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Consider an n by n grid. We want to colour its cells in two colours: some black, and some white. We will consider two colourings as the same if they can be obtained from each other by a rotation (not by a reflection). (a) If n = 2 the problem is small and can be solved by brute force. Draw all the distinct colourings.

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Try to order the colorings by the number of cells colored in black. – Dennis Gulko Mar 10 '12 at 13:50
You can use Burnside theorem . – alpha.Debi Mar 10 '12 at 16:03
@alpha : The Burnside theorem will tell you how many colorings there are, but (AFAIK?) it won't list them all. – Michael Hardy Mar 11 '12 at 21:15
What is AFAIK ? (I am not good enough in the english language). – alpha.Debi Mar 12 '12 at 6:45

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