ABSTRACT
Let’s start with a little tale. Long ago a brave and loyal subject performed a great service for the king of a rich and mighty nation. In gratitude the king offered to reward the subject. “Choose anything I can give,” said the king. “A carriage of gold, a basket of jewels, even a fine palace. Anything you desire is yours.” Pointing to a chessboard that was at hand, the subject responded, “Today place a single penny on the corner square of that chessboard. Tomorrow place double that amount, two pennies, on the next square. On the third day put double that amount, or four pennies, on the next square. Proceed in this manner of doubling the previous day’s pennies each day until you reach the last (64th) square. Each day I will come to collect my reward until such time as the last square is filled. This is my request.”
