Helicopter cube solving (and patterns)

[Kenneth]

Jaap, if you see this, never ever you will be able to calculate the number of possible states for this one

However, this only takes into account whether something can or cannot move due to the presence or absence of the cut. It does not take into account interference with the movement due to the exterior shape of the pieces. Even pieces that are kind of non-adjacent interfere, for example the state of the UL axis can block the UR axis from turning completely freely. I don't know how much of a restriction this is, or if this causes there to be shapes that you could assemble but not reach by twisting unless you filed the pieces down.

That is what made me write that =)

There are so many restrictions but still so many combinations, I don't think we even found all possible moves yet and when/how do we know we have?

Creating a 3D model than checks if any piece in the actual layer has a corner under the turning plane or if any piece around it is sticking up and blocks the way and then letting it brute force for all combiantions is the only way I can think of.

 

[Kenneth]

Intresting walk around jumbling with useful effects:

UR(72) LF UF LF UF(108) UR(-72) UF LF UF(-108) LF

Add UF UR UF UR

Do first UR(-108) and it can do "2 centeres" (3 cycle but 2 U) and 2 diagonal LL corners...

If you are a bad boy you can even cheat : UR(72) UF(-72) UL(-72)!? UF!! UL(72) UF(72) UR(-72)

Warning, it pops during the mid UF if you try counter clockwise, go CW and it works.

More madness but valid moves, it leaves two fliped centres and corner orientation parity!!!

UR(72) UF UR(108) LF(-72) UB(108) UL(72) (Nice shape here) LF(-72) UB(72)

Per, never mind that video, I tried but it was so hard to follow the moves because of shapeshifts and the fact that I constantly had to rotate it so it faced the camera, it was just confusing.

 

[Kenneth]

Two seconds penalty?

Spoiler

I was trying to speedsolve, but why on earth did I miss my last U move :fp

 

[coinman]

New simple pattern, the white and yellow sides are intact.

 

[mrCage]

Two seconds penalty?

Spoiler

I was trying to speedsolve, but why on earth did I miss my last U move :fp

 

[Kenneth]

I think we need to agree about some nice notation for the turns that are not 180 degrees. Each side have six diffrent positions. 0, 72+, 108+, 180, 108- and 72-. Would it be wrong to use UR1, UR2, UR3 (alt UR only as is used already), UR2' and UR1' ?

Note that this is as for 3x3, not fixed positions but how much you shall rotate relative to the posittion the side has when you start the turn.

Some terms might be nice too, I think "F2L" is wrong, FLC = first layer cubies, LLC, last layer cubies?

More?

 

[qqwref]

Of course F2L is wrong, it's just first layer and last layer. There are pretty clearly two layers on this thing. If you want to talk about just the centers (or corners) on one side you can talk about sides (so FS centers would be the first step of my method).

I like the idea to use six positions no matter what (to describe jumbling) but maybe it would be better to use UR+, UR2+, UR3+, UR2-, UR- or something like that, just to emphasize that we aren't talking about normal turns. Putting something like UR3 might be confused with just doing UR 3 times.

 

[Kenneth]

Oki, FL and LL then =)

For notation, I use your style. To expand it a bit, I got this idea last night: many algs are having moves like UR UL xx UR UL yy ... and so on, to shorten these why not use H = UR + UL and I = UF + UB?

Then a H-PLL is H I H I H I or 3X( H I )

Or even UH and UI, then FH = FR FL and FI = UF DF

Then the H-PLL is 3x( UH UI )

A bit like slice notation... mabye a special metric?

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I'm looking a bit at CLL, if I get it right the whole group of 192 cases may be reduced to 80 cases; 8 orientations (solved, U, T, L, S, -S, H and pi) times 10 permutations (solved, A, A', H, E, O, O', M, diag and adj two swap). Then there are some duplicates too but I have not fully checked all of them.

