The story is told in a dozen countries and is almost certainly a legend, but the arithmetic inside it is real, and that is why it has lasted.
A clever man shows a king a new game played on sixty-four squares. The king offers him any reward. The man asks for rice: one grain on the first square, two on the second, four on the third, and so on, doubling to the end of the board.
It sounds modest, and the king agrees without thinking. For the first ten squares he is right to feel calm — the tenth square takes only 512 grains, less than a handful.
By the twenty-first square the pile has passed a million grains. By the fortieth it is more rice than the kingdom's granaries hold. The sixty-fourth square alone would need billions of tonnes — more than every square before it put together, because each square doubles everything that came before.
That last sentence is the whole idea, and it is worth reading twice. In doubling, the newest step is always bigger than the entire history of the process.
It is also why the king's mistake is so easy to make. He judged the offer by its first few terms, which is exactly how people judge a small percentage of growth today — and exactly why compound growth surprises them thirty steps later.