The story is old and told in many countries, and the details change, but the arithmetic never does. An inventor brings a new game to a king, who is delighted with it and offers him any reward he likes.
The inventor asks for grains of rice. One on the first square of the board, two on the second, four on the third, and so on: each square carrying twice what the square before it carried, to the sixty-fourth.
The king laughs and agrees. It sounds like a modest request. On the tenth square there are only five hundred and twelve grains — not yet a handful.
By the twentieth square the number has passed half a million. By the twenty-first it is over a million, and the granary keeper has begun to count in sacks rather than grains. Long before the last square, the sums have run past every store in the kingdom, and past every harvest that kingdom would ever gather.
What makes the story last is not the size of the final number. It is the first half, where nothing appears to be happening. Anyone watching the early squares would have agreed with the king. The mistake was not in the arithmetic. It was in judging a doubling by its beginning.
A gift of a thousand grains a square, on every square, would have cost sixty-four thousand grains — a sack or two. The inventor asked for something that starts at one, and it broke the treasury.