From MathKids
Once upon a time there was a king who loved to play chess. One day the king proposed that if anyone in his kingdom could beat him at chess, the king would grant them any reasonable wish.
A poor farmer stepped forward to meet the king's challenge. Much to the king's surprise, the farmer beat the king quickly and with seeming ease. True to his word, the king agreed to grant the farmer's wish.
Wanting to wish for something that seemed reasonable, the farmer suggested the following:
"I propose that you place on the first square of the chess board one penny, and on the second square, two pennies, on the third, four pennies, and so forth, until the last square is reached." After a moments thought, the king granted the request, as it seemed that the farmer had, in fact, asked for very little money.
As the king began to place the money on the chess board, however, he soon realized his terrible mistake. Let's see why.
The chess board consists of 8 x 8 = 64 squares. On the first row of the board, the king placed:
for a total of $2.55. Notice that the amount of money is doubling between squares (exponential growth).
On the second row, the king placed:
Combined with the first row, there was a total of $655.35 on the board.
On the third row, the king placed:
Combined with the first two rows, there was a total of $167,772.16 -- and there were still five rows to complete!
Continuing along like this, the fully loaded board will contain