# Problem 189: Tri-colouring a triangular grid
Consider the following configuration of 64 triangles: We wish to colour
the interior of each triangle with one of three colours: red, green or
blue, so that no two neighbouring triangles have the same colour. Such a
colouring shall be called valid. Here, two triangles are said to be
neighbouring if they share an edge. Note: if they only share a vertex,
then they are not neighbours. For example, here is a valid colouring of
the above grid: A colouring C' which is obtained from a colouring C by
rotation or reflection is considered distinct from C unless the two are
identical. How many distinct valid colourings are there for the above
configuration?