# Message #52

From: ojcit <oscar@its.caltech.edu>

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.

-Jay