Helicopter cube solving (and patterns)

[Kenneth]

Per, yep, I can... but a little later, have some other things atm.

Michael, yes complicated, but with a clear definiton as you say, then mabye.

Portponky, ok, mabye not 72, but... we will see =)

 

[coinman]

Michael, can you try to find A-perm algs (Clockwise and anti-clockwise.) with the Ksolver? I don't know how to use it
Preferably algs that preserves the UFR corner.

 

[qqwref]

There are two optimal algs (for counterclockwise perm):
UF UR (UL UF UL UB)2 UR UF (12f*)
UR UF (UL UB UR UB)2 UF UR (12f*)
You can just invert it for the clockwise one.

 

[coinman]

I have now published a embryo to a heli cube corners last guide http://www.speedsolving.com/forum/showthread.php?p=377177#post377177

Pleas comment, advise and give me more algs!

All calculations of numbers of cases is done by my brother so don't blame if it's wrong

 

[Kenneth]

Portponky, ok, mabye not 72, but... we will see =)

Not! I was in a hurry and just read briefly what you wrote, now I looked at it and yes, you are right, it is not possible.

BTW guys, I just got it and have no energy to read the whole tread, I got a situation where I can solve all byt two swapped centres, did that happen to you too?

The method I tried so far is mostly intuitive, solve D face centres, solve rest of first half centres, 7 mover to put D corners, solve L and B LL side centres, use nx(UR UF) to solve the rest of the centres then "Niklas" + some algs my brother showed me for LL corners.

7 mover, to solve RFD, oriented in U at ULF, do RF UR UB UL UB UR RF (or the mirror setup and solving). It is intuitive, you move the two centres from RFD to top half, then split them, move in the corner and back up.

With no jumbling and that method it feels much like solving magic exept for the last corners

So now I'm trying jumbling scrambling and jumbling solving using the same sub steps.

 

[Portponky]

BTW guys, I just got it and have no energy to read the whole tread, I got a situation where I can solve all byt two swapped centres, did that happen to you too?

Yes, there is a parity situation caused by jumbling. My rough unjumbling guide has an algorithm for solving this. It's actually pretty simple, any jumble with matching colours top and bottom will fix the parity case.

It's really hard to notate the jumble moves :confused:

 

[coinman]

BTW guys, I just got it and have no energy to read the whole tread, I got a situation where I can solve all but two swapped centres, did that happen to you too?

Yes!
But i have a alg that swaps two centers only. UR UL jumble front left or right corner UF UR UL.

This thread is also about patterns but i haven't seen any :rolleyes:
I found a nice star and did it on two sides of the cube. It takes no jumbel moves to do it.

The other side.

 

[mrCage]

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

Including jumbling, you mean, right? I think it could be calculated, it won't be easy, but it could be done. Of course we have to define what a state is carefully. Do we want to count (for instance) solved state and solved state with UF+72 as the same, or are they different because different moves can be done in each position? How much of the puzzle can actually be jumbled? Does it still count as a state if many axes can't be turned? And so on. There is a clear limit to how much jumbling can take place (each axis holds two groups of pieces, and each turnable group MUST hold two centers and a corner).

Here is an interesting jumble: (UB- RD- FL-) (FD- RB- UL-). It leaves three 'twisted' center pairs and only three turnable axes.

Interestingly there are over 24000 times as many cube-shape states possible if you allow jumbling than possible if you don't. Because a jumbling move can typically only move 2 centers out of place at once (of 24), it would require a huge number of moves to evenly, randomly scramble among these states!

Care to make a slow motion video of a jumbling sequence (from solved) non-solvable with normal non-jumbling turns!! Please!!!.

Try this: UL- FR- UF180 UL+ FR+ UF180.

Hmmm. Again adouble swap. Doable without jumbling. :confused:

Per

PS! My bad. Doable, but i wanted a single swap. Doable too, right!!??

 

[jaap]

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

Including jumbling, you mean, right? I think it could be calculated, it won't be easy, but it could be done. Of course we have to define what a state is carefully. Do we want to count (for instance) solved state and solved state with UF+72 as the same, or are they different because different moves can be done in each position? How much of the puzzle can actually be jumbled? Does it still count as a state if many axes can't be turned? And so on. There is a clear limit to how much jumbling can take place (each axis holds two groups of pieces, and each turnable group MUST hold two centers and a corner).

Right. For simplicity I would consider each of the three ways to align an 'axis' with its adjacent ones to be a valid position, regardless of whether the 6 pieces actually around that axis allow any of the adjacent ones to turn. This analysis wouldn't be very hard. I might try this out soon, while I wait for this puzzle to be delivered to me.

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.

Care to make a slow motion video of a jumbling sequence (from solved) non-solvable with normal non-jumbling turns!! Please!!!.

Try this: UL- FR- UF180 UL+ FR+ UF180.

Hmmm. Again adouble swap. Doable without jumbling. :confused:
Per

No it isn't. We already established that without jumbling centres lie in 4 orbits of 6 pieces. This double swap exchanges pieces from different orbits. A double swap is only possible without jumbling if each swap lies within one orbit (though the two swaps need not be in the same one).

My bad. Doable, but i wanted a single swap. Doable too, right!!??

