The Islamic story of wheat on the chessboard answers questions

Wheat on the Chessboard

Indian chess
The Hindu god Krishna and Radha playing a game like chess

About 1260 AD, Ibn Khallikan, a Kurdish historian living in the Abbasid Empire (modern Iraq), wrote an encyclopedia with biographies of many famous men (though no women). One of the biographies includes a story about chess and the meaning of "exponential growth." The story takes place in India, because Ibn Khallikan knew that chess was a game that came from India, and maybe because a lot of math ideas came from India too.

According to this story, King Shihram was a tyrant who oppressed his subjects. One of his subjects, a wise man named Sissa ibn Dahir, invented the game of chess for the king to play, to show him that a king needed all his subjects and should take good care of them. King Shihram was so pleased that he ordered that the game of chess should be preserved in the temples, and said that it was the best thing he knew of to train generals in the art of war, a glory to religion and the world, and the foundation of all justice.

Then King Shihram asked Sissa ben Dahir what reward he wanted for this great invention. Sissa answered that he didn't want any reward, but the king insisted. Finally Sissa said that he would take this reward: the king should put one grain of wheat on the first square of a chessboard, two grains of wheat on the second square, four grains on the third square, eight grains on the fourth square, and so on, doubling the number of grains of wheat with each square (an exponential rate of growth).

"What a dummy!" thought the king. "That's a tiny reward; I would have given him much more." He ordered his slaves to bring out the chessboard and they started putting on the wheat. Everything went well for a while, but the king was surprised to see that by the time they got halfway through the chessboard the 32nd square required more than four billion grains of wheat, or about 100,000 kilos of wheat. Now Sissa didn't seem so stupid anymore. Even so, King Shihram was willing to pay up.

But as the slaves began on the second half of the chessboard, King Shihram gradually realized that he couldn't pay that much wheat - in fact, to finish the chessboard you would need as much wheat as six times the weight of all the living things on Earth.

(London, 1843-1871, Biographical dictionary of Ibn Khallikan, vol. III, p. 71).

Learn by doing: try this for yourself with grains of rice
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Professor Carr

Karen Eva Carr, PhD.
Assoc. Professor Emerita, History
Portland State University

Professor Carr holds a B.A. with high honors from Cornell University in classics and archaeology, and her M.A. and PhD. from the University of Michigan in Classical Art and Archaeology. She has excavated in Scotland, Cyprus, Greece, Israel, and Tunisia, and she has been teaching history to university students for a very long time.

Professor Carr's PSU page

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