Fewest Moves: New World Record 20 moves

[Zane_C]

For any scramble or for a specific scramble? The former sounds very difficult to work out.

I was initially asking about any scramble (so an approximate average). But now that you've mentioned that, I'll limit my question to a specific scramble (FMC WR scramble). The reason I ask is so I can get an idea of how great of a feat it would be to find one of the God solutions.

 

[Stefan]

According to http://cubezzz.dyndns.org/drupal/text/fullcube.txt there are 2.467*10^20 scrambles of 18 moves and according to http://cube20.org/ there are about 2.9*10^19 states requiring 18 moves. So if I'm not mistaken, the majority of states (too lazy to do check the other lenghts now) average about 8.5 optimal solutions.

Though, what did you mean with "unique optimal solutions"?

 

[Kirjava]

according to http://cube20.org/ there are about 2.9*10^19 states requiring 18 moves

huh?

I thought cube20 didn't bother solving all cases optimally?

EDIT: Ah, it's an estimate.

 

[cuBerBruce]

According to http://cubezzz.dyndns.org/drupal/text/fullcube.txt there are 2.467*10^20 scrambles of 18 moves and according to http://cube20.org/ there are about 2.9*10^19 states requiring 18 moves. So if I'm not mistaken, the majority of states (too lazy to do check the other lenghts now) average about 8.5 optimal solutions.

The 2.467*10^20 figure includes many suboptimal scrambles for positions of lesser distance. So the actual average number of optimal solutions will be less than 8.5. (I note this assumes we count only "canonical" scrambles, where the same face can't be turned twice in succession and adjacent commuting moves are done in a specific order.)

My belated congratulations to Tomoaki!

 

[Stefan]

Ah right, so I was indeed mistaken. Thanks for catching it. Exam and US trip coming up, so I was sloppy :-(. Well, even better if that's just an upper bound, making the feat even more impressive.

 

[Zane_C]

Thanks Stefan and Bruce.

Though, what did you mean with "unique optimal solutions"?

I only used the word 'unique' to emphasise 'different optimal solutions for the same scramble'.

 

[Soullark]

is that possible? to solve under gods number?

 

[littlewing1208]

is that possible? to solve under gods number?

God's number is an upper bound. Take a solved cube and do a U. The solution is U' .

God's number says that any given state takes at maximum 20 moves to solve.

 

[qqwref]

All God's Number means is that for all scrambles you could theoretically tie or beat the WR.

However, there are some scrambles where beating the current WR is impossible (you can only tie it)... although they are very rare.

 

[DavidCubie]

http://www.youtube.com/watch?v=yF2J39Xny4Q

So if this is true, FMC world record (fewest moves) won't be broken never, it's 20 now.

 

[antoineccantin]

http://www.youtube.com/watch?v=yF2J39Xny4Q

So if this is true, FMC world record (fewest moves) won't be broken never, it's 20 now.

:fp As he says, 20 moves is the MAX number of moves it can take.

http://www.youtube.com/watch?v=_Hfscd5HL78

 

[tx789]

when it reaches 1 it will never be broken

 

[antoineccantin]

when it reaches 1 it will never be broken

It can't with the current regulations, because the scramble would be solved, with penalty.

 

[MaeLSTRoM]

It can't with the current regulations, because the scramble would be solved, with penalty.

Umm no because FMC doesn't have a +2? So its still a valid scramble and 1 would be a valid solution....

 

[Musicalboy2]

http://www.youtube.com/watch?v=yF2J39Xny4Q

So if this is true, FMC world record (fewest moves) won't be broken never, it's 20 now.

If I remember correctly, most scrambles have an optimal solution of 18 moves, and there are more scrambles with an optimal solution of 12 moves than there are scrambles with optimal solutions of 20 moves.

 

[Mike Hughey]

http://www.youtube.com/watch?v=yF2J39Xny4Q

So if this is true, FMC world record (fewest moves) won't be broken never, it's 20 now.

I think it's interesting this comment was just made, since Guus just thoroughly beat it unofficially in the weekly competition two weeks ago.

17 moves! And he found it in just 20 minutes!

It certainly seems like this UWR should be pretty challenging to break (at least with competition-valid scrambles).