Are there local maxima in the number of moves required to solve a Rubik's Cube?

[Mike Hughey]

Don't lock up. Don't even lock up. Lock up and you're dead. They are fast, faster than you can believe. Don't turn slow, don't drop the cube, and DON'T LOCK UP. Good luck...

Spoiler

 

[Edward]

Spoiler

A Cubing Angel
How are you not dead?

 

[Mike Hughey]

A Cubing Angel
How are you not dead?

I haven't locked up ... yet ...

 

[Edward]

I haven't locked up ... yet ...

Keep it up. The Mad Man with The Twistable Box should be there soon.

 

[Stefan]

You must not be a Doctor Who fan:
http://tvtropes.org/pmwiki/pmwiki.php/Main/TimeyWimeyBall

Ah, ok. But it didn't exactly help that he omitted the first "—" in there. That screws it up.

 

[Nils]

welcome to the forums Nils)

Thank you

How so? His answer and explanation are wrong

How you mean? What other definition of local minima and local maxima do you know of other than the definition used in analysis and differential calculus? Local maxima and minima requires continuity. You going to tell me all the things they teach me here at university are incorrect?

He also seems to confuse himself, first stating that the domain is discrete and then asking what the domain is...

I was just wondering what the domain was since i don't fully understand what she means with SA and A. Did she means A to be the move itself and SA to be the combination of move S and A, or S times move A?

_____
Nils



PS: "whats the half of a dozen" Good one

 

[cuBerBruce]

How you mean? What other definition of local minima and local maxima do you know of other than the definition used in analysis and differential calculus? Local maxima and minima requires continuity. You going to tell me all the things they teach me here at university are incorrect?

The question is talking about local maxima of an integer-valued function over the elements of a Cayley graph. The function has no local minima, except for the global minimum at the node representing the solved state.

I'll note that there can be two types of local maxima. For a "weak" local maxima, neighboring nodes can have the same distance value as the local maximum node. For a "strong" local maxima, all neighboring nodes have a distance value less than the local maximum node.

I was just wondering what the domain was since i don't fully understand what she means with SA and A. Did she means A to be the move itself and SA to be the combination of move S and A, or S times move A?

Unfortunately, susan12's pasting of the text lost the subscripts in the original version.

 

[Nils]

The question is talking about local maxima of an integer-valued function over the elements of a Cayley graph. The function has no local minima, except for the global minimum at the node representing the solved state.

I'll note that there can be two types of local maxima. For a "weak" local maxima, neighboring nodes can have the same distance value as the local maximum node. For a "strong" local maxima, all neighboring nodes have a distance value less than the local maximum node.



Unfortunately, susan12's pasting of the text lost the subscripts in the original version.

Oh sorry my bad :S , i did not knew that there was also a definition of local maximum in group theory? Or is it the same as in analysis?

edit: Ok i think i understand it Thanks!