The Indian Story Used to Explain rO: Chess and Indian Mathematics

Once upon a time many centuries ago (at least more than 1,500 years ago) in India, according to a folklore, a sage gifted a game of war, which he had invented, to a king. This game was chaturang (Sanskrit for Chess). Chaturangi sena (army) means an army consisting of all the four units - infantry, cavalry, chariots and elephants.

The king was extremely delighted to receive this game. He told the sage to ask for any gift he wished. The sage asked the king to give him as many grains of wheat that would fill the chess board in a manner that the first square contains one grain, the second 2 grains, the third 4 grains, the fourth 8 grains, and doubling the number of grains in each successive square till he reached the last square i.e. the sixty-fourth square.

The king smiled at the sage's request for such a small simple gift, when the sage could have asked for anything expensive or precious. The king soon realised that the entire annual grain production of Bharat varsha (then undivided India) wouldn't satisfy the sages demand. Actually the amount of wheat demanded by the sage is more than the entire world's wheat production for more than 2000 years. The king was horrified that he wouldn't be able to honour his word. But the kind sage forgave the king. The king told the sage that he was even more delighted by the sage's mathematical trick then the game he had gifted him.

This story is very popular since many centuries. Even Nobel laureate Physicist George Gamow had written about it in his book "One, Two, Three,..., Infinity".

How much do you think is the total number of grains demanded by the sage from the king? It is 18446744073709551615.

You must be wondering how I arrived at the correct answer. It is thanks to ancient Indian mathematics.

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