perform one turn in HTM and the new state is also optimally solved in 20 moves HTM?
Yes, there are, for example:

B1L1B3L3F2D3R1B3U1D2B1L1B2R1D1R3B2R2B2R3
L2F3L2D1F2B2L1B3R2B1D3R3F1U1L1R2D2B2L3R2

Both of them optimal 20f*, and the difference between them is an F/F' turn.

A cluster of 9 cube states with 20f* has been found, see below (they form a connected graph, where an edge means a single move):

Here is a cluster of 9 (by position):

There are only six unique mod-M+inv in this set of 9.

FL RU BL LU FR RD BR LD UF DF UB DB FDR BRD URB UFR DFL FUL BLU DLB C_4h A 8
FU RU BL LU FD RD BR LD RF LF UB DB FLD BRD URB RFD LFU FRU BLU DLB C_4 A 4
FU RU BD LU FD RD BU LD RF LF LB RB FLD BUR LUB RFD LFU FRU BDL RDB C_4 A 4
FR RU BD LU FL RD BU LD DF UF LB RB FUL BUR LUB DFL UFR FDR BDL RDB C_4 A 4
FR RU BR LU FL RD BL LD DF UF DB UB FUL BLU DLB DFL UFR FDR BRD URB C_4h A 8
FD RU BR LU FU RD BL LD LF RF DB UB FRU BLU DLB LFU RFD FLD BRD URB C_4 A 4
FD RU BU LU FU RD BD LD LF RF RB LB FRU BDL RDB LFU RFD FLD BUR LUB C_4 A 4
FL RU BU LU FR RD BD LD UF DF RB LB FDR BDL RDB UFR DFL FUL BUR LUB C_4 A 4
FU RU BU LU FD RD BD LD RF LF RB LB FLD BDL RDB RFD LFU FRU BUR LUB C_4h A 8

The scrambles are here:

B1L1B3L3F2D3R1B3U1D2B1L1B2R1D1R3B2R2B2R3
L2F3L2D1F2B2L1B3R2B1D3R3F1U1L1R2D2B2L3R2
F3U1B3U3F2L3D1B3L2R1B1U1B2D1L1D3B2D2B2D3
L1B3L3F2D3R1B3U1D2B1L1B2R1D1R3B2R2B2R3F2
L3B2F3L3B1D1L1U3B3R3F3D1L2F1D2F3B2L1D2L2
L3F1L1B2D1R3F1U3D2F3L3F2R3D3R1F2R2F2R1B2
B1U3F1U1B2L1D3F1L2R3F3U3F2D3L3D1F2D2F2D1
L2B1L2D3B2F2L3F1R2F3D1R1B3U3L3R2D2F2L1R2
U1L1U2B2R2F3D1L3F3B3D3F1R3F1B1R2B3D2R2D3

There are many more smaller clusters.

Source:
http://cubezzz.dyndns.org/drupal/?q=node/view/523 -> "Length of the neighbors of the 20f* positions"
 
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What are the conditions required for a 1LLL case to be solvable by F <R,U> F'? A certain corner permuation? A certain edge orientation?

Eg: F R U R' U' F', F R U' R' U' R U R' F', F R' U' R2 U' R2 U2 R U' F' etc.
 
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What are the conditions required for a 1LLL case to be solvable by F <R,U> F'? A certain corner permuation? A certain edge orientation?

Eg: F R U R' U' F', F R U' R' U' R U R' F', F R' U' R2 U' R2 U2 R U' F' etc.
My intuition says that it can't be a diag corner swap case, and (more obviously) can only have 2 unoriented edges. But I can't prove any of that.
 
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What are the conditions required for a 1LLL case to be solvable by F <R,U> F'? A certain corner permuation? A certain edge orientation?

Eg: F R U R' U' F', F R U' R' U' R U R' F', F R' U' R2 U' R2 U2 R U' F' etc.
It's pretty much "do an F move and see if the position is 2gen-able". So, keeping in mind that any edge that comes from UF or goes to UF gets flipped, you can do any combination of:
- 3 cycle of any 3 edges
- any legal corner twist
- swap UL and UR, UFL->UBR->UFR->UBL->UFL (or the same cycle but inverted) - this is equivalent to F ([RU'R': U] + 3cycle to solve UF and UB again) F' or the same with U' in the conjugate
- swap UFL<->UFR and UBL<->UBR
 
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What is the shortest (or a short) sequence of moves Q, such that every position can be solved by crossing out some moves of Q and then executing the rest in the original order?

For instance: say your sequence is R U R2, then you could execute nothing or R or U or R2 or R U or R R2 (= R') or U R2 or R U R2. But you can't do U U or R2 U.

There is an obvious theoretical lower limit of 66 moves (with fewer, there are not enough subsets of Q's moves) but I think the real minimum will be quite a bit more than that. We could also create an upper bound by defining a method that solves one piece at a time and just writing down all the solutions in order, i.e. start with a list of algs to solve DB from every position, write them in order, then get a list of algs to solve DF from every position without disturbing DB, write those in order at the end, etc. etc. I don't know how big this would actually be.
 
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It's an extremely grey area, though. Sure, something like Ritalin can improve concentration and memory, but I'm sure there are some foods that also have effects on those things, even if not to the same degree. Is there really a difference between a nutritional chemical, and a pharmaceutical chemical, if they have the same effect, just to different degrees? But if someone could take vitamin supplements to improve their mental ability, they can also eat certain foods to do that too. Then should we regulate cubers' diets to prevent this kind of thing? I think it's hard to draw the line between what's OK and what isn't, and honestly, there seems to be no "magic bullet", like steroids in weightlifting, that would provide an unreasonably large advantage in cubing.

It seems like chess has grappled with this kind of thing too. There have been some drug tests in the past decade or two but many players (even very good ones who pass the tests) think they are a bad idea. Chess is far more mental than normal cubing, but when you compare it to FMC...
If the delagate somehow found out a competitor was using they could use 2k3) (if a competitor) Behaves in a way that is unlawful, violent or indecent; or intentionally damages venue facilities or personal property within the venue.
 
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