# Message #589

From: lucas_awad <lucasawad@gmail.com>

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.