## The Complexity of the Puzzle

The outside faces of the cubies have stickers of 6 different colors,
one for each of the 6 faces of the main cube. As you rotate the slices, the
stickers become shuffled and the faces of the main cube become a jumble
of colors. It looks like a simple puzzle, but as you move further away
from the starting position, you begin to realise, as one writer put it,
that you are like a small child who has let go of a helium balloon only
to see it move more and more beyond reach or hope of return.

Mathematicians calculate that a 3x3x3 cube can be shuffled into
43,252,003,274,489,856,000 different patterns, yet they conjecture that all
positions can be solved in 20 moves or less. The method that can do that
(as yet undiscovered) is called
God's
Algorithm. Practical methods can take more than 100 moves. As
there are 12 face-move possibilities at each step, the chances of solving
the cube by trial and error are rather remote. Some cubes have 9-part
pictures on the faces and that makes them even more complex, because you
then have to get the orientations of the stickers correct as well as the
positions.