Lesson 3: Investigating Exponential Relationships
The King’s Chessboard
King Shihram was a tyrant who oppressed his subjects. One of his subjects, a wise man named
Sissa ibn Dahir, invented the game of chess for the king to play, to show him that a king needed
all his subjects and should take good care of them.
Then King Shihram asked Sissa ben Dahir what reward he wanted. Sissa answered that he didn't
want any reward, but the king insisted. Finally Sissa said that he would take this reward: the
king should put one grain of rice on the first square of a chessboard, two grains of rice on the
second square, four grains on the third square, eight grains on the fourth square, and so on,
doubling the number of grains of rice with each square.
"What a dummy!" thought the king. "That's a tiny reward; I would have given him much more."
He ordered his slaves to bring out the chessboard and they started putting on the rice.
Was Sissa a dummy?
Determine how much rice the King would need to provide. Start with 1 grain in the top left
corner, then move left to right through the rows, doubling each time.
Perhaps a few tables of values would help the process…
Square #
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
Grains of Rice
Square #
Grains of Rice
Square #
Grains of Rice
Square #
Grains of Rice
Hmmmm… that’s half the board. Let’s try graphing it.