# Message #1822

From: Andrey <andreyastrelin@yahoo.com>

Subject: God’s number for 3^N

Date: Wed, 06 Jul 2011 16:26:53 -0000

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