Super-supercube challenge!!

[mrCage]

Some here may be familiar with the concept of super-supercubing. Normal supercubing involves positioning (or orienting) the center cubies (typically a picture cube).
Super-supercubing extends this concept to also involving inner shells on a larger cube. A 4x4x4 cube will also have a 2x2x2 inner cube, a 5x5x5 will have an inner 3x3x3, and so on.

Now the challenge. For a 5x5x5 super-supercube, find a way to twist 2 corners on the inner 3x3x3 without affecting the outer 5x5x5. What is the minimal length of such an algorithm? A super-super cube simulator (cubixplayer2) is available from the spedsolvingrubikscube yahoo group file section and was coded by me quite a few yrs back now

Per

PS! I'm unable to attach that file with this new design. I may find a solution later:fp

 

[bobthegiraffemonkey]

Spoiler

Use a commutator like [r' d' r d r' d' r, u] (all inner slices only). r u r' u r u2 r' l' u' l u' l' u2 l also works (inner layer sune+antisune). Optimal is the same as flipping two corners on a 3x3x3. Any supercube friendly alg on a 3x3x3 will work when applied to the inner layers, since T-centers and wings follow the center orientation of the inner 3x3x3 and the X-centers follow the 3x3x3 edges. Also, circle cubes mimic these puzzles, as pieces inside the circles correspond to pieces in inner layers.

 

[mrCage]

Spoiler

Use a commutator like [r' d' r d r' d' r, u] (all inner slices only). r u r' u r u2 r' l' u' l u' l' u2 l also works (inner layer sune+antisune). Optimal is the same as flipping two corners on a 3x3x3. Any supercube friendly alg on a 3x3x3 will work when applied to the inner layers, since T-centers and wings follow the center orientation of the inner 3x3x3 and the X-centers follow the 3x3x3 edges. Also, circle cubes mimic these puzzles, as pieces inside the circles correspond to pieces in inner layers.

Spoiler

That's correct. So an optimal solution might be for instance (r' d2 r b u2 b')*2.

 

[cmhardw]

I miss the super-supercube applet! I will have to download it again and fiddle with it. Yes I agree that the circle 4x4x4 cube is very similar to this concept, only it takes a regular 4x4x4 and places a 2x2x2 inside of it. If the 4x4x4 center pieces, the ones not in the circle, could be restickered to make it a supercube 4x4x4 then this would be exactly a 4x4x4 super-supercube.

Shameless plug on my website, but I am very proud of this formula. The number of combinations to a super-supercube is absolutely staggering and here is an explicit formula for it that I derived back when Per first came out with this applet.

 

[mrCage]

I miss the super-supercube applet! I will have to download it again and fiddle with it. Yes I agree that the circle 4x4x4 cube is very similar to this concept, only it takes a regular 4x4x4 and places a 2x2x2 inside of it. If the 4x4x4 center pieces, the ones not in the circle, could be restickered to make it a supercube 4x4x4 then this would be exactly a 4x4x4 super-supercube.

Shameless plug on my website, but I am very proud of this formula. The number of combinations to a super-supercube is absolutely staggering and here is an explicit formula for it that I derived back when Per first came out with this applet.

Chris!! Calling my windows .exe application an applet is like calling a master magic a cube:fp

Per

 

[qqwref]

Spoiler

That's correct. So an optimal solution might be for instance (r' d2 r b u2 b')*2.

I thought of this before I saw the spoiler

The Crazy Cube-II and III are equivalent to the 4x4 super-supercube. They also have the property of being a 2x2 inside a 4x4 but the 4x4 centers must be solved exactly.

 

[mrCage]

The Crazy Cube-II and III are equivalent to the 4x4 super-supercube. They also have the property of being a 2x2 inside a 4x4 but the 4x4 centers must be solved exactly.

Links to these would be helpful. A quick search resulted in nothing.

Per

 

[cmhardw]

Chris!! Calling my windows .exe application an applet is like calling a master magic a cube:fp

Per

Once again, my tech savviness shows itself haha. Wasn't done intentionally, just out of ignorance.

