The ancient indian game of chaturanga, from which the modern game of chess was derived, was played on a board with 64 squares. a certain folktale tells the story of a raja who promised a reward of one grain of rice on the first square of the board, two grams on the second square, four on the third, and so on, doubling the number of grains on each successive square.

Question

Physics

Adrianna Shaffer

5 July, 18:13

The ancient indian game of chaturanga, from which the modern game of chess was derived, was played on a board with 64 squares. a certain folktale tells the story of a raja who promised a reward of one grain of rice on the first square of the board, two grams on the second square, four on the third, and so on, doubling the number of grains on each successive square.

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Carl Newman · Answer 1

On the 1st square: 1 grain of rice (or 2^0).

On the 2nd square: 2 grains of rice (or 2^1) ... and so on

a) The relation is:

R (n) = 2^ (n - 1)

This is the number of grains on the n-th square.

This is an example of the exponential growth.

b) For n = 64:

R (64) = 2^ (64 - 1) = 2^63

R (64) = 9,223,372,036,854,775,808

And if the mass of 1 grain of rice is 25 mg = 0.000025 kg

m = R (64) * 0.000025

m = 230,584,300,921,369.4 kg ≈ 2.3 · 10^ (14) kg