Why is the superflip 'difficult'?

[guysensei1]

Why is the superflip position 'difficult' to solve? Is there some reason as to why 12 flipped edges needs at least 20 moves to solve?
How was it discovered that this position (among others) needed the most moves to solve?

 

[mitch1234]

Superflip is just one of 830618 positions that requires 20 moves to solve. Saying that the superflip is the position that needs the most moves to solve is wrong

 

[guysensei1]

Superflip is just one of 830618 positions that requires 20 moves to solve. Saying that the superflip is the position that needs the most moves to solve is wrong

I never said it was the only one that needed the most moves!

I just asked how they proved that the super flip was (one of) the most 'difficult' positions.


Another question: why superflip, and not one of the many other distance 20 positions?

 

[Baku]

From "why superflip" I think you mean that why is superflip recognized as one of the 20 move positions. This is simply due to the fact that superflip just has an appealing pattern with all of the flipped edges whereas most of the other 20 move positions (most likely) just look like any other scrambled cube.

 

[Renslay]

Superflip is just one of 830618 positions that requires 20 moves to solve. Saying that the superflip is the position that needs the most moves to solve is wrong

By 830618, you mean "about 490,000,000", right?

 

[brian724080]

It's not, it's just one of the positions that require 20 moves to solve. I'd love to get the superflip in competition.

 

[TDM]

It's not, it's just one of the positions that require 20 moves to solve. I'd love to get the superflip in competition.

Wouldn't everyone? ((M' U')4 x y)3 easy wr

 

[Future Cuber]

What is a super flip????
I know im a noob

 

[guysensei1]

Wouldn't everyone? ((M' U')4 x y)3 easy wr

Haha, we need someone to sub 3 the superflip.



Anyway, back to my original question. The main point hasn't been answered. Without knowledge of what god's number is, how did they show that the superflip needed the most moves?

 

[Marvin]

What is a super flip????
I know im a noob

I'm not trying to come off as rude, but this question could've easily been avoided if you looked it up on the speedsolving wiki.
http://www.speedsolving.com/wiki/index.php/Superflip

 

[Future Cuber]

I'm not trying to come off as rude, but this question could've easily been avoided if you looked it up on the speedsolving wiki.
http://www.speedsolving.com/wiki/index.php/Superflip

Ooooookkkk...I get it
I was lazy... to search in the speedsolving wiki

 

[Renslay]

Anyway, back to my original question. The main point hasn't been answered. Without knowledge of what god's number is, how did they show that the superflip needed the most moves?

Michael Reid ran an optimal solver (in 1995), and found that neither of it's neighbour (using the Superflip's high degree of symmetry) can be solved in 18 moves (actually, he studied the neighbours with distance 2 and 3).

http://www.math.rwth-aachen.de/~Mar...l_reid__superflip_requires_20_face_turns.html

The optimal solver is based on Kociemba's Two Phase algorithm (1991-1992), see also http://kociemba.org/math/optimal.htm.

And he didn't show it requires the most turns, he just showed that it requires at least 20 turns (and also gave a 20 move solution). It was much later (with different techniques and computer power) when God's number was proven to be 20, thus making superflip one of the farthest state from the solved one.

 

[DeeDubb]

I think I get the OPs question, and it's more asking about the theory behind it. What makes 12 edges that all require permutation and orientation with 12 solved corners more difficult than almost all random scrambles? Why does having solved corners make it further away from solved than unsolved corners? Maybe these questions haven't been asked/answered before.

 

[ryanj92]

I think its just notable because its a distance 20 position with so much order behind it.
Does anyone know how many of the distance 20 positions have 12 flipped edges.

As for the theory, idk, but any zz solver will tell you that changing the orientation of 12 edges is pain wrt movecount

 

[guysensei1]

I think I get the OPs question, and it's more asking about the theory behind it. What makes 12 edges that all require permutation and orientation with 12 solved corners more difficult than almost all random scrambles? Why does having solved corners make it further away from solved than unsolved corners? Maybe these questions haven't been asked/answered before.

Yes this.

Also, is there some fundamental reason behind why a distance N position MUST require N moves?


EDIT:

As for the theory, idk, but any zz solver will tell you that changing the orientation of 12 edges is pain wrt movecount

y axis color neutrality is useful! unless all your edges were permuted but flipped.

 

[Stefan]

Also, is there some fundamental reason behind why a distance N position MUST require N moves?

Yes, the definition of distance.

 

[guysensei1]

Yes, the definition of distance.

Well. Fair enough. I guess the question doesn't make sense huh?

 

[Renslay]

Also, is there some fundamental reason behind why a distance N position MUST require N moves?

I don't understand this question.

If it must not requires N moves, it wouldn't be a distance N position...

Any distance N position is a distance N position because it requires N moves at least (by definition).

Edit: ninja'd.

 

[goodatthis]

I think there's a few reasons:

1. It was one of the first distance-20 positions discovered, and set the lower bound for God's Number.
2. It's a cool looking pattern.
3. Superflip+Fourspot (Fourspot looks like this: M2 E M2 E') is the only known distance-26 position in QTM (where half turns count as two moves), so Superflip has significance in this sense.
4. It's more symbolic than any of the other distance-20 positions, because it's not just a random looking scramble. It's sort of like finding some sort of algebraic relationship (like 22/7) for pi, which would be mind blowing. It's sort of like if a random scramble is a transcendental number, Superflip is the algebraic number in the sequence. Not sure if this makes sense, but it make sense to me.

These are just what I think, but I really don't know why it is so difficult mathematically.

 

[mark49152]

This doesn't directly answer the question, but I would suggest it's to do with its symmetry. In the same way that it was one of the first 20f* positions found because you only have to prove there are no sub-18/19 move solutions to a very small number of neighbours (3 or 4?), a position with much less symmetry has many more "chances" to have a shorter solution.