Helicopter cube solving (and patterns)

[Portponky]

I didn't study the method you got to solve the LL corners in 16 moves but maybe i should, is it hard to recognize the cases? I solve the corners intuitionally, this can take quit a lot of moves.

It's really easy to orient corners optimally, the pattern is the same as the sune move.

Permutation is pretty straight forward. You can get very good result by spamming these three moves:

U{LR B LR} - swap the two corners on UF
U{LR BF LR} - swap the two corners on UF and the two on UB
U{RBR LFL RBR} - diagonal swap UBL and UFR corners

On the LL centers i mainly used the (RU FU)*3 and the (UF FR UR FR)*2 sometimes i also use (UR UF UL)*4 that moves six centers in two three cycles and the double jumble to swap four centers

The problem i se with solving the centers last is that it varies a lot from solve to solve how many centers you have to move. A lot of times they are also spread out in ways that force you to do set-up moves to solve them with the algs above. Or is there ways to control this?

I use the same method and the setup moves and bad corner distribution can be a pain. I think this will improve by figuring out / learning more center permutations.

Solving the centers after F2L is easy if you don't have to preserve corners so i was thinking that a method for LL corners that don't effects centers cud be more efficient.

I just had a shot at this and you are right, the centers are quite easy. If there were full corner orient/perm algs it would be fast, but one of the major problems is you can't rotate the top layer so you get four times as many cases as a face turning cube.

 

[coinman]

I also now rediscovered how to swap two corners without turning them. It takes a four centers jumbling twist. Just do UR UL jumble UF UR UL. You can save a quarter turn on the first UL by stopping in the jumbling position.

Ah, of course. This is a quite nice way to do this. I don't mind that it involves jumbling because you'd have to jumble to get to this position anyway

Na you can get to this position without jumbling but the only alg i know is looong. Do FU RU FU LU FU RU FU now four centers and two corners to the left are swapped. The four centers you can fix by turning the cube so you have them in FR and do ((UR FR)*3 (UF FR)*3)*3 = 25 moves so i prefer doing it the jumbling way

U{LR B LR} - swap the two corners on UF
U{LR BF LR} - swap the two corners on UF and the two on UB
U{RBR LFL RBR} - diagonal swap UBL and UFR corners

I already found the two first algs but not the "U{RBR LFL RBR} - diagonal swap UBL and UFR corners". But trying this i wanted to restore the centers and by adding one more UL UF UL i found a 12 move diagonal corner twist. The shortest one this far, and i think optimal this time. The whole alg being U{RBR LFL RBR LFL}
And if you start with UL and finish with UF it will twist two parallel corners in the front in 12 moves, nice! The whole alg being U{LRB LRF LRB LRF}.

 

[qqwref]

I also now rediscovered how to swap two corners without turning them. It takes a four centers jumbling twist. Just do UR UL jumble UF UR UL. You can save a quarter turn on the first UL by stopping in the jumbling position.

Ah, of course. This is a quite nice way to do this. I don't mind that it involves jumbling because you'd have to jumble to get to this position anyway

Na you can get to this position without jumbling but the only alg i know is looong. Do FU RU FU LU FU RU FU now four centers and two corners to the left are swapped. The four centers you can fix by turning the cube so you have them in FR and do ((UR FR)*3 (UF FR)*3)*3 = 25 moves so i prefer doing it the jumbling way

Oh, hang on, I misread you and thought you were talking about swapping two *centers* without turning them. Doing UL UR and then the jumbly UF swap, then UF UL UR, will swap two U centers and two others, thus quickly solving the parity issue which can come up when solving a jumbled cube.

I can switch two corners (with normal orientation) and leave centers alone in 15 moves, but there might be something better out there.

I already found the two first algs but not the "U{RBR LFL RBR} - diagonal swap UBL and UFR corners". But trying this i wanted to restore the centers and by adding one more UL UF UL i found a 12 move diagonal corner twist. The shortest one this far, and i think optimal this time. The whole alg being U{RBR LFL RBR LFL}
And if you start with UL and finish with UF it will twist two parallel corners in the front in 12 moves, nice! The whole alg being U{LRB LRF LRB LRF}.

