THE NUMBER THE NUMBER DEVILDEVIL

by

Hans Magnus Enzensberger

This is the story of Robert . . .

Robert has a new teacher – Mr. Bockel.

Mr. Bockel loves to eat pretzels. He also loves to torture Robert with problems about Robert’s least favorite thing . . .

3 6 NUMBERS! 9 4

4 6 7

9 0 1

2 5 8Luckily for Robert, he meets in a dream someone who can help him . . . .

7

0

4

9

1

5

2

THE NUMBER DEVIL!

The First Night

The thing that makes numbers so devilish is that they are simple.

All you have to do is start with one.

You can make all of the numbers out of one.

Try it!

1 x 1 = 1

Now try:

11 x 11 = 121

Now try this:

111 x 111 = 12,321

What do you think will happen if you do this?

1,111 x 1,111 = 1,234,321

or this:

11,111 x 11,111 = 123,454,321

Now You Try!

How many ones do you need to multiply to get a six?

111,111 x 111,111 = 12,345,654,321

What about 7, 8, and 9?

1,111,111 x 1,111,111 = 1,234,567,654,321

11,111,111 x 11,111,111 = 123,456,787,654,321111,111,111 x 111,111,111 = 12,345,678,987,654,321

The Second Night

Although The Number Devil showed Robert how to make all of the

numbers from one, something is still missing . . .

Do you know what it is?

00Zero was the last number to be

discovered.

The ancient Romans didn’t have zero.

They wrote their numbers like this:

1986 = MCMLXXXVI

Our numbers are much easier to write because we use zero, and our numbers hop.

Hop?

Number Hopping

Number hopping is really easy!

Try one:

1 = 1

1 x 1 = 1

1 x 1 x 1 = 1

Don’t see it?

Number Hopping

Try Two:

2 = 2

2 x 2 = 4

2 x 2 x 2 = 8

2 x 2 x 2 x 2 = 16

See it?

21 = 2

22 = 4

23 = 8

24 = 16

Number Hopping

Now try it with 10:

101 = 10

102 = 100

103 = 1,000

Now make 10 hop four times:

104 = 10,000

Number Hopping

That’s the beauty of zero.

It lets you hold a space and move on.

You can always tell a number’s value by it’s position:– The farther to the left it is, the more it’s worth;

the farther to the right it is, the less it’s worth.

Number Hopping

Remember 1986?

Here’s how it hops:

6 x 1 = 6

8 x 10 = 80

9 x 100 = 900

1 x 1,000 = 1,000

6 + 80 + 900 + 1,000 = 1986

The Third Night

Now that we know about zero, there is one thing we cannot do with zero!

Any guesses?

We cannot divide by zero.

It is strictly forbidden!

Now that we’ve dealt with zero and one, what about the rest of the

numbers?

On this third night The Number Devil decided to tell Robert a secret.

There are two types of numbers -

the garden variety, which can be divided evenly,

and the rest, which cannot.

These numbers are such prima donnas!

Let’s see if we can find all the prima donnas up to 50.

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 33 34 35 36 37 38 39 40

41 42 43 44 45 46 47 48 49 50

First we take out all of the even numbers because they are divisible by 2. Don’t forget that 2 is a prima donna number.

2 3 5 7 9

11 13 15 17 19

21 23 25 27 29

31 33 35 37 39

41 43 45 47 49

Now do 3.

3 is a prima donna number, but we can take out all the other numbers divisible by 3.

2 3 5 7

11 13 17 19

23 25 29

31 35 37

41 43 47 49

We don’t have to bother with 4 because 4 is 2 x 2, so they are already gone.

5 is a prima donna, so take out all the numbers that end in 5.

2 3 5 7

11 13 17 19

23 29

31 37

41 43 47 49

We can forget about 6, 6 is 2 x 3, but 7 is a prima donna number so take out any numbers divisible by 7.

2 3 5 7

11 13 17 19

23 29

31 37

41 43 47

Well, there you have it –

the prima donnas!

See how helpful The Number Devil was to Robert?

Want to see what else The Number Devil shows Robert?

Want to know The Number Devil’s name?

Curious?

Get the book!

THE NUMBER THE NUMBER DEVILDEVIL

by

Hans Magnus Enzensberger

Technology & The Number Devil

• Robert used a calculator to help him with The Number Devil’s lessons.

• The first mechanical calculator was invented in 1642 by the French Mathematician Blaise Pascal.

He called it The Pascaline.