Stage: 4 Challenge Level: 
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 $3
\times3$, $5 \times5$, $7 \times7$, $9 \times9$ squares.
Prove that for an $n \times n$ tablecloth (where $n$ is odd) the
number of colours needed is ...
$$ (n+1)(n+3)\over 8$$
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Learning through exploration. Creating expressions/formulae. Patterned numbers. Mathematical reasoning & proof. Dynamical systems. Interactivities. Reflections. Rotations. Generalising. Visualising.
Published March 2003,June 2010.
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