But if you solve one corner (1+11 cases) it will be a group of 54 left that is reduceable to 44 (18 3-cycles, 18 2-swap + 1 CO, four pure CO and four cases with 2 corners solved) and solving one corner only is almost intuitive, if you did not jumble it you can do that before the last two adjacent centres (that always is 2-gen solving).

Nice CLL using walk around jumbling:

UR1+ UF UR2+ UB UF UR2+ UB UR1+ (UF UB UR UF UB UR).

OR with the "slice notation" : UR1+ UF UR2+ UI UR2+ UB UR1+ (UI UR UI UR).

But, it is not possible to do the first UI in any order =)

BTW, I timed a fully scrambled solve last night and it was 8:57 minutes, (cube shape was compleated around 1:40 and then many errors during FL) I claim this to be the UWR until someone claims a better one

I used a stopwatch but to my suprise it was stackmatable...

EDIT: hmm, maybe COLL = preserve LL centres (and FL of course) and CLL = ignore LL centres? ... then it is COLL I'm looking at =)

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I found a few PLL's too, but how useful is that? half a billion cases and horrible recognition

 

[ribonzz]

Helicopter cube eh? I just want to order it.

 

[coinman]

Did my first avg of 12 today, result 1:45.88. and a new non lucky single PB 1:15.55.
Messed up a few solves so i think i can do better. Still need to learn more algs.

 

[qqwref]

BTW, I timed a fully scrambled solve last night and it was 8:57 minutes, (cube shape was compleated around 1:40 and then many errors during FL) I claim this to be the UWR until someone claims a better one

Clearly I could beat this, but... how do you define "fully scrambled"? If you provide a scramble I will happily time it for you. PS: qqTimer will scramble helicube completely without jumbling, so you can just add turns onto that.

 

[Kenneth]

I'm sure I also can beat that, it was my first ever attempt to time a full solve.

When scrambling I did shape shift from the first move and then jumbled around for a while. When I was in a position where two adjacent sides was possible to turn I did a random number of 2 gen moves on them.

Locks may be unlocked by turning one of the locking sides, like in this example

UR1+ UF UR2+ -- here it is not possible to turn UF but if you do UB it is. Keep doing like so until you got a good scramble.

I can make up a long written scramble later, got to fix some food first...

 

[Portponky]

I don't think it would be normal to scramble the puzzle in that way. This isn't really a normal shapeshifting puzzle because most of the shapeshifting moves lock the entire thing up. This means you get a really sporadic difficulty. Also it's really hard to notate what has been done.

I think that it should either be scrambled with regular moves (1st type), or jumbled using the standard jumble move that doesn't change its shape (2nd type). That seems to be more what the intention of the puzzle is.

 

[qqwref]

I don't think it would be normal to scramble the puzzle in that way. This isn't really a normal shapeshifting puzzle because most of the shapeshifting moves lock the entire thing up. This means you get a really sporadic difficulty. Also it's really hard to notate what has been done.

Exactly, that is why I was skeptical of saying "this is the UWR for a fully scrambled puzzle", because it's too hard to define. Helicopter cube shapeshifting will be like the Square-1 shape, some are very easy and some take a lot of moves unless you really know what you're doing.

I think that it should either be scrambled with regular moves (1st type), or jumbled using the standard jumble move that doesn't change its shape (2nd type). That seems to be more what the intention of the puzzle is.

Yeah. I already have a scrambler of the 1st type; the 2nd type might be doable for automated scrambling, but the problem is that you'd need a lot of jumbling moves to really randomize the orbits completely - maybe 8 or more separate (FR- UL- UF UL+ FR+) type things. I don't really know if doing a bunch of those (how many?) would make a good scramble.

 

[Kenneth]

Michael, try this one:

UR1+ UF UR2+ UB BL UF1+ RF UF1- DR UR UF UR1- UB1+ FR1+ UR FR UB UR UB1- BL UB DB DF2+ UR1+ UL1- BL UL BL

It probably have to be longer because it leaves some blocks. But as a start it will do... I guess most of the blocks will be destroyed when the cube shape is getting fixed again

 

[mrCage]

A while ago i promised a supertwist pattern. Well, here it is. Not all that short.

