Megaminx U move without U moves.

[ichcubegerne]

Hello, I was wondering if any efficient algorithms for doing a U or U' move on the Megaminx are known that do not actually do any U moves (without doing rotations ofc). Me and @xyzzy have been discussing it a bit and so far the best that we found was this 21 mover:

 Twizzle link 

[R' L F2 BL2' BR2 B2' D2' DR2 FL R', FR]

A rather simple setup of the full layer to another layer. Can someone find something better?

 

[NmeCuber]

It blows my mind how you guys found that. Could you explain how you found it?

 

[PapaSmurf]

It blows my mind how you guys found that. Could you explain how you found it?

You can get a feel for it by pausing after the first 10 moves and looking at the FR face. You can see all the white pieces on the same side, just round the wrong centre. So then they turn the FR face to move all the white pieces, then undo the setup.

 

[Deleted member 36445]

d Y

or

z R z'

 

[Eric4112]

d Y

or

z R z'

wait thats actually genius just do a random move and then flip it to the top lol

 

[ichcubegerne]

I was just able to independently verify the values up to depth 14. It might spit out one more before it runs out of memory.

d Y

or

z R z'

Not what I meant, I edited the post

 

[Deleted member 36445]

Not what I meant, I edited the post

So you have to achieve the "U state" by only doing external moves but no <U> moves are allowed....

this is interesting for robot solvers when you don't have grippers for all layers.

but in some cases rotations would be more practical to implement hehehe

 

[ichcubegerne]

So you have to achieve the "U state" by only doing external moves but no <U> moves are allowed....

this is interesting for robot solvers when you don't have grippers for all layers.

but in some cases rotations would be more practical to implement hehehe

The reasons that I originally asked this is because such a sequence is a pretty simple proof that the Megaminx group can be entirely generated, even if you take away one of the faces from the generating set. This sequence beeing as simple as possible (or short as possible) ist just an added bonus, that makes the proof more elegant. However it is still a subjectively interesting question to me and a lot of puzzle theorists, if someone can find something better, just as a puzzle task essentially. My personal guess is that an optimal such alg would have at least as many moves as a respective alg on a 3x3, which is 13 moves. It is not feasible to brute force such a depth on the megaminx for me, unfortunately, so finding the most efficient such alg and proving that that holds true is an interesting open problem to me.

 

[Deleted member 36445]

The reasons that I originally asked this is because such a sequence is a pretty simple proof that the Megaminx group can be entirely generated, even if you take away one of the faces from the generating set. This sequence beeing as simple as possible (or short as possible) ist just an added bonus, that makes the proof more elegant. However it is still a subjectively interesting question to me and a lot of puzzle theorists, if someone can find something better, just as a puzzle task essentially. My personal guess is that an optimal such alg would have at least as many moves as a respective alg on a 3x3, which is 13 moves. It is not feasible to brute force such a depth on the megaminx for me, unfortunately, so finding the most efficient such alg and proving that that holds true is an interesting open problem to me.