6The 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
7What do you think will happen if you do this? Now try:11 x 11 = 121Now try this:111 x 111 = 12,321What do you think will happen if you do this?1,111 x 1,111 = 1,234,321or this:11,111 x 11,111 = 123,454,321
8How many ones do you need to multiply to get a six? Now You Try!How many ones do you need to multiply to get a six?111,111 x 111,111 = 12,345,654,321What about 7, 8, and 9?1,111,111 x 1,111,111 = 1,234,567,654,32111,111,111 x 11,111,111 = 123,456,787,654,321111,111,111 x 111,111,111 = 12,345,678,987,654,321
10Although The Number Devil showed Robert how to make all of the numbers from one, something is still missing . . .Do you know what it is?
111986 = MCMLXXXVI They wrote their numbers like this: Zero was the last number to be discovered.The ancient Romans didn’t have zero.They wrote their numbers like this:1986 = MCMLXXXVI
12Our numbers are much easier to write because we use zero, and our numbers hop.
13Number hopping is really easy! Try one:1 = 11 x 1 = 11 x 1 x 1 = 1Don’t see it?
14Number Hopping Try Two: 2 = 2 2 x 2 = 4 2 x 2 x 2 = 8 See it?21 = 222 = 423 = 824 = 16
15Now make 10 hop four times: Number HoppingNow try it with 10:101 = 10102 = 100103 = 1,000Now make 10 hop four times:104 = 10,000
16Number 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.
17Number Hopping 6 + 80 + 900 + 1,000 = 1986 Remember 1986? Here’s how it hops:6 x 1 = 68 x 10 = 809 x 100 = 9001 x 1,000 = 1,000,000 = 1986
19We cannot divide by zero. It is strictly forbidden! 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!
20On this third night The Number Devil decided to tell Robert a secret. 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.
21There 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.
22234567891011121314151617181920212223242526272829303132333435363738394041424344454647484950First we take out all of the even numbers because they are divisible by 2. Don’t forget that 2 is a prima donna number.
23235791113151719212325272931333537394143454749Now do 3.3 is a prima donna number, but we can take out all the other numbers divisible by 3.
245 is a prima donna, so take out all the numbers that end in 5. 23571113171923252931353741434749We 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.
252357111317192329313741434749We can forget about 6, 6 is 2 x 3, but 7 is a prima donna number so take out any numbers divisible by 7.
26Well, there you have it – the prima donnas! 2 3 5 7 11 13 17 19 23 29 3137414347Well, there you have it –the prima donnas!
27Get the book! Curious? 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!
28by Hans Magnus Enzensberger THE NUMBER DEVILbyHans Magnus Enzensberger
29Technology & 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.