Hi,
Something not all that related to magic, but what would you consider to be the most magical whole number between 0-9? Of course there are numbers such as pi and root 2, which are of course very interesting (these don't count as they are not whole); but what rational numbers do you think are the most interesting? Are there any magical uses for interesting properties of numbers?
Personally I think that 9 is the most interesting number. Some simple, interesting properties include:

• That any number whose digits add up to 9 is divisible by 9 to create a whole number. One of the most interesting things about this is that 111111111 when divided by 9= 123456789
  9/111111111
  
  
• If you hold up all your fingers, and put one down, and count the fingers on either side of your finger that is down, then you will get a number divisible by 9.
  
  (((.( )))))
  left right
  
  In this diagram the index finger of the left hand is down. This tells us that 4X9 is 36, 3 on the left hand side of the finger which is down, 6 on the right of the down finger.
  

I am sure that you will be familiar with these properties, but they are just quick examples off the top of my head. What other numbers have "magical" properties such as these?
Cardially yours,
owen

Hi Owen,

I think that 4 is an 'interesting' number as both adding 2 to itself and multiplying two by itself gives this number.

ie: 2 + 2 = 4
and 2 x 2 = 4

Not sure how I could relate this to a magical effect though.

There's a book by 'David Wells' called 'The Penguin Dictionary of Curious and Interesting Numbers' which has loads of interesting stuff, as the title suggests.

Best wishes,

Brian.

Relating to Brian's post, I've always been fascinated with pairs of numbers that, whether added to each other or multiplied by each other, result in the exact same number.

Besides 2+2 and 2x2, there are others (2x2 and 2+2 are the only whole numbers however).

3+1.5=3*1.5
4+1 1/3=4*1 1/3
5+1.25=5*1.25
6+1.2=6*1.2

Notice a pattern? Here's the formula:

(X)+(X/(X-1))=(X)*(X/(X-1))

Subtraction can also work:

4-.8=4*.8
7-.875=7*.875
9-.9=9*.9

Here's the formula for the subtraction version:

(X)-(X/(X+1))=(X)*(X/(X+1))

Notice that this is similar to the previous equation, just with the + and - signs switched.

Hi all

This is my first post on the Café, so please don't flame the newbie in magic (a few months, still reading Giobbi, Bobo, etc.).

A number which could have some properties useful for magic (although I can't think of any right now) is 1/7.

1/7 = 0.142857142857....... with the same numbers ad infinitum.

If you multiply it by 2 you get :
2/7 = 0.285714285714....... etc., which is a permutation of the previous one.

3/7 = 0.428571428571.......etc., which is also a permutation.

All multiples of 1/7 (except 7, 14, etc.) will have this series of digits after the decimal point.

Best wishes,

Mathias.

Hi Mathias,

There are other fractions which have similar properties, although there may be two sets of 'cyclic' recurring digits.

For example the 13ths have either '307692' or 153846' as a set of recurring digits in their decimal forms, starting on one of the digits in the group and recurring.

Hope that makes some sort of sense.

Brian.

Great findings guys,

magictrickster, I am interested by that book and I will certainly check it out. It is amazing what properties one can find, as at face value numbers appear to be pretty boring.

owen

P.S. I believe I have met you several times at the Magic Circle!

Hi Owen,

Yep, we've met a few times at the Magic Circle - At the Junior Day and the YMOTY heats/final - some or all of those I think.

I think I've also seen you at Blackpool Convention this year if I'm not mistaken (I'm a member of Blackpool Magicians Club and Magic Circle). Please come and chat if you ever see me around, and cheers for remembering me.

Best wishes,

Brian.

The digits one through nine are all interesting numbers, so the Largest Most Interesting Whole Number is 9.

That makes the number 10 the smallest uninteresting number. But wait, that classification, "smallest uninteresting number" is kind of interesting in itself. So I guess 10 is the Largest Most Interesting Whole Number.

So that makes the number 11 the smallest uninteresting number. But wait, that classification, "smallest uninteresting number" is kind of interesting in itself. So I guess 11 is the Largest Most Interesting Whole Number.

So that makes the number 12 the smallest uninteresting number. But wait...

Jack Shalom

Jack,
Great point, I hadn't thought of that...I think that is a good point which could be added into an act...somehow!!!

