MathDB

At the vertices

A, B, C, D, E, F, G, H

of a cube,

2001, 2002, 2003, 2004, 2005, 2008, 2007

and

2006

stones respectively are placed. It is allowed to move a stone from a vertex to each of its three neighbours, or to move a stone to a vertex from each of its three neighbours. Which of the following arrangements of stones at

A, B, \ldots , H

can be obtained? (\text{a}) 2001, 2002, 2003, 2004, 2006, 2007, 2008, 2005; (\text{b}) 2002, 2003, 2004, 2001, 2006, 2005, 2008, 2007; (\text{c}) 2004, 2002, 2003, 2001, 2005, 2008, 2007, 2006.

Problem Statement