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Topic: Math to arrive at the number 9!
Message: Posted by: matthewjohnson (Feb 16, 2004 11:02PM)
Hi everyone,

I am writing this post because I believe I have come up with a brand new mathematical equation for arriving at the number 9 (& it's cool too!), let me explain.

In many tricks such as Magicard by Mark Jenest it is necessary for the magician to have a spectator arrive at the number 9 by using a series of mathematical equations. My problem is that every time I have seen this performed the math always seems to be very contrived. This is where my idea comes in!

Without giving too much away just yet it allows you to get the spectator to arrive at the number 9 with only a few additions and subtractions (no multiplications) and best of all it can be done without having to ask a spectator to think of a number between 10 and 20 or any other contrived stuff like that. It is a very practical and MAKE SENSE kind of method.

What are your methods of forcing the number 9?

Let me know as I plan on releasing this method to the magical fraternity if indeed it is new!

Looking forward to your feedback,

Matthew Johnson.
Message: Posted by: landmark (Feb 17, 2004 12:38AM)
Here's an easy way:

1) choose any number with different digits

2) reverse the digits

3) subtract the lesser number from the greater number

4) add up all the digits in the result

5) repeat step 4 until there is only one digit.

Or here's an even easier way:

1) choose any number

2) add up all the digits

3) subtract your result from your original number

4) continue adding the digits until only one digit remains

Here's yet another way:

1) choose any number

2) put a zero on the end of the number

3) subtract the original number

4) add all the digits until you get one digit

Jack Shalom
Message: Posted by: matthewjohnson (Feb 17, 2004 04:27PM)
Thanks Jack!

I appreciate you answering my thread. Those methods look great although they still sound a little contrived, what I mean by this is not to be rude but to say that the math does not have any reason for being, or may be it does! What patter would you offer to support the math and make it appear normal? Do you know what I mean?! Just asking someone to go through this mathematical problem to arrive at a number would appear a little odd to the spectator, as far as the spectator is concerned why not just ask them to pick a number.
The fact is we do have to go through some kind of mathematical equation to get to the number 9, but every version I have seen up to now does not offer a logical reason for being, it simply sounds as though the spectator does not have any free choice and has to go through the magicians little routine in order to reach the number he wants.

I have come up with a method that uses something personal to the spectator and therefore has a logical reason for being. This is then echoed in the patter used to describe the math, which again is logical to the spectator.

I don't know may be I am making a mountain out of a molehill but if we can make something better why not give it our best shot.

Looking forward to your thoughts out there.

Message: Posted by: rgranville (Feb 17, 2004 04:45PM)
For ideas on how to justify the arithmetic behind number-based tricks in general (as well as to the methods discussed here), I recommend Richard Busch's [i]Number... Please[/i].
Message: Posted by: matthewjohnson (Feb 17, 2004 06:30PM)
Hi rgranville,

Thanks for the tip regarding the book. I will look into that as I think the words we use to describe the things we do and why we do them are very important! …More important than the things we do in many cases.

Yours with many thanks,


Posted: Feb 17, 2004 7:34pm

I am looking for a few more suggestions on the math to arrive at the number 9 and then I will post my thoughts to the routine I have come up with.

Don't let the whole math thing put you off. I don't do math tricks far from it, however I do think that this little bit of math magic that I have to offer would be of use to many magicians across the board.
Message: Posted by: Scott Cram (Feb 17, 2004 11:18PM)
My two favorite methods for getting numbers that have a digital root of nine (all of which can be reduced to the single digit of nine via the usual method):

From Jim Steinmeyer's "Impuzzibilities":
Ask someone to take out some dimes and pennies - as many as they want, but at least one of each. Ask them to total the value of the coins in cents, and remember the total. From that number, subtract the total number of coins. The total will be always be a multiple of 9. (For example, let's say they have 4 dimes and 8 pennies. The number of cents is 48, and the number of coins is 12. 48-12=36 - a multiple of 9!)

From Harry Lorayne's "Apocalypse":
You hand the spectator a calculator (preferably a simple 4-function calculator), and show that the numbers are arranged in a 3x3 square:


You ask them to enter any three digit number created from any row, column or diagonal entered in any order (if you choose the 159 diagonal, for example, you can enter 159, 195, 519, 591, 915 or 951). You then tell them to hit the multiplication sign, and then enter a three-digit number from any other row, column or diagonal. This number will also be a multiple of nine - albeit a very large one.
Message: Posted by: Nir Dahan (Feb 17, 2004 11:27PM)
You can use 3 blank memo cards, write the numbers "1" "2" "3" on the 3 pieces, 1 number on each piece, then turn over the pieces and continue writing "4", "5" and "6" on the other side of so you get the numbers arranged 3/6 2/5 1/4.
Mix the pieces of paper and make sure the numbers 1,2,3 are showing face up, turn around ask the spectator to turn around 1 piece of paper while your back is turned, and sum up the numbers he sees which are now face up. (They will always total 9.)
This solution doesn't require any summing up of digits and looks quite fair. Its main disadvantage is that it is easy to backtrack. So either remove the pieces or switch in pieces with other number distributions.
Hope this helps.

Message: Posted by: hoodrat (Feb 18, 2004 03:45AM)

Really liked your method of using a bunch of pennies and dimes to generate a multiple of nine. Very unique!
Message: Posted by: magicgeorge (Feb 18, 2004 10:15AM)
A dime is 10c?
That method is kind of cute I suppose in the UK one could use pennies, ten pence and pound coins.
Message: Posted by: Scott Cram (Feb 18, 2004 10:44AM)
On 2004-02-18 04:45, hoodrat wrote:

Really liked your method of using a bunch of pennies and dimes to generate a multiple of nine. Very unique!
Correction - you like [i]Jim Steinmeyer's[/i] method using a bunch of pennies and dimes to generate a multiple of nine.

It is ingenious, though, isn't it?

On 2004-02-18 11:15, magicgeorge wrote:
A dime is 10c?
That method is kind of cute I suppose in the UK one could use pennys, ten pences and pound coins.
Yes, a dime is 10 cents.

If you use something like a pound coin, I'd remind your audience to calculate the whole thing in pence. You don't want them to try and calculate 1.41 pounds minus 6 coins. 141 pence minus 6 coins would be preferable.
Message: Posted by: matthewjohnson (Feb 18, 2004 11:11AM)
Thanks for you response!

I like the pennies idea and the cards idea. I like these because they add a little more substance to the run of the mill math problem.

My method (I believe it's original, let me know!), uses math just the same as the other methods but I believe has a little more reason for being, anyway here it is.

The math starts with the spectator’s age, anyone’s age, as long as it is between 10 and 99 you don't have to know the age. The spectator adds the two digits of their age together e.g. 57, 5+7=12. Now they minus the 12 from their age, e.g. 57-12=45. Finally add the two digits in the last number to get 9 e.g. 45, 4+5=9.

This method always works without you knowing the age as long as the age is between 10 and 99.

Now because the number used in the method is of a personal nature to the spectator we could use patter such as this,

Magician - "I have never met you before so if I could tell you how old you are that would be kind of cool, right!" "Most people could probably guess within a few years but if I could tell you exactly, that would not be a bad trick".
"However if I said exactly how old you were in front of all these people at the party that would be kind of rude as you may not want them to know how old you are, so I tell you what, lets play around a little with the numbers in your age so as to mask or disguise it from these guys!"

"Take the digits in your age and add them together, you get a new number, if I could tell you that number that would be a better a trick, however some of the smart people in the crowd could probably still do the math, so lets disguise it even more."

"You know that new number you got, minus it from your age, you did that great! You are now thinking of a one digit number" At this point they will say no as they more than likely have a two digit number, it is now you throw in a casual joke "Oh, I'm sorry your not quite as old as I thought you were, I'm Going to be in trouble for that one!"

"Ok well take the two digits and add them together. Now you have a one digit number right, RIGHT!"

The number is 9 do with it what you want.

It is hard for me to describe the feeling that goes with this patter, believe me it reads much longer than it plays. I wanted to offer you some of the patter and performance that goes into selling the thing.

What do you think? Have you seen it before?

I look forward to your response.

Message: Posted by: balducci (Feb 19, 2004 12:50AM)
Your words are very nice, I can see it being a disarming approach to use.

Of course, your numerical method / mathematical equation is exactly the same as the dimes and pennies one. (It uses the tens and ones in the exact same way.)
Message: Posted by: hoodrat (Feb 19, 2004 01:57AM)

I like your idea of using a person's age as long as it's between 10 and 99. One could also use the last two digits of a year as long as that year was any one from 1910 to 1999.
Message: Posted by: balducci (Feb 19, 2004 08:17AM)
Upon reflection, I see that this dimes and pennies / 10s and 1s trick works for any number, so long as you are counting in base 10, and so long as you are not starting with a single digit number,


7892 - (7+8+9+2) = 7866, 7+8+6+6 is divisible by 9, etc., further reduce to 9 from here using your favourite approach.

235652 - (2+3+5+6+5+2) = 235629, 2+3+5+6+2+9 is divisible by nine, etc.

Sorry if I'm stating the obvious here, I don't know if this is widely known or not.

Anyway, this would let you work the trick with $100, $10, and $1 bills.

Or you could use the year of birth,


1964 - (1+9+6+4) = 1944, 1+9+4+4 is divisible by 9, etc.
Message: Posted by: matthewjohnson (Feb 19, 2004 10:35AM)
Thanks guys for responding to my message.

