From:

~~~ ~~~ Subject:

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?