Random Cubing Discussion

[Stefan]

Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy

 

[Kirjava]

Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy Buffy

lol, 420

 

[qqwref]

For fun, I computed some God's Algorithm tables for a puzzle that looks like a 2x2x2 but has four possible moves instead of three: U, R, F, and rotating the UFR corner (a move I called "w"). There are 3 times as many positions as on a normal 2x2x2.

Moves   HTM      QTM
0       1        1
1       11       8
2       90       51
3       717      306
4       5315     1722
5       36372    9288
6       226396   47915
7       1202923  227469
8       4243588  945926
9       4886281  2942196
10      420636   4862890
11      150      2659285
12               385150
13               2501

A sample HTM antipode: F R F2 U' R F R' F' R2 F2 w
A sample QTM antipode: F R U' w U' R F' R w' U2 F' U'

 

[TheNextFeliks]

So basically, is parity caused by non fixed centers or just by number of layers?

 

[rj]

So basically, is parity caused by non fixed centers or just by number of layers?

Non fixed centers.

 

[Stefan]

A sample HTM antipode: F R F2 U' R F R' F' R2 F2 w
A sample QTM antipode: F R U' w U' R F' R w' U2 F' U'

Same god's number as regular 2x2x2 in HTM, and smaller in QTM. Fascinating.

Maybe we should be thankful if the scrambler accidentally twists a corner

 

[Stefan]

I just realized Michal was really unfazed in the WC2011 final. I seem to notice odd word parts today, earlier saw a "quick navigation" button here but thought of a different word.

 

[cmhardw]

Neat alternative scrambling/solving approach

Stefan's recent post about simulating the cube gave me an idea for a neat way to scramble/solve.

Spoiler

Not sure if new, but I came up with a neat way to simulate.

Represent the state as a string like
"UF UR UB UL DF DR DB DL FR FL BR BL UFR URB UBL ULF DRF DFL DLB DBR"
which for those 20 pieces tell their current location. If we do a U turn, we get:
"UL UF UR UB DF DR DB DL FR FL BR BL ULF UFR URB UBL DRF DFL DLB DBR"
This says the first piece (UF) is now at UL, etc.

This can be implemented by changing exactly those locations having the turn name (U)
"UF UR UB UL DF DR DB DL FR FL BR BL UFR URB UBL ULF DRF DFL DLB DBR"
and cycling all other characters in that cubie location ("U" cycles F->L->B->R->F):
"UL UF UR UB DF DR DB DL FR FL BR BL ULF UFR URB UBL DRF DFL DLB DBR"

So a state is given as such a string, and moves are defined by for example "U"=>"FLBR". It's really easy and natural to implement, no ugly numbers, which is why I find it neat. Could also be used for Megaminx and Pyraminx, for example (edit: darn, I just realized there aren't many people face-turning the pyraminx ).

A "turn" of a face would mean to cycle all the pieces that were on that face in the solved state as they would cycle on the solved cube.

Example:
Assume a cube has BOY color scheme and is in the standard scrambling orientation with white on top and green on front. I will now do the "turn" U. This takes the cube from solved to the state of having done the turn U normally.

Next I will do the "turn" L. On a solved cube this cycles the corners as orange-white-green -> orange-green-yellow -> orange-yellow-blue -> orange-blue-white -> orange-white-green. On a solved cube the turn L would cycle the edges as: Orange-white-> orange-green -> orange-yellow -> orange-blue -> orange-white.

Before doing the turn L my cube currently has the U layer turned once clockwise. Doing the turn L will cycle all the pieces as described above. In blindfold cycle notation this will mean that to the state of [U layer turned once clockwise] my turn L will do the cycles:
(BUL -> LFD -> LDB -> BRU -> BUL) and
(BU -> LF -> LD -> LB -> BU)

When scrambling/solving this way, effectively you would do "turns" by doing a 3 cycle on corners, a 3-cycle on edges, setup to a (T-perm, R-perm, etc.) then setdown. It would be tedious, but interesting! I'm not entirely sure how I would approach solving it.

--edit--
double turns would be performing two 2-cycles on corners, and also on edges so you would have multiple options for doing double turns.

 

[Stefan]

Chris, would that mean that the scramble
U' F2 U F2 U' B2 F2 L2 D' L2 D' L' R U' B' U2 F2 D B' F2 D2 (normal turns)
would have the solution
U F2 U' F2 U B2 F2 L2 D L2 D L R' U B U2 F2 D' B F2 D2 (your kind of turns)
?

