Message #1825

From: Andrew Gould <agould@uwm.edu>
Subject: RE: [MC4D] God’s number for 3^N
Date: Wed, 06 Jul 2011 19:13:12 -0500

A couple problems I’ve noted for FTM:

When N = 3: your lower bound gives 20.25 when we know it’s actually 20.

When N = 3: your possible twists is 24 when I count 18.

When N = 4: your possible twists is 192 when I count 184.

I’m wondering if your FTM lower bound equation is a bit high.mainly because
it beat my lower bound :-)

3^4: your FTM lower bound is 60.75, mine is 56.

–

Andy

From: 4D_Cubing@yahoogroups.com [mailto:4D_Cubing@yahoogroups.com] On Behalf
Of Andrey
Sent: Wednesday, July 06, 2011 11:27
To: 4D_Cubing@yahoogroups.com
Subject: [MC4D] God’s number for 3^N

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 probably
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.

Andrey