A chessboard is only an 8×8 grid but holds a lot of power! Part II

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Continued from Part I

Curious, the king did as he was told. The sage said that, as the first installment starting from that day, he wanted just a single grain of rice to be put on the first square (the algebraic notation was unknown then, otherwise he would have said a1 square)! The king could not believe his ears and amusingly asked the sage what he would do with a single grain when his granaries held millions of tons (or whatever it came to by the number and weight system of those days)!

The sage said that he had not finished stating his demand. For the first day (that is for the first square) he wanted that single grain but next day he wanted twice that amount meaning 2 grains of rice. For the third day he would need double the previous day’s quantity which comes to 4 grains and so on till the king reached the 64th square.

Whatever talents the king might have got, mathematics was certainly not one of those and so he condescendingly agreed thinking all the while about the foolishness or idiosyncracy of that holy man!

I am writing this for modern chess players who have a much better concept of mathematical formulae than that king of Varanasi. You will realize that the Sage’s demand would need the king to give 2 raised to the power of 64 grains (actually one grain less) to the sage!

And how big a number is that? Not much, only 18,446,744,073,709,551,616! Taking the average weight of a grain of rice to be 25mg (there was no genetically modified hybrid rice grains those days, which can weigh three times as much!) 40 grains would be 1gm and 40000 would make 1kg. So the above number of grains would weigh 461,168,601,842,738kg or to simplify matters, about 461,169 million tons! It is estimated that the whole world now produces about 550 million tons of rice annually. To produce that chessboard full of rice, it will need 838 years by current standards and remember that in the times of that boastful king, the rice production was certainly nowhere near the figure we used!

What is the upshot of all this in relation to our story? There simply was not that many grains in the world for the king to give to the sage! The king of course realized it before he could cross the sixth row of the chessboard and had to seek forgiveness from the sage for his brash behavior and promise. Understanding the repentance of the king, the sage gave him his blessings and asked him to distribute whatever grain had been collected to the people of his kingdom. The sage went away happy in the knowledge of leaving the king a much wiser person!

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