--- In 4D_Cubing@yahoogroups.com, "Andrey"
>
> My estimates show that lower counting limit L for God's number for 3^N =
is 2/9*N*3^N for QFTM (as implemented in MC5D and MC7D - with 2*N*(N-1)*(N-=
2) possible twists) and 3/4*3^N for FTM (where any twist of face is counted=
as 1, so we have N!*2^(N-1) possible twists). Actual God's number is proba=
bly between L and 2*L.
> By the way, if we take puzzle 2*1^N (with only one twisting face), its =
God's number in QFTM is N. But counting limit gives something like
> N*(log(2*N)/(2*log(N)) that is N/2*(1+o(N)). So lower limit is almost the=
half of the actual number.
>=20
> Andrey
>
Without having analysed your results fully (as I am not qualified to commen=
t not having the same empirical savvy) I would think your lower bound limit=
is much closer to the truth than my "shooting from the hip" suggestion of =
3^N in an earlier thread. As a matter of great interest to me had you any t=
houghts on the lower bounds for the 2^N case? Surely (and sorry for calling=
you Shirley -;)) - the effort should be concentrated on the 2^N case as th=
is is likely to be more more tractable? This proved to be the case in a nea=
t presentation for the 2x2x2 cube group (whereas the 3x3x3 is extremely unw=
ieldy):
http://cubezzz.dyndns.org/drupal/?q=3Dnode/view/177
P.S. Sorry looks like you'll have to cut and paste this link - don't have t=
he time to work out how to make it auto clickable.