SISSA LEGEND: THE ORIGIN OF CHESS

Long ago, in one of the kingdoms of ancient India, in what is now Pakistan and Afghanistan would be there he lived a king miserable. This king, rich and powerful, had lost all his joy at losing a son in the war.


Melácolico and devastated by the death of his beloved son, the king himself was abandoned, and neglected his kingdom and lived in it. Such was the state that was engulfing the king that his closest advisers and ministers were trying to cheer him: inviting singers, musicians or dancers to try to distract and thereby engage the king returned to his kingdom. And yet he could not stop thinking that victory in the war had meant the loss of his son. The king was extremely unhappy.


Concerned about the state of the kingdom as a result of the sadness of the king, a wise man Sissa decided to create a game that got back part of his joy to the king, besides him understand his mistakes in the war.


After long reflection, Sissa, with its prepared game, decided to appear before the king to show it. So he opened a box and appeared before the King: A beautiful wooden board with 64 squares and 32 wooden figurines also. After explaining his king was a war game that involved two people, and explain your rules, they began to play.


Excited about the game that had just discovered, King played for hours and days and weeks against all his ministers, counselors and anyone willing to challenge him. Grateful that at last someone had managed to distract him, he offered to Sissa whatever is wanted. After much prodding, as Sissa refused to accept their gifts, the wise agreed and asked him to change his game the following:


"I want a grain of wheat on the first square of the game, and 2 in the second, and 4 in the third and so on ..." The king, surprised that someone with so much wisdom, able to create a game like this, you ask so little, he ordered his aides to estimate the total number of grains of wheat and give to the Sissa.


After a few hours calculating, aides approached him and informed the king, "Your Majesty, there is in the realm enough wheat to pay the debt with Sissa wise ..." The number of grains of wheat amounted to:


T_ {64} = 1 + 2 + 4 + \ cdots + 2 ^ {63} = \ sum_ {i = 0} ^ 2 ^ {63} i = 2 ^ {64} - 1


That is, 18 446 744 073 709 551 615 Wheat grains!


The king gasped, never could have imagined that what the sage was asking was impossible to pay even with its enormous wealth! However, pleased to have gotten the king returned to be happy and mathematics lesson he had given the kingdom, Sissa resigned to this.


FINISH