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Two thousand years ago, a noble Arabian king wished to reward his minister of science. Although the modest minister resisted any reward from the king, the king finally forced him to state a desired reward. Impishly the minister said that he would be content with the following token: “Let us take a checkerboard. On the first square I would be most grateful if you would place one piece of gold. Then on the next square twice as much as before, thus placing two pieces, and on each subsequent square, placing twice as many pieces of gold as in the previous square. I would be most content with all the gold that is on the board once your majesty has finished.” This sounded extremely reasonable, and the king agreed. Given that there are 64 squares on a checkerboard, roughly how many pieces of gold did the king have to give to our “modest” minister of science? Why did the king have him executed?

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