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## 'Redblue' printed from http://nrich.maths.org/

Consider a cube and paths
along the edges of the cube.

Mark one vertex red.

Colour other vertices red
if they can be reached from a red vertex by travelling along an
even
number of edges of the cube.

Colour vertices blue
if they can be reached by travelling along an odd
number of edges from a red vertex.

Is it possible to have
vertices which are both red and blue at the same time (call these
redblue vertices)?

Now do the same for a
tetrahedron.

Do the same for other
solids, for example the octahedron, dodecahedron and icosahedron,
and prisms with different cross sections. Remember the paths must
be along the edges of the solids. Decide how to record what you
find. What property does the solid need if it is to have redblue
vertices?