--- In

speedsolvingrubikscube@yahoogroups.com, h_kociemba

<no_reply@...> wrote:

>

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

about

> > 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

> > 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

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

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