Flipping!

[Ville Seppänen]

((M' U')*4 y' x')*3 I think that's the best alg for it (optimal is 20 moves HTM ).

 

[Sa967St]

((M' U')*4 y' x')*3

and ((M'U)*4 yx')*3 if you prefer M'U over M'U'

 

[siva.shanmukh]

This is in no way about increasing speed, reducing move count or anything like that. But this is an interesting puzzling problem.

I lately found that an adjacent edge flip on a solved cube can be solved by using only 3-cycle edges(U PLL) and cube rotations. I jus want to know what is the least number of 3-cycles used to do this. I didn't count mine but am sure i did it in the most crude way.

 

[Ville Seppänen]

first try: 11
this is fun I'm sure this is not the best.

 

[Derrick Eide17]

This is in no way about increasing speed, reducing move count or anything like that. But this is an interesting puzzling problem.

I lately found that an adjacent edge flip on a solved cube can be solved by using only 3-cycle edges(U PLL) and cube rotations. I jus want to know what is the least number of 3-cycles used to do this. I didn't count mine but am sure i did it in the most crude way.

R U' R' U R2 U2 r' R' U' R U r U2 R2

 

[Ville Seppänen]

This is in no way about increasing speed, reducing move count or anything like that. But this is an interesting puzzling problem.

I lately found that an adjacent edge flip on a solved cube can be solved by using only 3-cycle edges(U PLL) and cube rotations. I jus want to know what is the least number of 3-cycles used to do this. I didn't count mine but am sure i did it in the most crude way.

R U' R' U R2 U2 r' R' U' R U r U2 R2

that's not really 3-cycling but while we're at it: R' U2 R2 U R' U' R' U2 r U R U' r'

 

[Derrick Eide17]

This is in no way about increasing speed, reducing move count or anything like that. But this is an interesting puzzling problem.

I lately found that an adjacent edge flip on a solved cube can be solved by using only 3-cycle edges(U PLL) and cube rotations. I jus want to know what is the least number of 3-cycles used to do this. I didn't count mine but am sure i did it in the most crude way.

R U' R' U R2 U2 r' R' U' R U r U2 R2

that's not really 3-cycling but while we're at it: R' U2 R2 U R' U' R' U2 r U R U' r'

Yes, I know its not 3 cycling, I was just proving him wrong that it can be done without

 

[Ville Seppänen]

Hmm... I think what siva said can be understood in 2 ways. You understood it like there's no other possible way to flip them except U-PLL's and rotations. I understood it like it is possible to flip them using only U-PLL's and rotations, although it is not necessary.

 

[Derrick Eide17]

Hmm... I think what siva said can be understood in 2 ways. You understood it like there's no other possible way to flip them except U-PLL's and rotations. I understood it like it is possible to flip them using only U-PLL's and rotations, although it is not necessary.

Message = Too Short.

 

[siva.shanmukh]

I wanted you to think the way Ville Seppänen thought. I don't say its not possible. But its interesting to restrict one self only two kinds of moves and yet be able to solve it. It essentially proves that all edges in a cube can be solved jus using cube rotations and u perms if the scramble is an even move scramble(quarter turn metric)

 

[MistArts]

I wanted you to think the way Ville Seppänen thought. I don't say its not possible. But its interesting to restrict one self only two kinds of moves and yet be able to solve it. It essentially proves that all edges in a cube can be solved jus using cube rotations and u perms if the scramble is an even move scramble(quarter turn metric)

Like U F U' R U' R' U F' ?

 

[siva.shanmukh]

No No No. It essential what happens when you do R U' R' U R2 U2 r' R' U' R U r U2 R2. After you do the alg above on a solved cube, you will end up flipping 2 adjacent edges. The challenge is as follows.
You have to solve the cube from here but you are restiricted on use of moves. You can only use cube rotations and U perms as the basic moves but not the RLUDFB moves.

 

[joey]

6 U-perms.

 

[Stefan]

Yeah, joey, but not prove that optimal.

 

[joey]

Yeah, joey, but not prove that optimal.

Did you mean I should now prove that it is optimal?

[pochmann-style]I won't. First you prove that it isn't optimal.[/pochmann-style]

 

[cmhardw]

Yeah, joey, but not prove that optimal.

Did you mean I should now prove that it is optimal?

[pochmann-style]I won't. First you prove that it isn't optimal.[/pochmann-style]

Haha this looks to me like mathematics' version of the game "chicken" ;-)

Chris

 

[siva.shanmukh]

WoW!! Only 6?? How did you manage to do it, can you write your solution here.. In no way am I able to solve it in 6 U perms. I am taking many more.

And is it possible to mathematically arrive at this number? Or prove that this is the least possible number?

 

[joey]

WoW!! Only 6?? How did you manage to do it, can you write your solution here.. In no way am I able to solve it in 6 U perms. I am taking many more.

Not for now, maybe later.

And is it possible to mathematically arrive at this number??

Yes.
1 2 3 4 5 6

 

[siva.shanmukh]

Yes.
1 2 3 4 5 6

I meant to ask if it is possible to mathematically find that 6 is the least number of moves to achieve this.

 

[Lucas Garron]

Yes.
1 2 3 4 5 6

I meant to ask if it is possible to mathematically find that 6 is the least number of moves to achieve this.

Well, yes. You find a solution with length 6 (not too difficult), and show that there are no shorter ones (slightly harder). There are a few ways to do this, like brute force checking.

But while we're at it...
An edge requires 3 U-perms to flip. I think we can extend this to 4 and 5 for this problem, by showing that you can't return every edge home while performing this flipping. I can't of something that'll easily prove 6, though, right now...