Helicopter cube solving (and patterns)

[mrCage]

Hey all!

I just wonder what method you guys use for helicopter cube solving. I just got mine today, and i do corners first solving quite easily - though not fast yet.

I have also been pondering about various patterns possible on this puzzle. One obvious one is the "2 spot pattern". Interchange all the face centers of 2 opposite face centers. I can do this in 24 turns, not all that efficient. The cube in cube pattern seems impossible. Can anyone prove this??

Per

PS! My helicopter cube (from Mefferts) does not seem to have shape shifting turns. Is this correct??

 

[qqwref]

There are shape shifting (jumbling) turns but they aren't obvious. Slowly turn one axis until an adjacent one will turn and you will see how it works. You can't really move corners out of position (except temporarily) but you can move centers into different orbits. So any pattern with solvable corners is possible.

My method (when it's been scrambled without jumbling) is as follows:
- First layer centers.
- Finish first layer by pairing the corners up with two centers each before inserting.
- Last layer corners (I solve one by one, then do last two at once).
- Last layer centers, do the 3-cycles first and then any 2-cycles in pairs.
I use three main algs: J-perm (UL UF UR UF UL), 2-2 cycle ((UF UR)3), 3-cycle ((UF FR UR FR)2) and inverse. And see, it works pretty well:
36.48, (1:01.38), (34.00), 51.96, 42.26, 41.95, 46.47, 57.55, 54.00, 45.83, 49.07, 47.68 => 47.32

 

[mrCage]

There are shape shifting (jumbling) turns but they aren't obvious. Slowly turn one axis until an adjacent one will turn and you will see how it works. You can't really move corners out of position (except temporarily) but you can move centers into different orbits. So any pattern with solvable corners is possible.

My method (when it's been scrambled without jumbling) is as follows:
- First layer centers.
- Finish first layer by pairing the corners up with two centers each before inserting.
- Last layer corners (I solve one by one, then do last two at once).
- Last layer centers, do the 3-cycles first and then any 2-cycles in pairs.
I use three main algs: J-perm (UL UF UR UF UL), 2-2 cycle ((UF UR)3), 3-cycle ((UF FR UR FR)2) and inverse. And see, it works pretty well:
36.48, (1:01.38), (34.00), 51.96, 42.26, 41.95, 46.47, 57.55, 54.00, 45.83, 49.07, 47.68 => 47.32

Hi. I have to sit down and contemplate over some diagrams to fully understand your method. Solving without shape shifting turns is always possible anyhow-evn if scrambled with them.

And yes i realised that cube in cube pattern is indeed possible. I managed to twist 2 wings (with 2 easy corner 3-cycles). And the centers are indeed possible to set up also.

Per

 

[TomZ]

Solving without shape shifting turns is always possible anyhow-evn if scrambled with them.

That's not true. There are many positions that you cannot achieve without jumbling.

 

[qqwref]

And yes i realised that cube in cube pattern is indeed possible. I managed to twist 2 wings (with 2 easy corner 3-cycles). And the centers are indeed possible to set up also.

It's not obvious that the centers can be setup in this way - at least, it's impossible without jumbling. Using non-jumbling moves there are four orbits (Urf Rbu Bdr Dlb Lfd Ful, and the same with y/y'/y2 rotation), each with one centers of each color, which the centers can't move out of, although with jumbling moves you can move the centers around freely.

 

[mrCage]

Solving without shape shifting turns is always possible anyhow-evn if scrambled with them.

That's not true. There are many positions that you cannot achieve without jumbling.

I think we would have to distinguish between normal helicopter cube and a picture version where the exact location of centers had to be fixed.

Center swap is possible when combined with another invisible swap...

Per

 

[mrCage]

There are shape shifting (jumbling) turns but they aren't obvious. Slowly turn one axis until an adjacent one will turn and you will see how it works. You can't really move corners out of position (except temporarily) but you can move centers into different orbits. So any pattern with solvable corners is possible.

My method (when it's been scrambled without jumbling) is as follows:
- First layer centers.
- Finish first layer by pairing the corners up with two centers each before inserting.
- Last layer corners (I solve one by one, then do last two at once).
- Last layer centers, do the 3-cycles first and then any 2-cycles in pairs.
I use three main algs: J-perm (UL UF UR UF UL), 2-2 cycle ((UF UR)3), 3-cycle ((UF FR UR FR)2) and inverse. And see, it works pretty well:
36.48, (1:01.38), (34.00), 51.96, 42.26, 41.95, 46.47, 57.55, 54.00, 45.83, 49.07, 47.68 => 47.32

I was able to create an adjacent 2 spot pattern by using combination of your 2 given center algs: UF FR UR FR UF UR FR UR, a dual swap. Use the symmetrical version to create the pattern.

I can also twist 3 non-adjacent wings (corners) in 16 turns.

Per

 

[bobso2]

where is a good place to buy this puzzle?

 

[mrCage]

where is a good place to buy this puzzle?

I got mine from Mefferts. Another good place is the Twisty store. Not sure which is faster:confused:

Per

 

[cubesolver77]

I would recommend the twisty store even though their is a wait that is it was originally made but i jumped too soon and ordered from mefferts without ordering it

 

[jaap]

Solving without shape shifting turns is always possible anyhow-evn if scrambled with them.

That's not true. There are many positions that you cannot achieve without jumbling.

I think we would have to distinguish between normal helicopter cube and a picture version where the exact location of centers had to be fixed.

Center swap is possible when combined with another invisible swap...

