The Legend of the Chessboard

There are many examples of how poorly our minds are equipped to think exponentially. Oh, we can do it – but we often realize our mistake too late. This story is a classic.

Long long ago in an ancient land, there lived a very wise man who happened to be the Vizier at the court of a great Sultan.
Months and years passed by and the great Sultan died, and his young prince replaced him. Being young, the prince lacked experience. He started spending more than what his father used to. The wise Vizier decided to teach the brash prince a lesson!

The prince set a contest and as a reward, decided to give the winner whatever he wishes, boasting of his wealth, being under the illusion that his wealth is virtually endless. The Vizier won, and asked the prince for the prize: a single grain of wheat and a chessboard!

“What?! Just a grain of wheat! Are you insulting my wealth?” yelled the prince.
“No! Your majesty!” The Vizier explained. “You have to promise to double that grain of wheat until the chessboard is full, so on the first day you give me one grain of wheat on the first square of the chessboard, on the second day you double it on the second square (giving me two grains), on the third, you double that on the third square (giving me four grains), and so on, until the sixty fourth square on the chessboard.”
“I would thought you being so smart”, the young prince said. “You would ask for something more substantial. Anyway, if this is your wish I will grant you that.”


The Legend of the Chess board and the Grain of Rice

The legend of a Chinese Emporer rewarding the inventor of chess with grains of rice is used to explain the concept of exponential growth.

About benvitalis

math grad - Interest: Number theory
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