Nice find, but I already posted these on the last page And yes, they're optimal.

 

[coinman]

I also now rediscovered how to swap two corners without turning them. It takes a four centers jumbling twist. Just do UR UL jumble UF UR UL. You can save a quarter turn on the first UL by stopping in the jumbling position.

Ah, of course. This is a quite nice way to do this. I don't mind that it involves jumbling because you'd have to jumble to get to this position anyway

Na you can get to this position without jumbling but the only alg i know is looong. Do FU RU FU LU FU RU FU now four centers and two corners to the left are swapped. The four centers you can fix by turning the cube so you have them in FR and do ((UR FR)*3 (UF FR)*3)*3 = 25 moves so i prefer doing it the jumbling way

Oh, hang on, I misread you and thought you were talking about swapping two *centers* without turning them. Doing UL UR and then the jumbly UF swap, then UF UL UR, will swap two U centers and two others, thus quickly solving the parity issue which can come up when solving a jumbled cube.

I can switch two corners (with normal orientation) and leave centers alone in 15 moves, but there might be something better out there.

I already found the two first algs but not the "U{RBR LFL RBR} - diagonal swap UBL and UFR corners". But trying this i wanted to restore the centers and by adding one more UL UF UL i found a 12 move diagonal corner twist. The shortest one this far, and i think optimal this time. The whole alg being U{RBR LFL RBR LFL}
And if you start with UL and finish with UF it will twist two parallel corners in the front in 12 moves, nice! The whole alg being U{LRB LRF LRB LRF}.

Nice find, but I already posted these on the last page And yes, they're optimal.

Aha, i now se that i missed your algs. They are virtually the same as the ones i came up with but from different angels.

This might sound a bit stupid but i newer used computer solvers, is there really a solver for helicopter cubes? Or is this Ksolve a general solver for al types of cubes? If so, how do you get it to work for something as different as a helicopter cube?

I like the try and error way, but i also started this way in 1980 Computers take away lot of the fun in exploring the cubes i think, but i guess it's useful when noting else works or the algs you find manually are way to long.

 

[qqwref]

This might sound a bit stupid but i never used computer solvers, is there really a solver for helicopter cubes? Or is this Ksolve a general solver for all types of cubes? If so, how do you get it to work for something as different as a helicopter cube?

It's a general solver for pretty much anything (there is no dedicated Helicopter Cube solver). You have to define the available pieces and what each available move does to them; then you can make a scramble file and it will search for sequences. I think it comes with an explanation of how to use it.
File is at http://www.svekub.se/files/ksolve.zip if you want to try.

Finding algs by hand can be fun, but when questions come up like "what's the optimal way to do this" I prefer to just go straight to computer solvers if possible. I'd rather have a solution I know is optimal than have a good alg that I can't improve, anyway.

 

[mrCage]

This might sound a bit stupid but i never used computer solvers, is there really a solver for helicopter cubes? Or is this Ksolve a general solver for all types of cubes? If so, how do you get it to work for something as different as a helicopter cube?

It's a general solver for pretty much anything (there is no dedicated Helicopter Cube solver). You have to define the available pieces and what each available move does to them; then you can make a scramble file and it will search for sequences. I think it comes with an explanation of how to use it.
File is at http://www.svekub.se/files/ksolve.zip if you want to try.

Finding algs by hand can be fun, but when questions come up like "what's the optimal way to do this" I prefer to just go straight to computer solvers if possible. I'd rather have a solution I know is optimal than have a good alg that I can't improve, anyway.

I prefer algs that are either easy to remember and/or easy to understand. Optimality is nice too but not really my primary goal

PS! Check the 333 pattern request thread. I prefer my 26 turn way to do this. i dont have have to memorise. I cycle the 3 bars in 14 turns and then twist 2 corners in 12 turns. "Only" 9 turns from optimal

Per

 

[mrCage]

You can solve all the last layer corners in 16 turns with the method I posted so unless you are making big savings on the centers this doesn't seem worth it. What is your method for the last layer centers?

