In a famous story, a wise man in India requests a reward promised by his king. The wise man shows the king a chessboard having 64 squares. "Put 1 grain of rice on the first square, 2 grains on the second square, 4 on the third square, 8 on the fourth square, and so on, doubling the number of grains each time, until all 64 squares are filled with the right number of grains. That will be my reward."

The king readily agrees because this does not seem to be a very large request, but soon he is ruined. He is unfamiliar with geometric series, and how fast they can increase. What is the total numb

Question

In a famous story, a wise man in India requests a reward promised by his king. The wise man shows the king a chessboard having 64 squares. "Put 1 grain of rice on the first square, 2 grains on the second square, 4 on the third square, 8 on the fourth square, and so on, doubling the number of grains each time, until all 64 squares are filled with the right number of grains. That will be my reward."

The king readily agrees because this does not seem to be a very large request, but soon he is ruined. He is unfamiliar with geometric series, and how fast they can increase. What is the total numb

anonymous · Answer

er of rice grains that the king must give the wise man?

a. 2^64 grains
b. 2^32 - 1 grains
c. 2^64 - 1 grains
d. 2^63 grains
e. 2^32 grains

anonymous · Answer

You need to remember the formula for the geometric series.

anonymous · Answer

here first term is 1 and r=2  and n=64
so S=a  (r^n-1)/(r-1) 
thus c. 2^64 - 1 grains  is the correct choice

anonymous · Answer

That worked out is a VERY large number! 9,223,372,036,854,775,807 in the 64th square! O.o