← The Arithmetic of the Chessboard · Lesson 2 of 3
The doubling story
An old story tells of a reward of one grain of wheat on the first square, two on the second, four on the third, doubling every square. The totals run 1, 3, 7, 15, 31: always one less than the next square’s amount.
So all sixty-four squares hold 2⁶⁴ − 1 grains, about eighteen billion billion, far more wheat than the world grows in a year.
How many grains are on the first ten squares together?
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