# 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/