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## 'Russian Cubes' printed from http://nrich.maths.org/

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 always goes second, Cath can choose the
faces she paints in a way that will ensure that both cubes are
identical.