# Ancient Indian legend: “The rice and the chessboard story”(learning about mathematics)

There are many different variations of this story, however,  here is one version:

The story goes that the ruler or India was so pleased with one of his palace wise men, who had invented the game of chess, that he offered this wise man a reward of his own choosing  and he said to the man: “Name your reward!”

The man responded: “Oh emperor, my wishes are simple. I only wish for this:

-Give me one grain of rice for the first square of the chessboard, two grains for the next square, four for the next, eight for the next and so on for all 64 squares, with each square having double the number of grains as the square before.

The emperor agreed, amazed that the man had asked for such a small reward – or so he thought. After a week, his treasurer came back and informed him that the reward would add up to an astronomical sum, far greater than all the rice that could conceivably be produced in many many centuries!

How Much Rice? We are all like the emperor in some ways – we find it hard to grasp how fast functions like “doubling” makes numbers grow – these functions are called “exponential functions” .

The number of grains of rice on the last square can be written as “2 to the 63th power”, or “2 times itself 63 times”, or                                          18, 446,744,073,709,551,615 grains of rice!!!

A grain of rice is approximately .2 inches long. Converting .2 inches to feet (divide by 12 inches to a foot) and then dividing that number by 5,280 feet in one mile, we get the length of the grains of rice, placed end-to-end, to be approximately 60,000,000,000,000 miles. How far is that? Alpha Centaurus, the nearest star, is located 25,000,000,000,000 miles from Earth. Placed end to end, these grains of rice would reach farther than from the Earth, across space to the nearest star, Alpha Centaurus, and back to Earth again!

As mentioned before, there are different variations of this story, including the origin of the chess game, some scholars argue that China is the true birthplace of Chess. Nevertheless, the story serves to provide a graphic lesson on exponential functions.

References:

http://www.dr-mikes-math-games-for-kids.com/rice-and-chessboard.html

http://www.singularitysymposium.com/exponential-growth.html