r here was once a great King who lived in a marvelous palace. To fend off boredom he collected all manner of interesting games and puzzles. One day an inventor came to his palace and told the King he had a game of such subtle complexity, yet apparent simplicity, the King would play no other. The King learned the game and soon agreed it was, without doubt, the best of all games. The game was, of course, ‘chess. The King asked the price of this game and the inventor told him it was a mere trifle. The King should give him one grain of rice on the first square of the board, two on the second, four on the third, and so on, doubling each square until he filled the board. The King called his treasurer to honor the bargain and the first bags were brought from the storehouse. The grains were placed on the board in each square but soon there was not enough space and the grains had to be piled on the table next to the board. Soon this, too, was not enough and every table and chair in the hall had to be covered. Even this was not enough and they began to stack whole bags up in the courtyard. When they reached the thirtieth square, the treasurer turned white. He sat and calculated for a while before saying with a trembling voice, “My great ruler, there is not enough rice in all the world to cover this board.” The ruler called the inventor and told him he could not honor the debt and the inventor should name another price. The King had two beautiful daughters, the first knew she was beautiful and deported herself accordingly, and the second, was bookish and shy, but perhaps more beautiful for this. The inventor asked for the hand of the second daughter and lived happily ever after. In the less favorable version of this story, the King becomes very angry and has the inventor beheaded. I prefer the romantic version. Placing rice on a chessboard and doubling it successively leads to wildly large numbers. Covering it completely requires 18,446,744,073,709,551,615 grains, abo