Text 4 b the victim of overwhelming numbers

1. І. Read and memorize:

to reward — винагороджувати

the game of chess — rpa в шахи

chess-board — шахівниця

square — квадрат

a bag of wheat —мішок пшениці,

to double — подвоювати

to enjoy — насолоджуватися, радіти

treasure — скарб

to order — наказувати

to count — рахувати

to take into account— приймати до уваги,

to increase — збільшувати

to fulfill — виконувати

pretty big — досить великий,

assuming (that) — припускаючи, (що)

to contain — вміщати, the amount

re­quested — потрібна кількість

incessant flow (of latter's demands) — безперервний noтік (вимог останнього).

King Shirham of India, according to an old legend, want­ed to reward his grand

vizier Sissa Ben Dahir for inventing and presenting the game of chess to him.

The desires of the clever vizier 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 eight grains to put on the fourth. And so, oh King, doubling the number for each succeeding square, give me enough grains to cover all 64 squares of the board". "You do not ask for much, oh my faithful servant", ex­claimed the king, silently enjoying the thought that his gener­ous proposal of a gift to the inventor of the miraculous game 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, with a grain for the first square, 2 for the second, 4 for the third and so forth, the bag was emptied before the twentieth square was taken into account. 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 India the king could not fulfil his promise to Sissa Ben. To do so would have required 18,446,744,073,709,551,615 grains... That's not so large a number as the total number of atoms in the universe, but it is pretty big anyway. Assuming that a bushel of wheat contains about 5,000,000 grains, one would need some 4,000 billion bushels to satisfy the demand of Sissa Ben. Since the world production of wheat averages about 2,000,000,000 bushels a year, the amount requested by the grand vizier 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 vi­zier and had either to face the incessant flow of the latter's demands or to cut his head off. What alternative did he choose?

ІІ. Read the text and answer the following questions:

1. Where did the story take place? 2. What is the legend about? 3. What is your opinion of the king's and the vizier's knowledge of mathematics? 4. Can you name the mathemat­ical rule of doubling each succeeding number? 5.When did the king realize his mistake? 6. How many bushels of wheat would be needed to satisfy the vizier's demand? 7. How many grains of wheat does a bushel contain? 8. Could the king sat­isfy the vizier's demand? 9. What is the author's suggestion as to the end of the legend? 10. Do you know any other stories about chess invention?