Math Arguments

Grains of Rice

There was once a king in India who was a big chess enthusiast and had the habit of challenging wise visitors to a game of chess. One day a traveling sage was challenged by the king. The sage having played this game all his life all the time with people all over the world gladly accepted the Kings challenge.


To motivate his opponent the king offered any reward that the sage could name. The sage modestly asked just for a few grains of rice in the following manner: the king was to put a single grain of rice on the first chess square and double it on every consequent one.

The king accepted the sage’s request.

Having lost the game and being a man of his word the king ordered a bag of rice to be brought to the chess board. Then he started placing rice grains according to the arrangement: 1 grain on the first square, 2 on the second, 4 on the third, 8 on the fourth and so on.

What do you notice about the problem?

How many grains of rice will the king need to pay?

What kind of volume will the final total be?

This is rice in a measuring cup: 20,000 grains is 400mL. I put a piece of paper on top of the rice so you could see the top better.