Chess and Mathematics

 

 

 Once upon a time many centuries ago in India, according, a sage gifted a game of war, which he had invented, to a king. This game was  Chess . 

 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 wouldn't satisfy the sage's demand. Actually the  wheat demanded  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 that he was even more delighted by the sage's mathematical trick then the game he had gifted him.

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

Here, the number of grains in each successive squares are doubled. That is, the common ratio amongst the number of grains in successive squares is 2. Such sequences of numbers which bear a common ratio amongst successive terms are called Geometric progression.

2^0 + 2^1 + 2^2 + 2^3 + 2^4 + 2^5 + … + 2^61 + 2^62 + 2^63 = 2^64 – 1

 It is 18446744073709551615.   

İst.h/Hatice Uysal Çatmakaş/Salihli Şehit Mustafa Serin AİHL