The foolish millionaire and the clever girl
There was once a very rich and greedy man who loved money more than
anything else in the world. He knew he had lots of money, but he didn’t
know exactly how much. So he hired a little girl to count all his money
for him.
It took the little girl six days to count all the money. When she
finished, she went to the rich man and said, “You have forty-two million
dollars.”
“Forty-two million!” exclaimed the rich man, and smiled a greedy smile.
Then he looked slyly at the little girl. “How much pay do you want for
counting the money?” he asked. He thought that because she was only a
child, he could trick her into taking a very small amount.
The little girl said, “Well, I worked for six
days, so I think you ought to pay me for six days. Give me two pennies
for the first day. Each day after that, just give me the amount you gave
me the day before multiplied by itself.”
The rich man thought about that. On the first day he would have to give
her two pennies. On the second day, he’d have to give her two pennies
multiplied by two pennies, or four pennies. On the third day, he’d have
to give her four pennies multiplied by four pennies, or sixteen pennies.
And on the fourth day, he’d have to give her sixteen pennies multiplied
by sixteen pennies, or 256 pennies.
He smiled to himself. Why, at this rate he would only have to give her a
few dollars worth of pennies! What a foolish little girl 1
So the rich man had his lawyer write up a contract, which both he and
the little girl signed. Now, she couldn’t change her mind.
On the first day, the rich man paid her two pennies. On the second day,
he gave her two pennies times two pennies, or four pennies. Each day
after that, he gave her the number of pennies he had given her the day
before, multiplied by itself. And by the sixth day, the little girl had
all the foolish millionaire’s money!
Here’s what happened:
On the first day the clever girl got two pennies.
On the second day she got two pennies times two pennies, or four
pennies.
On the third day she got four pennies times four pennies, or sixteen
pennies.
On the fourth day she got sixteen pennies times sixteen pennies, or 256
pennies.
On the fifth day she got 256 pennies times 256 pennies, which is 65,536
pennies.
And on the sixth day she got 65,536 pennies times 65,536 pennies. And
that comes to 4,294,967,296 pennies. That’s more than four billion
pennies, which amounts to more than forty-two million dollarsI So, the
foolish millionaire had to give the clever little girl all his money.
What the foolish millionaire didn t realize was that he had agreed to
square the amount of money the girl received each day. To square a
number, you multiply it by itself. If you then square the answer, and
continue to do this, you very quickly get a huge number. Most people
don’t realize just how quickly this happens.
No one has any trouble squaring a small number. You know that 2 X 2 is
4. But how much is 2,000 X 2,000? If you answer quickly, you might say
four thousand (4,000). But it isn’t. It’s four million (4,000,000) I
Square the number three and then square your answer. Then see what
happens as you continue to square each answer
