Re: [Speed cubing group] Re: wow... just........ wow..
- 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 -----
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-
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!
[Non-text portions of this message have been removed]
- --- In firstname.lastname@example.org, h_kociemba
> > 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 optimalAh, 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:
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.