According to legend, Sissa Ben Dahir, the Vizier of the court of King
Shirham of India, worked diligently and invented a new game that was
called Chess. The King decided to grant Sissa the reward of his choosing.
Sissa pondered carefully and requested the following from the King:
One grain of wheat on the first square of the chessboard,
two grains of wheat on the second square, four grains on
the third square, eight on the fourth square, and so on.
The King thought this was a very modest request and
said that he would grant the Vizier's request.
At right is a chessboard with 64 squares.
1. Make a table showing the
number of grains of wheat on
the first ten squares and the
total grains of wheat on
squares 1 through n, for
n = 1, 2, 3,..., 10.
2. Using the information from the table, look for a
pattern and write an expression for the number of
grains of wheat that would be placed on square n.
3. How many grains of wheat would be placed
on the last square?
4. Look for a pattern and write a formula for the total
number of grains of wheat on the board after wheat
has been placed on square n.
5. What is the total number of grains of wheat that
Sissa received?
6. One grain of wheat weighs approximately 0.000008 kilogram.
Find the total weight of wheat the Vizier requested.
7. In 2000, the world's wheat production was
approximately 580 million metric tons. At this
rate, how many years would it take to fill Sissa's
request? One metric ton is 1000 kilograms.
Original content Copyright by Houghton Mollin Harcourt. Additions and changes to the original content are the responsibility of the instructor
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