Chris

 

[qqwref]

Crazy 4x4-II is here:
http://witeden.com/goods.php?id=36

The III is similar but the circle is slightly larger, so that it has a little piece on each corner as well. The II and III are mathematically equivalent.

 

[mrCage]

New challenge(s). Now i want an edge 2-flip (adjacent edges) and a same layer 4-flip.

Per

 

[qqwref]

Perhaps not optimal, but:

Spoiler

(F E F2 E2 F) U (F' E2 F2 E' F') U'
(F B E F2 E2 F B') U (F' B E2 F2 E' B' F') U'

 

[mrCage]

Perhaps not optimal, but:

Spoiler

(F E F2 E2 F) U (F' E2 F2 E' F') U'
(F B E F2 E2 F B') U (F' B E2 F2 E' B' F') U'

Spoiler

Looks good. For the 4-flip consider this alg: R' D' B' D L' D2 L B D R D' F D2 F'. An alg i discovered about 20 yrs ago!!:tu
Somehow this did not work for inner cube as it left some unsolved wing centers on the outer 5x5x5. Weird! I will look into why this is so.
Consider this instead [F' R' E2 R2 E' R' F, U2]. Based on same idea as you. This was by backup solution

Per

 

[mrCage]

This is the toughest one i could think of. Do the superfliptwist on the inner cube. While leaving the outer 5x5x5 intact!
The superfliptwist flips all the 12 edges and twists all the 8 corners, but such that no adjacent corners are flipped the same way

Per

PS! This thread already has enough information for making a crazy long solution! I am working on some various ideaa, but as of yet they are not very fruitful ...

 

[mrCage]

Here is a rough outline of how it might be done. Make a fliptwist on 1st layer by applying the following 8 turns twice: r' d' r2 f' r' f2 d' f'. The side effect on wing centers of outer cube can be cancelled by a few outer layer conjugate turns before doing same on opposite layer. This leaves 4 edges to be flipped on inner cube on the E layer. For these i would use a conjugate version of qqwref's edge 4-flip.

How much all of this could be optimised, i have no idea ...

Per

 

[mrCage]

Here is a slightly optimised complete solution. The steps are rearranged to achieve a slight cancellation before fliping the edges of the inner cube's middle layer.

1. F2 B2 R2 L2 (reposition outer cube, cage)

2. (r' u' r2 b' r' b2 u' b')*2 (inner cube top layer fliptwist)

3. F2 B2 R2 L2 (undo repositioning)

4. (r' d' r2 f' r' f2 d' f')*2 (inner cube bottom layer fliptwist)

5. [f r' d f' b u' r b', E2] (inner cube middle layer 4-flip on edges, E is the single middlemost layer obviously)

Anyone has some ideas to optimise this further??

Per

 

[mrCage]

I think we have run out of flip and twist challenges. This time do a classic pattern on the inner 3x3x3: the cube in cube pattern. As always leave the outer 5x5x5 untouched!

Per

 

[qqwref]

First idea:
U R' F2 R b R' F2 R b' U'
D' L B2 L' f' L B2 L' f D

 

[mrCage]

First idea:
U R' F2 R b R' F2 R b' U'
D' L B2 L' f' L B2 L' f D

Hmmm. The upper case turns do nothing on the inner cube, so the first 10 moves cycles 3 edges on outer 5x5x5 and does nothing on inner 3x3x3. Similar with the last 10 moves, unless i misunderstand your notation. Hmmm.

My complete and correct solution so far has 40 turns. Not all that good i know
I will post it later.

Per

 

[qqwref]

WTF are you talking about? Those are all turns relative to the inner cube. And the lowercase turns turn two adjacent layers at once.

 

[mrCage]

WTF are you talking about? Those are all turns relative to the inner cube. And the lowercase turns turn two adjacent layers at once.

Ok, as I thought a notation confusion:tu I am used to upper case for the outer layers of the 5x5x5, and lower case for single inner slice turns of the 5x5x5. These slice turns are equivalent to turns of the outer layers of the inner 3x3x3. I wish there was a scripted Java applet available for this stuff. Maybe Randelshofer takes on the challenge??

Per

PS! Correctly understanding the notation your 2 sequences both cycle 3 centers of the outer 5x5x5 cube ...