 

[cmhardw]

Chris, would that mean that the scramble
U' F2 U F2 U' B2 F2 L2 D' L2 D' L' R U' B' U2 F2 D B' F2 D2 (normal turns)
would have the solution
U F2 U' F2 U B2 F2 L2 D L2 D L R' U B U2 F2 D' B F2 D2 (your kind of turns)
?

I don't know. I did look at:

Scramble: U L (my turns)
Which has solution U' L' (normal turns)

I don't know why this is the case, it's not intuitively obvious to me. This is interesting! I'll try looking at other scrambles to see this relationship and figure out why it is (I feel like you already have).

 

[bobthegiraffemonkey]

I don't know why this is the case, it's not intuitively obvious to me. This is interesting! I'll try looking at other scrambles to see this relationship and figure out why it is (I feel like you already have).

I also suspect Stefan has the answer, but anyway:

Spoiler

Consider your turns as setting up to solved state using the moves scrambled so far, then
U L [your turns] = U (U' L U) [normal turns] = L U [normal turns]

 

[Stefan]

Yeah, I was mainly asking to confirm I had correctly understood what Chris is talking about

Spoiler: My explanation

I guess similar to bob's explanation, just in my words and with a larger example...

If scramble was
(in normal turns) U' F R2 D'
and we want to do
(in Chris's turns) U F' R2 D,
then we can do that first Chris-U not as two 3-cycles and a double swap but instead by properly setting up the U pieces in the U layer and simply doing a normal U turn there (and then undo the setup). So do (D R2 F') U (F R2 D'). But that solves the cube with the first four moves and then rescrambles it with the last three moves. So it's now like the cube was only scrambled with F R2 D'. Repeat with the remaining moves.

Spoiler: My suggestion for solving

Speedblind-plan a solution, e.g., D R2 F' U, then apply the moves in reverse order using Chris-style moves.

 

[qqwref]

A 4-twist on 3x3x3: r U2 R' U2 y' R2 D2 r U' r' D2 r' U' L U l2' U'

 

[kunparekh18]

A 4-twist on 3x3x3: r U2 R' U2 y' R2 D2 r U' r' D2 r' U' L U l2' U'

R2 U' R' U' R U R U R U' R2 U R' U R U' R' U R U2 R'

 

[bundat]

I personally find the concept of inspection weird.


Especially in a world where many noncubers hide the cube from you when scrambling, as if they think you can actually memorize a hand scramble instantly and do it backwards to solve the cube.
"Solving it in your head", before the timer even starts, would most likely be unacceptable by those standards.

And personally, I agree, because the recorded time excludes a portion of the "solve" (despite being purely a thinking step, I feel it is still part of the "solving process", so it shouldn't be excluded from the recorded time).

To put it into perspective, someone could probably memo during the 15 second inspection, put on a blindfold, and 3-style it and get a 15 second "solve time".
A time which just seems incorrect to me, because it excludes the thinking time, and is just the time for the mechanical part of the solve. And he didn't even have to look at the cube the entire recorded "solving time". (Of course, this isn't the actual case, and people just plan [x]cross [+pair] or 1st block [+some 2nd block], but this is just to make a point)



And for an event where the world record is 5.55 seconds, and world class cubers can easily get sub-8 or even sub-7 times, 15 seconds inspection just seems ridiculous to me.


Granted, changing the rules now would be troublesome and probably unacceptable (issues with existing records and whatnot), but maybe a separate event (or events) would be nice.

Like:
"no inspection 3x3"
"no inspection 3x3 OH"
"no inspection 2x2"

Also, personally, I think inspection looks so much like the pause when someone has bad/no lookahead, and has to stop to look for the next step. Except it's untimed.

 

[Kirjava]

Holding inspection and non inspection events seems a bit cumbersome.

What procedure would you use for no-inspection?

 

[Stefan]

I personally find the concept of inspection weird.

Both no-inspection and reduced-inspection have been discussed before, no-inspection has even been tried at some comps a while back but failed.

 

[rj]

Holding inspection and non inspection events seems a bit cumbersome.

What procedure would you use for no-inspection?

Same as BLD, you remove the cover thyself.

 

[cmhardw]

Same as BLD, you remove the cover thyself.

We would need a standard cover so that all competitors use covers of the same shape/dimensions and weight no matter where they compete.

 

[rj]

We would need a standard cover so that all competitors use covers of the same shape/dimensions and weight no matter where they compete.

Well, don't we have that for BLD?