Date: Fri, 24 Jul 81 22:20:00 -0400 (EDT)
From: Dan Hoey <Hoey@CMU-10A>
To: Cube Lovers
Subject: A new problem

Suppose you buy a new cube and the arrangement of the colors is
different from your old cube.  Naturally, you want the new one to
be like the old, so you decide to switch the colortabs around.

A.  What is the smallest number of faces you have to recolor?

B.  What is the smallest number of colortabs you have to move?

Note the hidden variable: the permutation of the new cube
with respect to the old one.  This variable has thirty values,
including the identity.  There are two kinds of answers I am
interested in.

1.  A minimax value -- a recoloring algorithm and a proof of its
optimality.

2.  A probability distribution of optimal recolorings.

Any takers?