I want some cubes painted with three blue faces and three red
faces.
How many different cubes can be painted like that?
James (using blue) and Cath (using red) paint the faces of a
cube in turn so that the six faces are painted in order "blue
then red then blue then red then blue then red".
Having finished one cube, they begin to paint the next one.
Show that, even though she goes second, Cath can choose the faces
she paints in a way that will ensure a second cube is identical
to the first one.