Here is a quick
sketch of the algorithm that solves the 2x2x2 Rubik's cube, also known
as the Pocket Rubik's cube. A lot of thinking is still
necessary to understand the algorithm and how to apply it. For
more information on the terminology that I use for cube moves and for a
slightly different and more detailed explanation of the solution, go to
Helmsoft.
There are three main steps:
 Do Top face.
 Put the bottom corners in the right
position.
 Fix the orientation of the bottom corners.
Top Face
I am not going to tell
you how to do the top face. You will have to figure it out by yourself, which is not
that easy, but it is not impossible either. It
might take some time the first time. One hint is the following. If you
want to put a corner somewhere, but you don't want to mess up what you
have done so far, hide what you have done some far, move the piece you
want to move, and then put what you have hidden back to its place.
Attention: Remember
that the pieces have three sides each. So it is not enough to make just
the top face correct, the sides have to match too. The cube should look
like in the picture below, where the white pieces are the ones that
haven't been accommodated yet.
Place
bottom corners.
Now you need to place the bottom corners in the right positions.
Don't worry about the orientation of the corners yet, only about the
position. We will deal with the orientation in the next step. The way
we do this is by applying the following algorithm that swaps two bottom
corners. You have to do it enough times to place all the corner in the
right positions. The first thing you need to figure out is which two
corners you want to swap. Here is the algorithm.
Orient
bottom corners
Now that we have positioned the bottom corners, all we need to do is to
put each corner in the right orientation. The bad news is that there is
no algorithm that rotates one corner. But there is a relatively simple
algorithm that rotates three corners. You will have to figure out how
to use this algorithm repeatedly until you get all the corners right.
Here is the algorithm.

Position the corner that you don't want to rotate
in leftback side. So, in the picture, the corners with light colors
are the ones you'll be rotating. The corner that you can't see is the
one the will stay fixed. The rotation is counterclockwise.



After you have this under control, we could start talking
about solving the 3x3x3 cube.
Antonio
Montalbán.
Department of Mathematics.
Cornell University.
Ithaca, NY 14853.
email: antonio at
math.cornell.edu
Updates of this
page can be found at www.math.cornell.edu/~antonio/MEC/mec.html
30/1/2005.