Nice Rice
There is a story that has been told down through the ages about a
king who wanted to reward a peasant for a good deed. I particularly
like the Chinese version of this story. In this version, the emperor
promises to grant any reasonable wish the peasant might have.
The peasant sees a chess table in the courtyard of the palace. He smiles and tells the
emperor, “My request is simple. On the first square of the board place one grain of rice.
On the second square place twice the amount of rice as the previous square. Continue
in this fashion until each of the squares on the chess board has the appropriate amount
of rice.”
The emperor smiles broadly.
“Of all of the riches you could have you choose such a simple wish. My respect for you
only grows larger,” says the emperor. With this approval he leaves the room.
a. Make a table of values to determine the number of grains of rice on the fifth and
tenth squares.
square
grains
Nice Rice
b. You probably noticed that there is a pattern in this table. Write out a function that
relates the number of squares s to the number of grains g(s).
g(s) = __________
Using this formula, you should be able to find the number of grains of rice on any of
the 64 squares on the chessboard.
c. Find the value of g(20) using your function. What does this mean?
g(20) = __________
d. As you might guess, the grains of rice are going
to pile up rapidly. If each of the squares is about
2.5 centimeters by 2.5 centimeters and has a
rectangular shaped solid container extending up
vertically, how tall will the container need to be?
Nice Rice
e. How high will the container need to be that corresponds to the 64th square?