Date: 24 July 1981 2220-EDT (Friday)
From: Dan Hoey at CMU-10A
To: Cube-Hackers at MIT-MC
Subject:  A new problem
Message-Id: <24Jul81 222049 DH51@CMU-10A>


        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?