Chessboard and Wheat Puzzle

Game of chess is a cerebral game. It is a game of strategy, advanced planning and endless possibilities. A chess player becomes so engrossed in it that he forgets about his other activities. Such was the condition of the main characters in the Satyajit Rays movie “Satranj ke Khilari”. The story is set in the reign if Nawab Wajid Ali of Lucknow and how by hook or crook the British East India Company took over the princely Avadh on the pretext that a king who is engrossed in licentious activities like dancing with nautch girls and singing cannot look after the well being of the subjects. This is mirrored in the addiction of two friends who oblivious of everything are always devising means to play the game somehow or the other.

The game is said to have originated in the Eastern India and its precursor was called Chaturanga having four limbs or the four divisions of the army represented by a piece. It then traveled to Persia where it was called Chatrang and when Moguls swayed the area, its name changed to Shatranj and it travelled to Southern Europe.
The board has 8 rows of 8 cells each. 64 cells in all. There are king, prime minister (queen in British version and now universally prevalent), two bishops, two knights and two rooks. They occupy the first row and second row is occupied by pawns when they play starts.
The original chess board was mathematically revolutionary, as reported by the infamous Wheat and chessboard problem. A common theory is that India’s development of the board, and chess, was likely due to India’s mathematical enlightenment involving the creation of the number zero.

Chessboard and Wheat Puzzle

The puzzle is about the inventor of chess in India by mathematician named Sessa or Sissa. He presented it to the ruler of the country, the ruler was elated and asked the inventor to choose his prize. The man, who was very clever, told the king that for the first square of the chess board, he would receive one grain of wheat, two for the second one, foimageur on the third one, and so forth, doubling the amount each time. The ruler, who did not understand the gravity of what was asked and who was not adept in mathematics laughed at the paltry prize. He was wrong as the numbers increase astronomically as the squares progress. However, when the treasurer took more than a week to calculate the amount of wheat, the ruler asked him for a reason for his slackness. The treasurer then gave him the result of the calculation, and explained that it would take more than all the assets of the kingdom to give the inventor the reward. The story ends with the inventor being beheaded.

I tried to calculate how much wheat it will be in the last square.

Going by the rule, the number of grains in first cell be 2^0, second 2^1, third 2^2 so 64th cell, the number of grains will be 2 ^63 (2 raise to power 63) which will amount to 9,223,372,036,854,775,808 grains
And weight of 1 grain is approximately =0.06479891 grams
So the weight of grains in the last square

=(9,223,372,036,854,775,808 * 0.06479891)/(1000x1000x1000000) =597664.4545 MMT !!!!!!!!!!!

Annual production of wheat in India in the year 2011-12 =94.88 MMT

At this rate, it will take 6299.1616 years for India to equal his demand even for the grains in the last cell not to talk of the vast numbers in the preceding cells.
Now you can imagine why the king who was at first laughing at the his demand, had him beheaded. Or should not the king had conceded and rewarded the inventor……

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Author: Ranjit Singh

I am working as a scientist in the India's premium E&P oil company. Besides the commitment to my job, I read lot of literature especially good fiction, history and science. I belong to Chandigarh and did my Masters in Chemistry from Panjab University Chandigarh specializing in physical chemistry. I am fond of surfing the internet for good articles, social networking and giving vent to writing for which I have aptly chosen the blog in Wordpress. Thanks

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