5x5 gods number

[FenTheGoat]

It’s at least 60. 60! Is more than the total scrambles while 59! is less. 60 is the upper bound, I have no clue past that, that is my input on this.

 

[xyzzy]

60! Is more than the total scrambles while 59! is less.

That's not how it works…

Why factorial? What's your reasoning for using the factorial here?

For that matter, the total number of scrambles is 2.8×10^74 while 59! = 1.4×10^80 and 60! = 8.3×10^81.

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There are a known lower bound of 52 moves and a known upper bound of 130 moves.

 

[artless1der]

That's not how it works…

Why factorial? What's your reasoning for using the factorial here?

For that matter, the total number of scrambles is 2.8×10^74 while 59! = 1.4×10^80 and 60! = 8.3×10^81.

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There are a known lower bound of 52 moves and a known upper bound of 130 moves.

He said 60. and then he EXCLAIMED that it is 60 ... !
but id does sound cooler with more maths in it
Well done

although, since the minimum # of moves to scramble a 5×5 is 60,
it does seem feasible that the God's Number could be that or less...

 

[artless1der]

There are a known lower bound of 52 moves and a known upper bound of 130 moves.

Noice.
Since God's # for 3×3 is 20
but Sebastiano Tronto's FMC WR solve is 16 moves...
and 25 others in the rankings have found solutions less than 20 moves...

perhaps a 48- or 50-movee on 5×5 is possible...
tho it seems unlikely to happen in this lifetime lol

 

[abunickabhi]

Noice.
Since God's # for 3×3 is 20
but Sebastiano Tronto's FMC WR solve is 16 moves...
and 25 others in the rankings have found solutions less than 20 moves...

perhaps a 48- or 50-movee on 5×5 is possible...
tho it seems unlikely to happen in this lifetime lol

Some brute force 5x5 solvers algorithms are able to get 70 move solutions. Although I think God's number is lower than that. Tough to find by math yo. The search space is huge!

 

[FenTheGoat]

That's not how it works…

Why factorial? What's your reasoning for using the factorial here?

For that matter, the total number of scrambles is 2.8×10^74 while 59! = 1.4×10^80 and 60! = 8.3×10^81.

---

There are a known lower bound of 52 moves and a known upper bound of 130 moves.

I miss-counted the digits. And I remember, I believe it was perms video, said that the lower bound (I said upper bound originally, but thinking about it again it’s lower bound) was found by doing 18! that’s because 17! is smaller than 43 quintillion, therefore, ever solve cannot done in 17 moves or less because there’s not enough moves, but 18 can, I hope that cleared a few things up!

 

[xyzzy]

And I remember, I believe it was perms video, said that the lower bound (I said upper bound originally, but thinking about it again it’s lower bound) was found by doing 18! that’s because 17! is smaller than 43 quintillion, therefore, ever solve cannot done in 17 moves or less because there’s not enough moves, but 18 can, I hope that cleared a few things up!

You did not answer why you thought factorial is the appropriate function here.

The number of reachable states after n moves is not n! . (Sanity check: how many states can you reach by doing 1 move?)

17! and 18! are both smaller than 43 quintillion.

(I'm not sure if you realise – I was the one who established the 130 moves upper bound.)

 

[xyzzy]

it does seem feasible that the God's Number could be that or less...

There is absolutely no way GN for 5 is ever going to be fully determined, at least not while the Earth still exists.

Nevertheless, I would also speculate that GN is around 60 moves. No way to tell how far off that is from the truth!

perhaps a 48- or 50-movee on 5×5 is possible...
tho it seems unlikely to happen in this lifetime lol

For all we know, people have gotten scrambles with sub-50-move optimal solutions. Doesn't mean that anyone knows which scrambles those were, or what the sub-50-move solutions to those scrambles were.

Some brute force 5x5 solvers algorithms are able to get 70 move solutions.

"Brute force" is definitely underselling the effort I and others put in. It's a lot of "force" for sure, but "brute force" makes it sound like it's a stupid naïve search that you just throw absurd amounts of compute at until it succeeds. (It's not.)

 

[abunickabhi]

There is absolutely no way GN for 5 is ever going to be fully determined, at least not while the Earth still exists.

Nevertheless, I would also speculate that GN is around 60 moves. No way to tell how far off that is from the truth!


For all we know, people have gotten scrambles with sub-50-move optimal solutions. Doesn't mean that anyone knows which scrambles those were, or what the sub-50-move solutions to those scrambles were.


"Brute force" is definitely underselling the effort I and others put in. It's a lot of "force" for sure, but "brute force" makes it sound like it's a stupid naïve search that you just throw absurd amounts of compute at until it succeeds. (It's not.)

Sorry for sounding wrong.

I do not want to undersell the progress that you and Ed Trice have done and shared on cubesolvingprograms forum.
The algorithms do do a good job going through the 5x5 state space.

 

[artless1der]

Some brute force 5x5 solvers algorithms are able to get 70 move solutions. Although I think God's number is lower than that. Tough to find by math yo. The search space is huge!

and our hands are so little (compared to God's)

 

[artless1der]

There is absolutely no way GN for 5 is ever going to be fully determined, at least not while the Earth still exists.

Nevertheless, I would also speculate that GN is around 60 moves. No way to tell how far off that is from the truth!


For all we know, people have gotten scrambles with sub-50-move optimal solutions. Doesn't mean that anyone knows which scrambles those were, or what the sub-50-move solutions to those scrambles were.


"Brute force" is definitely underselling the effort I and others put in. It's a lot of "force" for sure, but "brute force" makes it sound like it's a stupid naïve search that you just throw absurd amounts of compute at until it succeeds. (It's not.)

perhaps the WCA would consider adding 5×5 FMC as an event...

but instead of sitting at a comp for months, instead entrants only have to pick up their 5×5 FMC homework to do bring back to the comp next year... ¯⁠\⁠(⁠°⁠_⁠o⁠)⁠/⁠¯

I'd be okay with that

 

[Thom S.]

It’s at least 60.

60 is the upper bound

You just contradicted yourself within 2 sentenses.

So, as always, xyzzy clarifies the concept in an understandable and correct way.
But
Half the posts in this thread by other people don't even classify as coherent thoughts, so I'm almost thinking it's lost effort in this case.

 

[OtaMota]

Why are we taking about 5x5 gods number when we could talk about 4x4 gods number instead?