Helicopter cube solving (and patterns)

[mrCage]

I posted a 16-move alg for that before, so I already have a 32-move solution for this. Sorry

Could you repost that 16-mover please. Missed it, and the thread is long and confusing:rolleyes:

Per

 

[qqwref]

It was at the very end of the first page (4th page for you? I have 40 posts per page) where I posted pure optimal CO algorithms for the last layer:

"H" orientation (symmetrical 4 twist):
- [(UF UB) UR UB (UR UL) UF UR]2 (16f*)
- [(UF UB) UR UF (UR UL) UB UR]2 (16f*)
- [UF (UL UB UL) (UR UB UR UB)]2 (16f*)
- [(UF UL UF) UB (UR UF UR) UL]2 (16f*)
- [UF (UR UB UR) (UL UB UL UB)]2 (16f*)
- [(UF UR UF) UB (UL UF UL) UR]2 (16f*)
- [(UL UB UL UB) (UF UL UF) UR]2 (16f*)
- [(UL UF UL UF) (UB UL UB) UR]2 (16f*)

 

[coinman]

Also try UR UL (x)*12
Almost superflip in 24 moves, not counting cube rotations..

Just got a 1:03.61 lucky solve, only corner orientation after fixing centers.

 

[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!)

Oops. So far i have needed 7 algs for the normal cube-in-cube. I will post if i find something better. Maybe a different cube-in-cube (2-cycle) across the UFR-DLB axis??

Per

 

[Kenneth]

Fun scramble Solved it in 3:03.85.

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

3:32.59

But I had a bit of luck in FL after the cube shape with more pieces solved than you can expect from random distrubution, so I guess my scrambling wasn't enough, more turns next time...

-----------------------------

Theory: OLL/PLL, how many are there?

OLL is to complicated for me to calculate but I think PLL is 24 CP times 8! centres (but you may have 1-4 two cycles of two centres of the same colour that will reduce the number, don't know how much though)

24 x 8! = ~1,000,000

A PLL skip in a million??

 

[mrCage]

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.

Why do jumbling for that? I do it like this:

UR UF FR (UR UF)*3 FR UF UR and then FR

Per

 

[qqwref]

I don't know if this is what he meant, but you can do pure swap of two corners (keeping orientation on both) with
UR UL (FR- UL- UF FR+ UL+) (UR+ FL+ UF UR- FL-) UF UR UL
Despite the relatively large number of moves the two sections in parentheses are quite fast. One way without jumbling is:
UR UL UF UL FL UF (UL FL)3 UF FL UR

 

[mrCage]

I don't know if this is what he meant, but you can do pure swap of two corners (keeping orientation on both) with
UR UL (FR- UL- UF FR+ UL+) (UR+ FL+ UF UR- FL-) UF UR UL
Despite the relatively large number of moves the two sections in parentheses are quite fast. One way without jumbling is:
UR UL UF UL FL UF (UL FL)3 UF FL UR

A pure corner swap is a swap of order 2 (swap*2=I). You restrict pure to the sense of PLL (or PC if you like).

Per

 

[qqwref]

What are you talking about? Those sequences ARE pure - no centers are moved, even if you had a supercube. This is possible because a single helicopter cube turn has an odd effect (2-cycle) on corners.

 

[mrCage]

What are you talking about? Those sequences ARE pure - no centers are moved, even if you had a supercube. This is possible because a single helicopter cube turn has an odd effect (2-cycle) on corners.

Yes, but i'm claiming my swap is pure also. Otherwise pls define pure

Per

PS! Example of impure swap would be to do my swap. Then twist UFR and UFL.

PPS!! UF is an impure corner swap with centers side effect

 

[qqwref]

"Pure" means "nothing else is affected". Your swap IS pure. The difference is that yours swaps two corners on the top layer but affects their orientation (with respect to the top), whereas mine swaps two corners on the top layer without affecting their orientation.

 

[mrCage]

"Pure" means "nothing else is affected". Your swap IS pure. The difference is that yours swaps two corners on the top layer but affects their orientation (with respect to the top), whereas mine swaps two corners on the top layer without affecting their orientation.

Then we agree! Words often come in the way

Per

PS! Do you have short pure center swap?? (jumbling obviously)

Mine is 12 turns. A conjugated 8 turn jumble.

 

[qqwref]

Well, there's UL UR2- FL+ UF FL- UR- UF UR UL, which coinman (I think) posted before, but it's not really pure - it also swaps two U centers.

 

[mrCage]

Neat pattern: (2 big flips)

UF - UL UF UR UF UL - UR UF UL UF UR - UF

Per

PS! Can be repeated on D layer for another striking pattern.

 

[qqwref]

Theory: OLL/PLL, how many are there?

OLL is to complicated for me to calculate but I think PLL is 24 CP times 8! centres (but you may have 1-4 two cycles of two centres of the same colour that will reduce the number, don't know how much though)

24 x 8! = ~1,000,000

A PLL skip in a million??

What do you mean "OLL/PLL"? And the centers can't move around freely, unless you're talking about a jumbled cube, but then you shouldn't use algs...

 

[mrCage]

Theory: OLL/PLL, how many are there?

OLL is to complicated for me to calculate but I think PLL is 24 CP times 8! centres (but you may have 1-4 two cycles of two centres of the same colour that will reduce the number, don't know how much though)

24 x 8! = ~1,000,000

A PLL skip in a million??

What do you mean "OLL/PLL"? And the centers can't move around freely, unless you're talking about a jumbled cube, but then you shouldn't use algs...

OLL/PLL does not seem good for speedsolving, especially if jumbled

Per

PS! I shortened my solution for cube-in-cube pattern. Still 5 rather lengthy algs ... Working on a different cube-in-cube of order 2. Also tricky!

 

[Kenneth]

Theory: OLL/PLL, how many are there?

OLL is to complicated for me to calculate but I think PLL is 24 CP times 8! centres (but you may have 1-4 two cycles of two centres of the same colour that will reduce the number, don't know how much though)

24 x 8! = ~1,000,000

A PLL skip in a million??

What do you mean "OLL/PLL"? And the centers can't move around freely, unless you're talking about a jumbled cube, but then you shouldn't use algs...

I'm talking about make top side white and then permute the sides of the top layer (jumbled, otherewise there are not so many combinations). I don't think it is a good way to solve it but it is still possible.

I was just thinking of it as a theoretical matter, pure curiosity

 

[mrCage]

SUPERFLIP AND SUPERFLIPTWIST

I's like to add 2 more patterns taken from 3x3x3 cube. The superflip i construct from the following 2 sequences:

(UR UF)*3 (UF LF)*3 Repeat 4 times then flip last 4 "center-edges" slightly differently.

Twist all 8 corners for the superfliptwist.

Per

 

[coinman]

A new pattern.

The other side.

 

[mrCage]

A new pattern.

Order 2 or 6 ?? (show the 3 other faces)

Per

PS! Nearly every pattern is possible. Every center configuration is possible by jumbling. Only corner orientation is retricted!!