The Story of Sissa

There was once a victim of overwhelming numbers
called King Shirham of India,
who, according to the old legend,
wanted to reward his grand Prime Minister Sissa for inventing
and presenting to him the game of chess.
The desire of the clever minister seemed very modest.
“Majesty,” he said kneeling in front of the king,
“give me a grain of wheat to put on the first square of this chessboard,
and two grains to put on the second square,
and four grains to put on the third.
And so, oh King, doubling the number for each succeeding square,
give me enough grains to cover all 64 square of the board.”
“You do not ask for much, oh my faithful servant,”
exclaimed the king,
secretly enjoying the thought
that his liberal proposal of a gift to the inventor
would not cost him much of his treasure.
“Your wish will certainly be granted.”
And he ordered a bag of wheat to be brought to the throne.
But when the counting began,
it was found that the bag was emptied
before the twentieth square was accounted for.
More bags of wheat were brought before the king
but the number of grains needed for each succeeding square
increased so rapidly
that it soon became clear that with all the crop of Indian
the king could not fulfill his promise to Sissa.
To do so would have required 18，446，744，073，709，551，615 grains!
Assuming that a bushel of wheat contains about 5 million grains,
one would need some 4×1012 bushels to satisfy the demand of Sissa.
Since the world production of wheat averages about 2×109 bushels a year,
the amount requested by the minister was that of the world’s wheat production
for the period of some two thousand years!
Thus King Shirham found himself deep in debt to his minister
and had either to face the incessant flow of the latter’s demands,
or to cut his head off.
We suspect that he chose the latter alternative.