The question you opened
One grain of rice, then double
A helper asks for rice: 1 grain on the first square, then double on every next square.
How much rice lands on square 20?
524,288 grains
Doubling 19 times turns one grain into 524,288. Each square carries more rice than every earlier square put together.
A helper is offered any reward and asks for something that sounds modest. One grain of rice on the first square of a board, two on the second, four on the third, and double again on every square after that. The first squares are almost nothing. Square 1 has 1 grain. Square 5 has 16. Square 10 has 512, which fits in a spoon. Square 15 has 16,384, roughly a small cup. And square 20 has 524,288 grains, which is about half a million, somewhere near a heavy sack.
The jump from a spoon to a sack happens in ten squares, and nothing about the early squares warns you it is coming. That is the point of the story. There is a second fact hiding here that is even stranger. Every square holds more rice than all the earlier squares put together. Square 5 has 16 grains, and squares 1 to 4 hold 1 plus 2 plus 4 plus 8, which is 15.
Square 6 has 32, and everything before it adds to 31. Always one grain short. So the total on the whole board is always double the last square, minus one grain. That means the first 20 squares hold 1,048,575 grains between them, just under twice what sits on square 20 alone. Carry on to a full board of 64 squares and the last square alone holds 2 multiplied by itself 63 times, a number with nineteen digits in front of it.
The helper was never asking for a small reward. Doubling is the fastest kind of growth most people meet, and it hides. It hides in folding paper, in bacteria in a warm kitchen, in a rumour passed to two people who each tell two more, and in money left alone in an account for a long time. The lesson is simple to say and hard to feel: when something doubles, the ending is nothing like the beginning.
Technique: Doubling beats adding, quickly