Message #3413

Subject: Re: Calculate number of permutation of restricted cube
Date: Thu, 30 Jun 2016 23:04:19 -0700

Why should I visualize it? What I need to prove now is why only 1344 positions are reachable. But is 1344 too large to visualize?

Just like how permutation of 2^4 = (15!/2) * (12^14 * 4) is calculated, hold one corner piece in its place and rotate the rest.

I tried to solve the puzzle by MPUlt (the structure of puzzle file is really difficult to understand, and I have not understand many parts yet) and can solve it intuitively, then I think number of permutation is correct.

Computer brute force given: