Checksum Magic

[BrianG]

I've discovered a little mathmagic trick, it requires a Euro bill, which I don't look at, and a volunteer. I explain that the Euro bill has a security feature built into the serial number that allows me to "read minds".

 

I ask the volunteer to pick a number between one and nine, I ask them not to pick a zero because it "gives me a headache", and then I ask the volunteer to see if that number is one of the digits in the bill's serial number. This is pure chance, often they say yes, but if not, I ask them to select one of the integers in the serial number and hold it "in there head".

 

Then I ask them to say the letter at the start of the serial number and the other 10 digits in the serial number, keeping there number back. I caution that if there number is on the bill more than once, they have to say the other occurrences, if they pick a one and it's on the serial number three times, they have to say it twice. I allow that they can read the other digits in any order, to prove I don't merely memorize all the serial numbers.

 

As they read the letter and the other 10 digits, I write them down. After a few moments, I tell them what number they are "thinking". It's fun, and not difficult, once you know the trick. It makes a great bar bet, so I'm always sure to read them back the number, to make sure no one is too drunk to read the number correctly.

 

Would anyone like to give it a try? Post the letter and 10 digits of a Euro bill serial number? I'll send back the missing number.

 

Then, I'll break the most important rule of magic, I'll tell you how it's done. I often show my work as I do this illusion. I don't really like mentalism, I like close-up magic.

 

Please give it a try.

[Theory5]

Ok here is one.

You said I can put the numbers in any order?

the letter is "s"

6305031502

 

I picked a 5 euro bill

[BrianG]

Ok here is one.

You said I can put the numbers in any order?

the letter is "s"

6305031502

 

I picked a 5 euro bill

 

Thank you, Theory5, the denomination is unimportant, the letters and numbers are what I need. You start with the "S", that's the 19th letter in the alphabet. Let's use the magic of nine, by that I mean mod nine, divide 19 by 9 and take the remainder, 1 and put it in your series:

16305031502

 

Now I'll convert this to a sum in base nine: 1+6+3+0+5+0+3+1+5+0+2 and find all the numbers that add up to nine: 1+(6+3)+0+0(5+0+3+1)+5+0+2 and since we are working in mod nine, where 9=0 if you are only looking for the last digit, we can strike out the nines and the zeros: 1+5+2 = 8

 

Now we take our sum, 8 and subtract it from 8, (9-1) and we get your missing number, 0. But since I said you can't use zero, and 9 in base 9=10, and we are only looking for the last digit, if you followed instructions, it's a 9.

 

Now I know that nine is the number or I'm getting a headache. To make it look like magic, I might say, it's not a small number, it's not an even number, I'm seeing an odd number, large number...

 

It's a nine! The number you are thinking of is 9!

 

Am I right?:)

[BrianG]

I use a simple matrix, so I don't have to do any memorization:

 

 

A F K P U Z

B G L Q V

C H M R W

D I N S X

E J O T Y

1,5,10,15,20,25

 

 

So all I have to do is remember every fifth letter, EJOTY, to make it easy to find the number value for the letter. Ejoty is my mnemonic.

[Theory5]

heh, yea its 9.

I dont understand what the letter has to do with it though.

[BrianG]

We are dealing with numbers here, so I have convert the letter, "s" to a number, it's the 19th letter in the alphabet. We are using base nine, the fancy term is mod nine, where we only care about the remainder, I divide 19 by 9 and get 2 with a remainder of 1, in base nine, it's: 21. I only care about one digit, the last significant digit, so I just use the remainder, 1. If the starting letter was a U, it would have a numerical value of 21 and the mod9 would be 3, 21/9=2 remainder 3.

 

Did my explanation help? I wish I knew more LaTex, then maybe I could express this better.

 

Thanks again, for helping me publish my magic trick. Never tell anyone your PIN!

[Theory5]

We are dealing with numbers here

Thats why I dont understand it! :-P

 

, so I have convert the letter, "s" to a number, it's the 19th letter in the alphabet. We are using base nine, the fancy term is mod nine, where we only care about the remainder, I divide 19 by 9 and get 2 with a remainder of 1, in base nine, it's: 21. I only care about one digit, the last significant digit, so I just use the remainder, 1. If the starting letter was a U, it would have a numerical value of 21 and the mod9 would be 3, 21/9=2 remainder 3.

 

Did my explanation help? I wish I knew more LaTex, then maybe I could express this better.

 

Thanks again, for helping me publish my magic trick. Never tell anyone your PIN!

 

Oh so you are using a base 9 system..

I think I understand now. And somebody could figure this out just by using different bases? are there tricks for finding multiple numbers or can you only do it with one number missing?

[BrianG]

The checksum for a Euro bill serial number is 8, (9-1), so I don't think there is any way to reconstruct more than one digit from the serial number. Checksums are used in all computer communications, that's why they work so fast and accurately. When you download a file, it often has a CRC, a cyclic redundancy check, that uses a checksum. Every byte of data usually has a checksum, too.

