A grain of rice on the first square, doubling on each

Question

The legend: the inventor of chess asked to be rewarded with one grain of rice on the first square of the board, two on the second, four on the third, and so on, doubling on each of the 64 squares. 1. How many grains is that in total? 2. Estimate the weight of that much rice, and compare it with world rice production (about 500 million tonnes a year).

Accepted Answer

2 to the 64 minus 1 grains, about 18.4 quintillion (1.8 times 10 to the 19). That is roughly 460 billion tonnes of rice, close to a thousand years of current world production. The count. Adding 1 + 2 + 4 + ... + 2 to the 63 gives 2 to the 64 minus 1 (each new term is one more than the sum of everything before it). Using 2 to the 10 is about 1,024, 2 to the 64 = 2 to the 4 × (2 to the 10) to the 6, about 16 × 1.024 to the 6 × 10 to the 18, about 1.8 × 10 to the 19. The exact value is 18,446,744,073,709,551,615. The weight. A grain of rice weighs about 25 milligrams, so 1.8 × 10 to the 19 grain…

A grain of rice on the first square, doubling on each

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