The Chessboard

We take that great old problem of the inventor of chess and the ruler of India and use it to see how powers of 2 grow in size. We start out with a chessboard and look at doubling each successive number. Then we seek a method of representing this doubling in a formula and introduce exponents and powers of 2. We ask you what kind of rule would you suggest that would keep your head and please the ruler?

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