Well i can do the centers in 2 steps. Position then orient - PCOC.

First step takes only 2 turns, while second step takes only 12 turns maximum. There may be cancellations. I will be back with details for second step.

Per

 

[mrCage]

You can solve all the last layer corners in 16 turns with the method I posted so unless you are making big savings on the centers this doesn't seem worth it. What is your method for the last layer centers?

Well i can do the corners in 2 steps. Position then orient - PCOC.

First step takes only 2 turns, while second step takes only 12 turns maximum. There may be cancellations. I will be back with details for second step.

Per

OK, brief details:

2-twist: UR UF UR UB UR UF UR UL or UR UB UR UF UR UL UR UF
3-twist: (UR UB UL UF)*3 or inverse
4-twist: (UR UL UB UF)*2 or UL UB UF UR UL UB UB UR

 

[qqwref]

I prefer algs that are either easy to remember and/or easy to understand. Optimality is nice too but not really my primary goal

You didn't look at the algs I posted for optimal pure flips - they are all easy to remember since every single one is something repeated 2 or 3 times. (For now I treat this as a coincidence but I'd like to understand why later.) I don't think you should shun optimal algs because in the case of the Helicopter Cube each turn does pretty obvious stuff so it is easy to understand how almost any alg works. I don't know of any way to do more than one useful turn at once so optimal algs are always faster as well. Fewer moves in this case should be easier to understand, not harder.

Well i can do the corners in 2 steps. Position then orient - PCOC.

2-twist: UR UF UR UB UR UF UR UL or UR UB UR UF UR UL UR UF
3-twist: (UR UB UL UF)*3 or inverse
4-twist: (UR UL UB UF)*2 or UL UB UF UR UL UB UB UR

Interesting, this may be closer to optimal than the other solution. Improved algs for 2-twist (I did not use computer for these, just my knowledge):
2-twist: UF UR UB UR UF UL (or inverse) or UF UR UF UB UL UB

The permutation step takes 0 moves for solved, 1 for J, 2 for E, 3 for hourglass, 4 for U2, 3 for U', 3 for Y, 2 for A (I hope you can figure out what I mean for all these ). So a maximum of 4 moves, then your solution has a maximum of 16.

For the interested my style is essentially solve one, solve another, solve last two. I don't know how efficient this is. The worst case for last 2 is 9 moves.

 

[mrCage]

I prefer algs that are either easy to remember and/or easy to understand. Optimality is nice too but not really my primary goal

You didn't look at the algs I posted for optimal pure flips - they are all easy to remember since every single one is something repeated 2 or 3 times. (For now I treat this as a coincidence but I'd like to understand why later.) I don't think you should shun optimal algs because in the case of the Helicopter Cube each turn does pretty obvious stuff so it is easy to understand how almost any alg works. I don't know of any way to do more than one useful turn at once so optimal algs are always faster as well. Fewer moves in this case should be easier to understand, not harder.

Well i can do the corners in 2 steps. Position then orient - PCOC.

2-twist: UR UF UR UB UR UF UR UL or UR UB UR UF UR UL UR UF
3-twist: (UR UB UL UF)*3 or inverse
4-twist: (UR UL UB UF)*2 or UL UB UF UR UL UB UB UR

Interesting, this may be closer to optimal than the other solution. Improved algs for 2-twist (I did not use computer for these, just my knowledge):
2-twist: UF UR UB UR UF UL (or inverse) or UF UR UF UB UL UB

The permutation step takes 0 moves for solved, 1 for J, 2 for E, 3 for hourglass, 4 for U2, 3 for U', 3 for Y, 2 for A (I hope you can figure out what I mean for all these ). So a maximum of 4 moves, then your solution has a maximum of 16.

For the interested my style is essentially solve one, solve another, solve last two. I don't know how efficient this is. The worst case for last 2 is 9 moves.