Brian,
Next time we cross paths, I shall certainly say hi!

owen

I thought the answer to this question was obvious, but as no one has posted it yet ...

The most magical number is zero because when it is multiplied with another number, it makes the other number disappear.

Anyway, I suppose everyone knows here already knows the anecdote about the Hardy-Ramanujan number 1729:

http://encyclopedia.thefreedictionary.co......0numbers

http://encyclopedia.thefreedictionary.co......cdote%29

Balducci,
Thanks to the links to the pages, very interesting...as for you thinking that 0 is the most interesting number, I am not so sure!

Owen

Then again, there's always 91: the smallest number expressible as the sum of two cubes in two different ways.

Nick

Interesting find NIH, but I did state at the beginning of this post:

"What would you consider to be the most magical whole number between 0-9?"

But still don't let this stop you. This was just a perimeter as there are literally thousands of numbers out there which display interesting properties.
Thanks again,
Owen

I realize this also doesn't quite fit the parameter, but it's between 0 & 9...

The golden ratio. 1.618033...

The fibbonacci sequence: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233...

I *KNOW* there's gotta be an astounding magic effect that can be presented with these, I just haven't seen it, or figured one out yet...

Anyone got anything on this?

Dave

By the way...take any two consecutive numbers in the Fibonacci sequence and divide the larger by the smaller. The result approaches the golden ratio as you go further and further into the Fibonacci sequence.

Well known characteristic of the Fibonacci sequence: the sum of the first n terms is always one less than the n+2nd term. So you can show a print-out of the first hundred Fibonacci numbers, ask the participant to draw a line after any of those numbers, and you can instantly announce the sum of all the numbers up to the line that was drawn.

Jack Shalom

Okay, I am about to break the rules too now, so don't call me a hypocrite but:
11 is interesting. I was talking to someone at my school who knows a couple of number tricks. One of the things that interested me was how to find any 2 digit number times by 11! I don't know if this method is common, but it is pretty simple:
If you are given the number 37, then you can find out that 11 X 37 equals 397! How? by adding the two digits together, and placing the result between the two original digits.
3+7 = 9, so 11 X 37 = 397! ***NOTE: See correction in following post***

If the number produced from adding them up is another two digit number, then the first of the two numbers is added to the first number of the total (if that makes sense).
Ex. 11 X 69
6 + 9 = 15
Therefore 609
+15
=759

Sorry to break the rules, but it was to good to leave out!
Owen

I am baffled by your arithmetic here.

11 X 37 = 407, according to my calculator. And, 3 + 7 = 10. I can make it work, however, if I apply the second part of your method, to wit:



That is, 3 + 7 = 10. 3 + 1 = 4. Therefore, 11 X 37 = 407. That is, the first digit of the answer is 4 (that is, 3 + 1); the second digit is the 0 from the 10; and the last digit is the 7. Right?

Sorry for the mistake there. I didn't use a good first example, because I actually mucked up the arithmatic. Try 11 X 27 this time: 2 + 7 = 9, therefore 11 X 27 = 297! Sorry about that, hope this sorts it out.

Owen

3^3 + 4^3 = 91
What's the second?

But as long as we're in the realm of magical 2 digit numbers, I'm partial to 37.

37*3=111
37*6=222
37*9=333

and 37*37=1,369

Also, think of a number less than 50, both digits odd...

Gregg,
That's an interesting point. I found something strange earlier today while I was fiddling with my calculator during maths. This may seem obvious to some, but at the time I found it quite interesting. Now we really are going beyond the boundaries as this uses up to 9 numbers! Here goes.

If you type in to your calculator (or write them on paper) all the numbers from 9 to 1 in that order (987654321), and then minus the same numbers you will obviously get naught (nothing interesting so far). Then if you take for instance, the top three consecutive numbers, in descending order (987), and then minus the bottom three consecutive numbers (again in descending order (321) you get 666!

This can be repeated for any consecutive numbers as long as there are the same amount of top numbers as there are bottom numbers, and the gap between the numbers is always the top amount minus the bottom amount:
you could try 98-21 resulting in 77, or 654 - -123, which can be written 654 +123.

I hope you can understand the idea from what I have written, I found it quite hard to put into words, but hopefully you understand.

owen