Message #3410

From: Melinda Green <melinda@superliminal.com>
Subject: Re: [MC4D] Calculate number of permutation of restricted cube
Date: Wed, 29 Jun 2016 16:31:28 -0700

That is an interesting result. Does your 1344 number exclude the
symmetries of the whole puzzle or other symmetries? Have you tried
visualizing the resulting graph with GraphVis or other tool?

-Melinda

On 6/29/2016 6:59 AM, phamthihoa4444@gmail.com [4D_Cubing] wrote:
>
>
> I want to calculate number of permutation of half-turn-only 2^4 cube.
>
>
> First, I split the cubies into two groups, called "even" and "odd"
> ones. Fix one piece in odd group. The permutation in each group is
> even. Thus an upper bound is 8!/2 * 7!/2.
>
> Intuitively I think single 3-cycle in each group is impossible, so
> there is much less permutation. But I can’t think how to prove it.
>
> Using computer brute force, there are 1344 (surprisingly small)
> permutations, if the program has no bug.
>
>
>
>