No, my 2 step corners has a maximum of 14 turns. I forgot to account for some PC cases that require 3 or 4 turns - but due to symmetry of these cases, we always get good cancellations combined with step 2.

Per

 

[Kenneth]

Ok, from now we use scrambling, chickens!!

CO, and you think that is the same as corner? orientation??

Spoiler

Aha, Centre! orientation, that's something!!

 

[Portponky]

Is there a way of jumbling it out of cube shape so that it remains stable? Usually it just seems to lock up the jumbled bit.

 

[Kenneth]

The state I have you do easy using a 4 move 2 gen alg (RF) and is compleatly stable.

UR 72+ UF 180 UR 180 UF 72+

the numbers are the number of degrees you shall turn the side (3x3 R = R 90+)

Edit : I think we can say there are levels on this puzzle, you stay in cube shape, with or without jumbling (the kind that just temporarly shape shifts) or else use full shape shift... that is far much harder to solve, mosty because you get confused from the odd looks of it.

Edit more: from that I got this great alg: R72+ F180 R180 F180 R180 F180 R108+ ... double 2 cycle centres.

 

[coinman]

This is my new V-cube

 

[Portponky]

The state I have you do easy using a 4 move 2 gen alg (RF) and is compleatly stable.

UR 72+ UF 180 UR 180 UF 72+

This does lock everything up. After doing it you can only turn: UF, BR, BL, DB, DL. The only edge with jumbled pieces you can turn is UF so it's fairly obvious you have to backtrack through that.

Edit more: from that I got this great alg: R72+ F180 R180 F180 R180 F180 R108+ ... double 2 cycle centres.

If I understand your notation right, this doesn't actually leave it jumbled and from the resulting state it can be resolved with UF UR UF UR UF UR FR UF UR FR UF FR UF FR UF UR UF FR

 

[Kenneth]

The state I have you do easy using a 4 move 2 gen alg (RF) and is compleatly stable.

UR 72+ UF 180 UR 180 UF 72+

This does lock everything up. After doing it you can only turn: UF, BR, BL, DB, DL. The only edge with jumbled pieces you can turn is UF so it's fairly obvious you have to backtrack through that.

Edit more: from that I got this great alg: R72+ F180 R180 F180 R180 F180 R108+ ... double 2 cycle centres.

If I understand your notation right, this doesn't actually leave it jumbled and from the resulting state it can be resolved with UF UR UF UR UF UR FR UF UR FR UF FR UF FR UF UR UF FR

That was just an example, I have gotten it into states where you can turn more sides. I was just now in a situation that took me about an hour to resolve to cube shape. I even found a jumble move that is doable with just a little force and it left two oriented centres when i got it back to cube shape (and possibly one oriented corner!! but it may happen when I poped it to to fix the centres). Don't now if it shall be considered a valid move though.

I did not say that 2+2 centres swap was unsolveable using normal moves.. but it is a short and fairly easy to do alg.

Actually I think it is possible to solve the whole puzzle in a 72 degree angle from where it is from start because I had a square of centres on one side and another on a adjacent side that was angled 72 degrees from the first.

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

 

[Kenneth]

Made a little video showing some shapes shiftings:

Spoiler

Edit, took me 10 minutes to get back from there, in the end I had a tricky situation with 2+2 oriented centres sitting in diagonal (UF and BD sides) with a number of moves possible, then I found a solution for that state too =)

 

[mrCage]

Made a little video showing some shapes shiftings:

Spoiler

Edit, took me 10 minutes to get back from there, in the end I had a tricky situation with 2+2 orinted centres sitting in dagonal (UF and BD sides) with a number of moves possible, then I found a solution for that state too =)

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

Per

PS! I did appreciate that 7 turn jumbling double swap.

 

[qqwref]

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.

 

[Portponky]

I doubt you can solve it at a 72 degree angle because the core doesn't rotate when you jumble it.

One of the fun jumbling things to do is turn UR, FL and DB all to an angle and then jumble each intersection by ninety degrees. It looks like a big mess.