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First, ANY number which the sum of all it's digits is evenly divisible by three, is divisible by three

Example: 15: 1+5=6, 6 is evenly divisible by three, so 15 is also

So, 112476234 1+1+2+4+7+6+2+3+4=30, 30 is evenly divisible by three, therefore so is 112476234 (112476234 / 3 = 37492078)

THAT means, if you take ANY number that is evenly divisible by 3, and add as many zeroes as you want ANYWHERE you want, the result is STILL evenly divisible by 3. ALSO, you can re-arrange the order of the numbers however you want, and still, it's evenly divisible by 3.

112234467 / 3 = 37411489 (112234467 is the same digits re-arranged)

To take it one step further, take a number, let's say 999996663332354923542
9+9+9+9+9+6+6+6+3+3+3+2+3+5+4+9+2+3+5+4+2=111

Take the 111, 1+1+1=3, three is evenly divisible by 3, therefore 111 is also (111 / 3 = 37), therefore 999996663332354923542 is also.

You can do this with ANY number, take a 474 digit number, add the digits to see if the original is evenly divisible by three. The sum of the digits is too big of a number to deal with, add THOSE up, and see, keep doing it until you have a manageable number, and you have it made. The same thing can be done with the number 9 to some degree

Here's another: We all know the Pythagorean theorem, a^2 + b^2 = c^2, but, did you know it works 3-dimensionally? In calculus, it's called "finding the length of a vector", where the three dimensions x, y, and z, are squared and added, and the square root of that sum is also the length of the vector, or hypotenuse.

Take any square number, lets say 49, which is 7 squared. If you want to know the square of the next higher number, in this case 8, you take the original number (48), and add 7, then 8 to it. 49 + 7 + 8=64 8 squared is 64. If you drqw this out of graph paper, it's easy to see why it works. You can also do this in multiple steps, if you remember how. To go from 7 to 10, it just goes 49 + 7 + 8 + 8 + 9 + 9 + 10 = 100 (10 squared), just remember to do the first and last numbers ONCE, and all inbetween TWICE. To go backwards, just subtrace: 49 - 7 - 6 = 36 (6 squared)

Ever add up a list of numbers twice and come up with two different answers? Take one of those answers and subtract it from the other. If the result is the number 9 or a 9 followed by some zeroes, then one of those times you transposed two adjacent digits. The 9 will also be in the same position as one of the digits you transposed, so if you come up with the number 900, then somewhre you transposed either the 2nd and 3rd digits from the right, or the 3rd and 4th digits from the right.

You've got a lot of time on your hands, right ?

I hate math but I like the #9 multiplication trick where the number always comes back to 9. 

5 x 9 = 45
4+5=9

9 x 4=36
3+6=9

9 x 525252=4727268
4+7+2+7+2+6+8=36
3+6=9

And so on...

Not really, just a few things I've picked up over the years. Don't be jealous of my 1337 math skilz. .

Here is a great math trick ...

http://www.youtube.com/watch?v=7WMi5TUJDso

What is the result if you add the infinite series

1 + 1/2 + 1/4 + 1/8 + 1/16....

If you're adding more and more positive numbers to the series an infinite number of times, then it has to reach infinity eventually, right? 

Nope, it would add up to 2 (assuming it could be done).

That blew my mind when I first heard it.   

That's weird, you'd think you'd get an asymptote that gets infinitely close to 2, but never actually gets there, because every time you add another number, you're only getting halfway closer.

Yeah, that's what I meant to say!  It's the entire concept of infinite series that converge on a particular finite number (the asymptote itself) that blew my mind, not that particular example.  And I was imprecise saying it "adds up" to two. 

That's nothing... here's something really weird, the mystic power of the number 1089.

Take any three digit number, each with a different digit, highest digit first ex 731.  Subtract from that the inverse of the number (137), you take 731-137, you get 594.  Now add the inverse of that number (594 + 495) and you get 1089.

Try it, it works with about any three digit number.

But, let's say you don't want to put the highest digit first, so you do 154 - 451, you get -297 (negative 297).  You add -297 to 792, you get 495.  Now, add 495 to 594, and what do you get?

1089!

It's freaking creepy!!!

Well, let's say you don't want the digits to all be different, so let's take 855 minus 558, you get 297.  297 plus 792 is, you guess it, 1089!

Now, watch this... 998 - 899, you get 99.  But, add 99 to 99, you get 198.  Add 198 to 891, and once, again, 1089.

I don't know what it all means, but it kind of scares me...

Man, I can SENSE all the women in this forum getting aroused at our cool-@$$ed math skillz. Man, we gotta cut down on this before someone ends up heartbroken, pregnant, or both. . .

Between the math skillz and the cool hair, I might need a bodyguard, maybe a whole entourage to keep all the women at bay. . . Yea, it's tough being a math nerd. .

Don't tell them about that starship Enterprise model you've got hanging in the bedroom - you'll get mobbed  :teddyr:

Uhhh, , HELLO, ,, it's the Millennium Falcon, , ,and it's not a MODEL, , it's a "scale replica". jees. .

The women folk are swooning as you speak.

Does it only work on single digits ?

It could be :
11 +24 + 76 + 234 = 345 Which can be divided by three into 115.

1 + 1+ 5 = 7...Hang on, I got lost somewhere...

You have to add each single digit. 345 IS evenly divisible, and 3 + 4 + 5 = 12, also evenly divisible. You're trying to divide the wrong number,

Oh, I see... :smile:

Multiplying on your fingers:

By nines:
http://www.youtube.com/watch?v=oamy8L2lDZM&feature=related


And by 6,7,8,9, or 10:
http://www.youtube.com/watch?v=_eFnzNw10Qc&feature=related

I was just looking at this and I see why it works. When you take a number, reverse it and subtract that from the original number, you ALWAYS get a number with a 9 in the middle and the first and last digits always add up to 9. So when IT is flipped and added, the two first digits always equal 9, the two third digits always equal 9, and the two middle digits always equal 18.