A cube where bands of stickers slide. Humans went from 240 to 107 moves in four days. AI needs about 50-60.

[Pawel_Skimmiq]

Hi, I'm Pawel, 60, from Warsaw. I made a puzzle and I need your theory brains.The puzzle looks like a 3x3, but the faces don't turn. Each move slides a closed band of 12 stickers around four faces. There are nine bands and they cross each other. Nothing on the cube is fixed. Single stickers just move along their tracks.AI did the heavy math for me. The nine band moves generate every permutation of the 54 stickers, so every color arrangement is reachable. The state count is 54!/(9!)^6, a 39-digit number. The proof and the write-up are here: skimmiq.com/human-method/For a year nobody solved it by hand. I honestly thought nobody would. Then last Tuesday I showed it on r/Cubers and they needed about an hour. First solves used mostly 4-move commutators. Then one solver started racing himself: 240 moves, then 150, then 140, then 107, in four days. All with replays. My AI solvers average about 50-60 moves.So my questions for you:

1. Can this become a staged, teachable method, or will it stay ad-hoc commutators?
2. Where is the practical floor for a human? Under 100? Under 80?
3. People say it is a relative of Hungarian Rings and Loopover. Do the tools from those transfer here?

There is a 60-second demo in the browser: skimmiq.com/pt/ and a state editor that shares any position as a URL, so ideas are easy to test and show. The r/Cubers thread is here: reddit.com/r/Cubers/comments/1vrq8zk/
Full disclosure: AI helps me write English (it is my third language) and it did the math above. The puzzle is mine. The questions too

 

[Fred]

I've been having a lot of fun with this puzzle. I initially solved it with LBL and then 8-move commutators for the last layer because I didn't want to mess stuff up elsewhere on the cube. Then I saw that people were doing certain 4-move commutators, and the trick is that those will permute certain other stickers, so you just need to make sure those are all of the same color (ie the color of your first layer).

Another idea to make the reachable state count even higher would be to make it a supercube. That is, every sticker would have a unique location for where it belongs, and a unique solved orientation too.

 

[Pawel_Skimmiq]

Great to see you here, Fred
Your own method is the second one in this puzzle's short history (the first is on skimmiq.com/human-method/, born in the Reddit thread).
The supercube idea is a funny coincidence: a "hard mode" with distinguishable stickers has been tempting me for a while i.e. by adding numbers or others symbols on the stickers . The math survives it (the band moves still generate everything), but my solvers would lose all the shortcuts they get from identical stickers. So the AI would suffer more than the humans. Maybe that is exactly the point
May I quote your method description on the human-method page, next to the first one?

 

[Fred]

Great to see you here, Fred
Your own method is the second one in this puzzle's short history (the first is on skimmiq.com/human-method/, born in the Reddit thread).
The supercube idea is a funny coincidence: a "hard mode" with distinguishable stickers has been tempting me for a while i.e. by adding numbers or others symbols on the stickers . The math survives it (the band moves still generate everything), but my solvers would lose all the shortcuts they get from identical stickers. So the AI would suffer more than the humans. Maybe that is exactly the point
May I quote your method description on the human-method page, next to the first one?

Sure, go ahead. Hmm, seems like I was just doing a less efficient version of the Bear method with slower commutators. Though I did also notice the trick of moving the band around and solving it at the end. It's the same idea as in CFOP where you solve the cross pieces relative to each other, then solve them all with a D move.

I preferred the original description on Reddit to the summary on your site. So I think directly quoting the method descriptions would make things clearer and more understandable.

 

[Pawel_Skimmiq]

Sure, go ahead. Hmm, seems like I was just doing a less efficient version of the Bear method with slower commutators. Though I did also notice the trick of moving the band around and solving it at the end. It's the same idea as in CFOP where you solve the cross pieces relative to each other, then solve them all with a D move.

I preferred the original description on Reddit to the summary on your site. So I think directly quoting the method descriptions would make things clearer and more understandable.

Thank you! You have been inadvertently improving my page
You are right about the descriptions: the authors' own words are clearer than my summary, so I will quote them directly. And your CFOP cross analogy (solve relative, align at the end) is the best one-line explanation of this trick I have seen. If you don't mind, that goes on the page too, credited to you.

 

[Fred]

Thank you! You have been inadvertently improving my page
You are right about the descriptions: the authors' own words are clearer than my summary, so I will quote them directly. And your CFOP cross analogy (solve relative, align at the end) is the best one-line explanation of this trick I have seen. If you don't mind, that goes on the page too, credited to you.

Yes, of course