RB (setup)
(UF UR UB UL)*3 (3 twist)
(DF DR DB DL)*3 (another 3-twist)
RB (undo setup)

(FU FR FU FL)*2 (FR FU FR FD)*2 (final 2-twist)

Did not try insertions

Per

PS! Soon to come, cube-in-cube (yes with jumbling!)

 

[qqwref]

Michael, try this one:

UR1+ UF UR2+ UB BL UF1+ RF UF1- DR UR UF UR1- UB1+ FR1+ UR FR UB UR UB1- BL UB DB DF2+ UR1+ UL1- BL UL BL

It probably have to be longer because it leaves some blocks. But as a start it will do... I guess most of the blocks will be destroyed when the cube shape is getting fixed again

Fun scramble Solved it in 3:03.85.

A while ago i promised a supertwist pattern. Well, here it is. Not all that short.

RB (setup)
(UF UR UB UL)*3 (3 twist)
(DF DR DB DL)*3 (another 3-twist)

(FU FR FU FL)*2 (FR FU FR FD)*2 (final 2-twist)

That's 42 moves :| The top and bottom are each a symmetrical 4-twist, and I posted a 16-move alg for that before, so I already have a 32-move solution for this. Sorry

 

[Kenneth]

Michael, try this one:

UR1+ UF UR2+ UB BL UF1+ RF UF1- DR UR UF UR1- UB1+ FR1+ UR FR UB UR UB1- BL UB DB DF2+ UR1+ UL1- BL UL BL

It probably have to be longer because it leaves some blocks. But as a start it will do... I guess most of the blocks will be destroyed when the cube shape is getting fixed again

Fun scramble Solved it in 3:03.85.

Nice, that cuts like 2:3 of the previous record

It had a fairly easy shape, I solved it in 30 seconds or so, but the rest was slow...

There is a situation that has two pairs of unoriented centres sitting in "half diagonal" (UR FL for example), the rest is a cube and that I have real problems with. It is not so intuitive, I struggled for an easy 20 minutes trying to solve it earlier today, eventually I got our of it but I'm not sure what I did =)

That state is near where you can do cube in cube but having it twisted in position! No, not "stickers twisted", the physical block is. Or rather, the smaller cubies are solved and the rest is twisted. And it is not 100%, it has one centre on each half that is wrong.

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As long as I got the last post I edit it =)

Nice jumbling that swaps two blocks and leaves the rest unaffected : UR1+ UF UR1- FL1- UL FL1+ UR1+ UF UR1-

Add UB before and after and it does PLL.

Another PLL: UR1+ UF UR2+ FL1- UB2+ UL UB2+ FL1+ UR2- UF UR1-

Both PLL's only 11 turns.

 

[Portponky]

Helicopter cube shapeshifting will be like the Square-1 shape, some are very easy and some take a lot of moves unless you really know what you're doing.

A square 1 is always very simple to return to a cube shape. Square 1 locks up because it is a bandaged puzzle, not because of its shapeshifting.

 

[qqwref]

Helicopter cube shapeshifting will be like the Square-1 shape, some are very easy and some take a lot of moves unless you really know what you're doing.

A square 1 is always very simple to return to a cube shape. Square 1 locks up because it is a bandaged puzzle, not because of its shapeshifting.

I dunno, it's not THAT simple, if you're from the perspective of someone who hasn't solved it hundreds of times... and still, some of the positions require 6 or 7 / turns to optimally solve, not even counting top and bottom turns. Sure, there are probably more (and more complicated?) shapes that a Helicopter Cube can go into, but I think the comparison makes sense. It's harder to completely scramble a Helicopter Cube mainly because you can't just go from one shape to others freely (more turns are blocked, in general).