A square tablecloth is coloured in. Colour the squares so that each square is the same colour as all the symmetrically placed squares and a different colour from the rest of the squares. This means that the tablecloth will look the same if it is turned around or turned over.

How many colours do you need for table cloths of side 3 x 3, 5 x 5, 7 x 7, 9 x 9 squares.

Prove that for an n x n tablecloth (where n is odd) the number of colours needed is ...

\frac{(n + 1) (n + 3)}{8}