Balducci thank you for the kind words on the patter. (The same Balducci?) Lets face it any trick where we are asking the spectator to do some math is going to be a little boring unless we give it some good patter, after all what is a Ceasar salad without the dressing!

Hoodrat thanks for your kind words too. Of course you don't have to know the number as you can tell just buy looking at a person whether they fit into the correct category.

Do you guys think by having a combination of the age idea with the patter, I have something I could publish on a DVD without ripping other people off.

Let me know,
Message: Posted by: balducci (Feb 19, 2004 11:07AM)
Actually, my Balducci name is taken from Gaetano Balducci (a dead Italian actuary who developed a famous principle used in insurance mathematics). The magical connection is honestly just a coincidence.

I don't think you would be ripping anyone off if you were to use your presentation on a DVD. Of course, you'd need a lot of additional material to make the DVD worthwhile. :)
Message: Posted by: matthewjohnson (Feb 19, 2004 03:28PM)

Interesting! (About your name).
I have enough material right now for a couple of DVDs. This would be the only math bit on there.

Keep a look out for the 1st DVD towards the later part of 2004.
Message: Posted by: Lior (Feb 19, 2004 03:43PM)
I think that the age thing is very old.
I remember using it in an old web site. I had to do
the Denmark Elephant.
It wasn't my idea and I don't remember where I got it.
I will try to find the book.
Message: Posted by: matthewjohnson (Feb 19, 2004 09:49PM)

You have seen the age thing before? I would be interested if you could let me know where you saw it and most importantly how it was presented with the patter. The patter is what makes the routine, so if the book does not offer any patter let me know and I will go ahead, but credit the book also.

Message: Posted by: Lior (Feb 20, 2004 12:56PM)
I found what was on my website on 1993.
It was interactive effect that said that you had to be
older than 18 to get in.
Then there was the "think of your age ... and all the math"
Then it went to think of country that start with ...
Then I did a joke that Pamela Anderson face blinked on the screen and it said again "don't think about Pamela, Think about the animal and country"
and only now The gray elephant picture was shown.
I am sure that I saw the age ploy in one of Martin Gardner's books or something like that.
Message: Posted by: chappy (Feb 20, 2004 04:17PM)
If you estimate the participants age to the nearest decade, e.g. thirties, forties, etc. then you could predict the outcome after only the first two phases.
twenties = 18
thirties = 27
forties = 36 etc

Is the principle too obvious? Perhaps.

Keep the presentation simple. Remove a business card with the correct number on the back, and place it on their hand, just another reason to use your b'card. Don't play it too seriously and make sure you've killed them with something previously.
Message: Posted by: hoodrat (Feb 20, 2004 05:17PM)

I was re-reading your posting above. Using a person's age to arrive at the number 9 is clever. However, if you do this effect in front of an audience with a volunteer, the audience members will also be doing the math in their heads at the same time using their own ages -- they will ALL arrive at the same number 9. I guess maybe your method would only be satisfactory to use in a one-on-one situation. Just some thoughts…
Message: Posted by: matthewjohnson (Feb 21, 2004 09:14PM)

Thank you for your kind words but I have to disagree when it comes to doing this for a crowd. Why would everyone else think to do the math at the same time if it is not addressed to them, this is the way magicians think. After the job is done no one is going to back track, in the grand scheme of things I just don't think it’s that important to people. It's just like saying that people will back track any math question, after all the idea of people doing the math at the same time works with any method, does it not?

Matthew J.
Message: Posted by: balducci (Feb 21, 2004 09:38PM)
If someone in the audience gets a nine as well they might just / probably would put it down to coincidence. 1 in 10 chance, after all.

It's not as though that person in the audience knows that EVERY OTHER person got a nine as well.
Message: Posted by: matthewjohnson (Feb 23, 2004 05:37PM)
That's what I'm saying! I don't think anybody would be that concerned. As I said before, the idea of someone else doing the math works with any equation, not just mine.
Message: Posted by: Parson Smith (Mar 28, 2005 10:56PM)
I tend to think that others in the audience will either do the math at the same time or do an easy backtrack BUT, if something else personal was added, maybe there would be enough cover. Good thing to think about.
Thanks Matthew.
Message: Posted by: Hushai (Mar 30, 2005 12:46AM)
In the Introduction to Karl Fulves's book "Self-Working Number Magic" (published by Dover Publications -- a great book for anyone interested in this kind of thing) he makes the following suggestion which is similar to much of what has been said on this thread: "In presenting the tricks in this book, try to connect the routines with numbers that have meaning to the spectator. Thus, instead of having a spectator jot down a random number, have him jot down the last two digits of his telephone number or the first two digits of his license plate number. He will then think that those digits are somehow important to the outcome, and this is the real secret of success with material of this kind" (p. iii). Sounds good to me!