A single swap of centres is not possible I think, even with jumbling. The restrictions qqwref describes above pretty much prove it.

 

[mrCage]

A single swap of centres is not possible I think, even with jumbling. The restrictions qqwref describes above pretty much prove it.

I managed to do this with jumbling actually. Don't ask me how Now i can't solve the puzzle. I'll try some more jumbling soon and i'll see what comes out of that.

Per

 

[mrCage]

BTW guys, I just got it and have no energy to read the whole tread, I got a situation where I can solve all but two swapped centres, did that happen to you too?

Yes!
But i have a alg that swaps two centers only. UR UL jumble front left or right corner UF UR UL.

This thread is also about patterns but i haven't seen any :rolleyes:
I found a nice star and did it on two sides of the cube. It takes no jumbel moves to do it.

The other side.

Sequence??

Per

 

[mrCage]

I will soon post a supertwist pattern (8 corners and without jumbling). The solution, so far, is quite lengthy - but it uses stuff already posted here. Combination of 3 sequences ...

Per

 

[jaap]

A single swap of centres is not possible I think, even with jumbling. The restrictions qqwref describes above pretty much prove it.

I managed to do this with jumbling actually. Don't ask me how Now i can't solve the puzzle. I'll try some more jumbling soon and i'll see what comes out of that.

Per

Then you'll have to do a double swap, but set it up so that one of the swaps exchanges two pieces of the same colour. If you had a superhelicopter cube (i.e. all pieces distinct) then you cannot so a single swap.

 

[Portponky]

The jumble move swaps four centre pieces, and also changes the corners in a way which can be commuted back with standard moves.

It swaps one centre piece from orbit A with a centre piece from orbit B.
It also swaps two centre pieces on orbit C.
(where A, B, C are three of the four centre orbits)

So you can do a single centre swap by arranging the centre in orbit A and the centre in orbit B to be the same colour. That way two centres in orbit C will swap and you will get a single swap situation. I have an algorithm in my guide which does this without scrambling up the almost-solved cube.

It should be noted that the single swap situation is actually orbit parity.

 

[Ton]

Imitative I would say

1 center, corners of that layer
Than the all the centers , than the last four corners

Did not figure out a method , just found a 3 cycle of edges and a 3 cycle of corners yesterday, together with the trivial 2 cycle of corners I can solve it

 

[coinman]

@Per. The Sequence is: two setup moves BR UL, then do the two corner flip alg [(UL UR) UB (UL UR) UF]*2 UL BR. Now you have two flip corners across the cube. Move three centers at a time around this flipped corner with (UR FR LR FR)*2 This alg is preformed three time per corner + cube rotations. If you don't get it please let me know.

 

[coinman]

Did not figure out a method , just found a 3 cycle of edges and a 3 cycle of corners yesterday, together with the trivial 2 cycle of corners I can solve it

There is two different methods (so far). One is doing F2L, LL corners, and LL + side half centers last. The other method is to do F2L, LL centers + side half centers, and LL corners last. I came up with idea to do the LL corners last and i hope and believe this is more efficient. I started a guide for this method, it's not ready but already usable. http://www.speedsolving.com/forum/showthread.php?t=21065

 

[Portponky]

Do you have any idea of the max/average move counts for either method? I already posted that the LL corners can be solved with very simple algs in 16 moves. From there I would guess the centres would take something like 25 average. What about centres first method?

 

[coinman]

Do you have any idea of the max/average move counts for either method? I already posted that the LL corners can be solved with very simple algs in 16 moves. From there I would guess the centres would take something like 25 average. What about centres first method?

I am not very good at calculating this kind of things but i think that the worst case for solving the centers after F2L is about 15 moves, average maybe 10. This is using the method to solve the centers after F2L mentioned in my corners last guide. Optimal is probably less, maybe 12 moves worst case?

I think LL corners can be solved in two steps in about 20 moves average.

As an example, if i have one corner in the right position but flipped and i chose to move the rest to the right position - i think this step is max 12 moves, and then flips them all - max 16 moves, then the worst case is 28 moves. A lot of the 3 corner cycles is preformed in 8 moves and the two corner flip is 12 moves so a good solve this way is 20 moves without skips.

The second way to do this is to solve and orientate one corner to it's final position in one alg, i think this always can be done in 8 moves and then solve the remaining 3 corners in one alg, which i think is 12 moves max. A bad solve this way is then 20 moves and a good is 16 moves (two 3 corner cycels) without skips.

I do it the first way most of the times now sins i know to few algs to be able to always solve the remaining corners after step one in the second way.

I will ask my brother to calculate this more correctly!
But i think i'm not to far off.

BTW i just got a 1:07.xx solve corners last but it was a bit lucky (only corner orientation after fixing centers), my non lucky PB is now 1:26.80.
OH 8:59.03

 

[mrCage]

@Per. The Sequence is: two setup moves BR UL, then do the two corner flip alg [(UL UR) UB (UL UR) UF]*2 UL BR. Now you have two flip corners across the cube. Move three centers at a time around this flipped corner with (UR FR LR FR)*2 This alg is preformed three time per corner + cube rotations. If you don't get it please let me know.

Why not the same pattern, but without the twisted corners? Also looks nice!!

Per