- I don't know anyone knows a 25 turn HTM scramble (without obvious cancellations) that result in the solved state again, but I do remember a challenge a year or more old that had a 13 moves one (if memory serves me correct) as a winner. I thought Stefan found it. There were also some longer ones naturally. I am not going to try to find a 25 moves one, but I think that if you search for that thread, you will see that one is extremely likely to exist.

----- Original Message -----

From: d_funny007

To: speedsolvingrubikscube@yahoogroups.com

Sent: Saturday, March 31, 2007 8:03 PM

Subject: [Speed cubing group] Re: wow... just........ wow..

Intuitively this must be the case, and I think it's a assertion that

everybody here is willing to believe. But this is much easier than

proving the other things being discussed, all this takes is finding a

single case. I wouldn't even call it a "proof," just a "example/counter-

example".

Just entertain me and see if anyone here can find a 25 turn HTM

scramble that produces the identity/solved state. I'm having a hard

time finding one. Oh and by "scramble," I am discounting the really

trivial cancellations and such.

> Whoa! There are positions not reachable in 25 turns? Proof please!

>

> Cheers!

> Stefan

>

[Non-text portions of this message have been removed] - --- In speedsolvingrubikscube@yahoogroups.com, h_kociemba

<no_reply@...> wrote:>

about

> > Which had to be expected. I think in a million random cubes,

> > three should be expected to be solvable in 13 moves or less.

Those

> > four you found with 13f, can you please find out their optimal

Ah, yes, I must've made a computation mistake. I tried again and get

> > solution lengths?

>

>

> For 1 million cubes, the theoretical distribution for the *optimal*

> maneuvers should look like this:

>

> 12f: ~1

> 13f: ~12

> 14f: ~160

> 15f: ~2200

> 16f: ~29000

> 17f: ~260.000

> 18f: ~690.000

> 19f: ~30.000

> 20f: probably less than 1

12 expected cubes for 13f as well now. I did it like this:

First I looked at the right column in this statistic:

http://cubezzz.homelinux.org/drupal/?q=node/view/68

Multiplied the last number twice more with 13 (roughly the branching

factor). Multiply with a million, divide by 4.3e19.

Yeah I know, probably there's a statistic somewhere out there about

the overall distribution, but I don't know where.

Cheers!

Stefan