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A beautiful story of chess

  • chris-u
  • on 11/5/11, 12:17 AM.

Muse - Uprising

Chess is one of the world’s most popular games. The Iranians and Indians might be their inventors based on ancient scrolls which have been found in both territories. On the one hand, chess was known in Iran as shatranj, on the other hand chess was known as chaturanga in India. Both shatranj and chaturanga are very similar to the current chess. Their pieces symbolized the four forces of their armies: infantry, cavalry, elephants, and carriages. There are a lot of stories about chess. According to the Indians there was a famous philosopher who lived on a high mountain. His power was very amazing and he was able to create this complex game in a night of magical inspiration.

 

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Legend has it that in the province of Taligana, in India, lived for many years a rich and generous king named Iadava. An adventurer named Varangul attacked Iadava’s kingdom. He had to wield his sword, and in front of his army, faced Varangul’s army. Iadava, who had a military genius, defeated Varangul in the fields of Decsina, but he paid a heavy price for his victory, his son Adjamir died in combat. There was so much sadness in Iadava’s heart that he locked himself in his castle, and no longer wanted to talk more with anyone. His only consolation was to repeat the maneuvers of combat in a sandbox, as a tribute to the memory of beloved son Adjamir.

 

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But one day it came to the sad palace, a young Brahmin named Lahur Sessa, from the village of Manir. He asked the guards to see the king saying that he had invented a game especially for him in order to cheer his hours of solitude. Iadava decided to receive Lahur Sessa in his palace. He had a great curiosity to see the game which had been invented for him. When Lahur Sessa was in front of the king, he gave him a beautiful board divided into sixty-four squares and thirty-two pieces: sixteen of white and sixteen of black. Each group of pieces represented according to Lahur Sessa, two armies, the army of Varangul and the army of the king. After some brief explanations, the king began to play with great enthusiasm, really was fascinated with the new game. And it happened that Iadava had to sacrifice a rook to win the game (changing one more valuable piece by other one less valuable). This opportunity was exploited wisely by Lahur Sessa. He told the king, "Sometimes we need to make a sacrifice to achieve a greater good for everyone."

 

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Iadava caught the acute observation which made a reference to his son Adjamir, sadly died in combat. Pleased with the beautiful game that Lahur Sessa had invented for him. Iadava told Lahur Sessa, "Ask me what you want to and I will give you immediately." Sessa kindly explained to Iadava, "I would like to receive a grain of wheat for the first square, two grains of wheat for the second square, four grains of wheat for the third, eight grains of wheat for the fourth, and so on until the sixty-fourth square." By hearing such a humble request Iadava began to laugh nonstop. After a while, he ordered that he would be given what he had requested. Later mathematicians confusedly came to the king to tell him that it was impossible to accommodate that request. The quantity of wheat was so great that all wheat from his kingdom was not enough wheat to pay what he had promised Lahur Sessa. This is the incredible account of wheat after reaching the sixty-fourth square: 18,446,744,073,709,551,615. Iadava was amazed by such an impressive figure. He told Sessa, "Unhappy is he who assumes the burden of a debt whose worth cannot be measured by the simple means of his own intelligence."Iadava embraced Sessa and appointed him to first vizier for life.

 

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Malba Tahan - The man who counted / Chapter 16 / The game plan

 

Written by Willhawk

The wheat and chessboard problem is a mathematical problem. If a

Chessboard

A chessboard is the type of checkerboard used in the board game chess, and consists of 64 squares arranged in two alternating colors...
were to have wheat placed upon each square such that one grain were placed on the first square, two on the second, four on the third and so on, doubling the number of grains on each subsequent square, how many grains of

Wheat

Wheat is a grass, originally from the Fertile Crescent region of the Near East, but now cultivated worldwide. In 2007 world production of wheat was 607 million tons, making it the third most-produced cereal after maize and rice .Globally, wheat is the leading source of vegetable protein in human...
would be on the chessboard at the finish?
To solve this, observe that a chess board is an 8×8 square, containing 64 squares. If the amount doubles on successive squares, then the sum of grains on all 64 squares is:

chessboardwheat

                                                        

sessa equation.png



This equals 18,446,744,073,709,551,615.

This problem (or a variation of it) demonstrates the

Exponential growth

Exponential growth occurs when the growth rate of a mathematical function is proportional to the function's current value...
.

The problem is sometimes expressed in terms of rice instead of wheat.

quick growth of exponential sequences

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