 

Thanks again, for helping me with this. I'd be happy to try this again, it really is a nifty little effect. Do you think I've explained it well enough, that you could do this on your own? Do you understand that 9=0 in mod9, so that's why you have to eliminate either the zero or nine, so you don't get them confused?

[Theory5]

The checksum for a Euro bill serial number is 8, (9-1), so I don't think there is any way to reconstruct more than one digit from the serial number. Checksums are used in all computer communications, that's why they work so fast and accurately. When you download a file, it often has a CRC, a cyclic redundancy check, that uses a checksum. Every byte of data usually has a checksum, too.

Wait, how is the checksum of Euro serials 8? Doesn't it need to follow an algorithm or something? And how did you find that bit of information? I live in the states where we don't often have Euro's and It would be interesting to find the same thing out about the dollar bill :-)

yea I am familiar with computer checksum programs and I have used a few to check huge files I have downloaded. I never bothered to find out what algorithm they use.

Thanks again, for helping me with this. I'd be happy to try this again, it really is a nifty little effect. Do you think I've explained it well enough, that you could do this on your own? Do you understand that 9=0 in mod9, so that's why you have to eliminate either the zero or nine, so you don't get them confused?

I get it, thanks. I'm not sure I could do this trick off the top of my head, I usually need to have something to refer to so I can make sure I am getting it right. I have trouble with modulo division, just cause its new to me.

but why don't you give me the serial of a euro and I will try to find the missing number.

[BrianG]

I found the checksum security feature when I Googled Euro Bill, to get an image to print on flash paper.

 

Here's a trial, I have a five Euro bill and I'll give you the serial number, but I'll keep one digit back:

 

X2767879131_

 

Can you find the missing digit?

[BrianG]

I think dollar bills are sequential, Euro bills are probably sequential too, but with an extra check digit. I don't know why the checksum is 8, but 9-1 seems to make sense. I learned about checksums in high school, when I started learning about computer programs.

 

In America we have UPCs on every product, and they have a checksum as the last digit on the right. Because the number should be entered in order, the checksum isn't as simple. For a UPC, each digit has a position, even or odd. You add up all the even position digits, and then add up all the odd position digits and multiply them by 3 and add them together, and subtract from 10:

 

 

 

 

Position x 1 2 3 4 5 6 7 8 9 10 11 Checkdigit

UPC number 0 2 8 2 0 0 1 0 0 1 2 2

 

So the odd even digits are 2 2 0 0 1 so we get 2+2+0+0+1=5

And the even digits are 0 8 0 1 0 2 so we get (0+8+0+1+0+2)*3=33

So we add them together and have 5+33=38

 

Since we only care about one check digit, 10-8=2, the small number on the far left of the UPC.

 

I'm trying to find a simple way to do this, and a good way to explain it to make it magic.

 

Thanks again, for your help.

[freeztar]

I found the checksum security feature when I Googled Euro Bill, to get an image to print on flash paper.

 

Here's a trial, I have a five Euro bill and I'll give you the serial number, but I'll keep one digit back:

 

X2767879131_

 

Can you find the missing digit?

 

24 mod9= 6

 

6+2+7+6+7+8+7+9+1+3+1

 

6+(2+7)+6+7+8+7+9+1+3+1

 

6+6+7+8+7+3=37

 

37mod9=1

 

Is that right?

[BrianG]

24 mod9= 6

 

6+2+7+6+7+8+7+9+1+3+1

 

6+(2+7)+6+7+8+7+9+1+3+1

 

6+6+7+8+7+3=37

 

37mod9=1

 

Is that right?

 

6+(2+7)+6+7+8+7+(9)+1+3+1

 

6+6+7+8+7+1+3+1 = (6+3)+6+(7+1+1)+8+7

 

6+8+7=21=9+9+3

 

Using the checksum, 8, we have 8-3=5

 

The digit left off the serial number was 5.

[Qfwfq]

I explain that the Euro bill has a security feature built into the serial number that allows me to "read minds".

There's no doubt that, by now, every single forger knows it.

 

You'd think Prodi's lads would have used a less noticeable checksum than that!

[BrianG]

I think a forger would copy a good bill, and that would have a serial number that obeys the checksum algorithm.

 

The UPC and EAN are very similar, the UPC is on American products, and the EAN on European. They both have a checksum of 10, in base 10.

 

The Euro bill serial number has a checksum of 8 in base 9.

[Qfwfq]

I think a forger would copy a good bill, and that would have a serial number that obeys the checksum algorithm.

Of course! If they know there's a checksum, that is.

 

As a security feature, it is obviously useless except for forgers that don't realise there might be valid and invalid serial numbers, so it would at the very least have to be not publicized. Otherwise it is only useful against data errors, which obviously is the purpose in UPC and EAN.

 

Euro notes were designed with quite a number of features against forgery, quite more challenging even for expert forgers, so the checksum isn't much of a security thing it was likely meant for automatic cash readers in banks where keeping track of the numbers might be required.

[BrianG]

The check digit on a Euro bill is the next to the last digit on the right. When you look at a stack of new bills, they are in number order but for that digit.