Message #589

From: lucas_awad <>
Subject: Re: [MC4D] Something interesting and strange about permutations
Date: Sat, 27 Sep 2008 01:46:24 -0000

It is interesting to see how MC3D works with reflections. As it can be
seen, a 90º rotation can be done by doing a reflection from an edge
and another one from a corner. 180º rotation can be done with two
reflections from different stickers of the same kind.

I want to speak about what I said about the special rotations that
should only be allowed in MC4D.
What I was thinking about was that if we say that a rotation is a set
of two reflections, and we are only allowed to do rotations in a 3D
cube, and reflections in the MC2D, then it would be logical to think
that in MC4D we should be allowed to do only a move that will be a set
of two rotations (where when saying rotation I mean a 90º rotation).

But ok, mathematically speaking we don’t have to be necessarily not
able to do simple rotation from MC4D to higher dimensions, as
reflections from MC3D.

So I think that the problem to determine the possible movements of a
puzzle is if we think matematically or physically (from the reality of
the rubik cube).

About the difficulty of the puzzles, I think that reflections make the
resolution much easier, although it may be not necessarily more
efficient. A demostration that it is easier is that with reflection we
can permute 3-color pieces doing two times a two-color series of the
MC2D, I mean, the same way as we do with a 4-color series of the MC4D,
that is not much more than doing two times a 3-color series. Perhaps
it’s hard to understand that reflections makes it easier, because when
I say easier I mean that a person who has never solved the cube would
have less difficulty, without considering the efficiency in the same way.