Message #52

From: ojcit <>
Subject: Re: [MC4D] Orientations of the centre cubes
Date: Mon, 08 Sep 2003 22:59:40 -0000

mahdeltaphi wrote:

> (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 (46)/2).
By making that change, you’re causing a fundamental change in the
underlying rules of the puzzle, perhaps almost as radical as
extending from 3 to 4 dimensions. The fact that a center face on
the original cube can be rotated is a necessary flaw, but one that I
believe the state counting already takes into account. As the
system configurations are defined traditionally, there is still only
one solution. It’s a similar problem to the one that comes up in
inverse trigonometry all the time (e.g. arcsin(1) = pi/2 + k*pi, for
any integer k. Although the k=0 solution is more pleasing, it’s no
more valid than any of the others.) So I guess my point is that if
you want to differentiate the orientations of the "fixed" faces,
you’re altering, not merely clarifying, the rules. In the original
cube, the correct orientation of any piece is defined by its
neighbors, not by the configuration it comes from in the factory.

Also, from an aesthetics standpoint, one of the most pleasing
aspects a solved 3x3x3 cube is the fact that each face is a solid
color, with 9 identical squares. I think the elegance would suffer
if you mark the center square.

Lastly, the center cubes in the 4D system are fairly difficult to
see as it is, and if they were marked with seven different colors
each, it would just be painful.

So I guess my vote is that if this feature is included, it should be
optional and non-default.