Message #35

From: Don Hatch <hatch@plunk.org>
Subject: Re: [MC4D] Orientations of the centre cubes
Date: Mon, 08 Sep 2003 17:19:57 -0400

On Sun, Sep 07, 2003 at 10:46:27PM -0000, mahdeltaphi wrote:

> The current implementation of the tesseract does not keep track of
> the orientations of the centre cubes of the 8 3x3x3 faces of the
> tesseract. Accounting for all permutations of pieces and their
> orientations, each rotation move on the tesseract seems to permit
> only even permutations. Consequently, in theory, it should be
> possible to have all the other pieces in place, and yet have the
> centre cubes of each of the 8 cubical faces in a variety of
> orientations. This was certainly the case of the original 3x3x3 cube
> (I used to mark the centre square of each 3x3 face to indicate in
> which direction it should be pointing, and doing so reduced the
> number of possible solutions down to 1 from a total of (4^6)/2). If
> the same result applied to the tesseract, marking the centre cubes
> would reduce the number of correct solutions from (6^8)/2 to 1.

This sounds plausible,
except there are 24 possible orientations of a cube (not 6)
so this number should be (24^8)/2 instead of (6^8)/2, I think.

Don

–
Don Hatch
hatch@plunk.org
http://www.plunk.org/~hatch/