Per

No. It is impossible to swap two centre pieces of the same colour, without shapeshifting/jumbling.
It is also impossible for example to make the top-right centre piece in the front face and the front-left centre piece in the top face the same colour.
Choose a single centre piece, and see where you can place that piece using only non-jumbling moves. It cannot be placed anywhere - it is very restricted.

 

[mrCage]

I can swap 2 corners like so:

1, swap some edges:
UR UF FR (UR UF)*3 FR UF UR

2, swap the same edges with single turn
FR

Per

 

[Portponky]

I made a guide for solving and unjumbling the helicopter cube. I think it's pretty similar to a lot of what is discussed here, so it may not be too helpful.

It is very easy to jumble in to a position that can't be solve without jumbling again. Just start from solved, do a single jumble move and try to solve it without re-jumbling.

 

[mrCage]

Solving without shape shifting turns is always possible anyhow-evn if scrambled with them.

That's not true. There are many positions that you cannot achieve without jumbling.

I think we would have to distinguish between normal helicopter cube and a picture version where the exact location of centers had to be fixed.

Center swap is possible when combined with another invisible swap...

Per

No. It is impossible to swap two centre pieces of the same colour, without shapeshifting/jumbling.
It is also impossible for example to make the top-right centre piece in the front face and the front-left centre piece in the top face the same colour.
Choose a single centre piece, and see where you can place that piece using only non-jumbling moves. It cannot be placed anywhere - it is very restricted.

Yes i see it now. But i still dont see the jumbling move. I can half see it, but to complete it i seem to have to undo it. Hmmm. I guess i'll just live without them

Per

 

[mrCage]

Hi!

Corner 3-cycle:
(FR FD FR FU)*2

Now use this to create a 2-twist on corners: (UFR-,UFL+)
1: (FR FD FR FU)*2

followed by a symmetric version
2: (FD FR FD FL)*2

Per

PS Double sune 2-twist on rubiks 333 springs to mind!!

 

[mrCage]

Corner 3-twist:

((FR FD FR FU)*2 FL)*2 (18 turns) Is this optimal??:rolleyes:

Per

 

[Portponky]

That's a cool move. I don't know if it is optimal.

I think you can solve the last layer corners in 19 twists maximum, but it will mix up the centers on the top half.

 

[mrCage]

That's a cool move. I don't know if it is optimal.

I think you can solve the last layer corners in 19 twists maximum, but it will mix up the centers on the top half.

Any reasoning for the 19 maximum. What are the steps ...

Per

 

[coinman]

Corner 3-twist:

((FR FD FR FU)*2 FL)*2 (18 turns) Is this optimal??:rolleyes:

Per

I found that (UR UB UL UF) *3 makes a 3 corner twist without mowing any centers.
Also (UR UL UB UF)*3 moves four corners without mowing any centers.

I got mine yesterday and solved it in about there hours without help from the internet but now i will only end up in strange positions on the last centers that i can't solve with the algs i found this far. I made a fev jumbling moves, maybe it's in unsolvable position.

 

[Portponky]

I got mine yesterday and solved it in about there hours without help from the internet but now i will only end up in strange positions on the last centers that i can't solve with the algs i found this far. I made a fev jumbling moves, maybe it's in unsolvable position.

It is very likely that it will require unjumbling to be solvable. The two obvious indicators are:

1. A center piece is in the same orbit as another center of the same colour. That is, two same-coloured center pieces can both get in to the same position.
2. You can solve almost all of it but two centers are always swapped.

I posted an unjumbling guide (see post #13), which is a bit rough at the moment but should help you if you are stuck.

Any reasoning for the 19 maximum. What are the steps ...

To orient them takes a maximum of two moves. Twist two edges (e.g. UF UR) and the orientation changes in a sune-like way. The permutation changes too but ignore that. Two sunes can orient any corner orientation so 2*2 = 4 moves can orient all four corners.

To permute them I thought the worst case was 15 but it's actually 12 so the corners can be solved in 16 max.

You can split it up in to 8 cases. I'll list the algorithms but because all of them are on the U face I've written them without the preceeding 'U's. So from here, FLR means UF, UL, UR.

1. Solved

2. R-style perm, two corners solved, two needing swapped along an edge.
LRBLR

3. E-style perm, two pairs of corners needing flipped along edges.
LRFBLR

Note: The above two moves are enough to solve the corners if you apply them enough times. This is more than enough for speed solving.

For the remaining cases I have constructed example algorithms using a method I'll explain.

4. H-style, where there is an hourglass like cycle (BL -> BR -> FL -> FR -> BL).
LFBR FBL RBFL

5. X-style, where two pairs of corners are diagonally swapped.
LFBR LFBL RBFL

6. O-style, where the corners are all correct relative to each other but they are a quarter turn out of a alignment with the correct position.
LFBR BLF RBFL

7. Y-style where two diagonal corners are swapped but the other two are solved.
LFBR BLB RBFL

8. A-style, where you have 1 solved and a 3-cycle
LFBR LB RBFL

Counting mirror images and reflections that should solve all corner cases (unless I've stupidly missed one) and the worst is the X-perm which takes 12.

The majority of those algorithms are wrapped in LFBR and RBFL. That's a handy setup move which puts it in a situation where you can make a lot of swaps without breaking the orientation. F and B swap the corners they usually would but without breaking the orientation, and L swaps the corners on the R edge without breaking orientation. R will break the orientation so you're restricted there.

If you can see how to permute the corners using F, B and R twists then just do LFBR, then do the twists you saw but using L instead of R, and then do RBFL.

Of course all of this will mess up the centers on the top half of the cube so it may not mesh well with your method.