Try This and Prepare to be Amazed

That is amazing. Numerical constants always reassure me that math is part of the natural world in some mind-boggling way. Also, multiply 9 by any number, then add up the digits. Keep adding up the digits, and you’ll get 9.

9 x 7 = 63. 6 + 3 = 9
27.619 x 9 = 248.571. 2+4+8+5+7+1 = 27. 2 + 7 = 9.

Meh. Its neat but not terribly amazing.
The operation of arranging four digits into ascending or descending order essentially maps every possible ordering of four given digits to the same number.
There are only ten different digits that could possibly appear, and by subtracting the ascending order from the descending order you’re just subtracting the smallest from the largest, second smallest from second largest, second largest from second smallest, and largest from smallest for the first, second, third, and fourth digits respectively.
There are only so many ways that you can subtract one digit from another, especially when you’re restricted to non-repeated digits.
There are many mathematical operations where repeating the same operation eventually settles on some particular number.
A different mathematical technique that is similar but much more useful is “Newton’s method” which can be used to get an approximation for any formula and only gets more accurate the more you repeat it.

Take two integers between two and twelve. Quintuple both and then use the Ackermann function on each. Raise them both to the i’th power and add a constant c in case you’ve accidentally taken an integral somewhere. (To be on the safe side)

Then give both numbers weapons and make them fight a random prime no less than 7 and no greater than 139969.

That’d be pretty cool!

Works every time.

I chose 3824

so…

4283 – 3824 = 459
954 – 459 = 495
594 – 495 = 99
99 – 99 = 0

am I missing something?

I’ve created a little spreadsheet to try it out. It’s really funny.
If you want to try:
http://spreadsheets.google.com/ccc?key=0AtjwtBQnQot5dC1TSDRIYVRRMnl3cD RodlpJVzFGS0E&hl=en

And yes, ther might still be errors as there was some hand labour involved to make it work without having to use scripts! And yes, you all could edit it, please only fill in the yellowish cell A2.

I like math graphics, but not long boring formulas. I love atracttors and fractals.

6174

7641 – 1467 = 6174

Weird.

@oli: Note that the instructions say to rearrange the digits from highest to lowest and lowest to highest in each step.

@kruemi-

I added another sheet to your calculator. Hope you don’t mind! Have a look. I would love to know what you think.

Is this trick base-dependent?

I know @Johnny Cat’s sum-the-digits is base dependent. In base nine, 9 is writtn 10, the sum of whose digits is 1. But for multiples of 8 in base nine…
9*9-1 -> 88 in base 9. Sum the digits:
88
17
8

Although I haven’t proven or seen it proved that this is generally true for 8 in base nine, or if the rule applies to “base minus one” in any (whole) base. Anyone know for sure?

Reminds me of this: http://xkcd.com/710/

@Kilockle

3087 is 8730-0387=8343

Should be:

3087 is 8730-0378=8352
8352 is 8532-2358=6174

Fun, than so many people get the math wrong (a simple subtraction) and claim to have found a flaw

On the other hand: For the idiot that destroyed the first sheet… well done!

rdennis, you may need to check you maths. If the lower number is always being subtracted from the higher, the number cannot drop to being three digits.

Here’s the maths for yours either way:

5834 is 8543-3458=5085
5085 is 8550-0558=7992
7992 is 9972-2799=7173
7173 is 7731-1377=6354
6354 is 6543-3456=3087
3087 is 8730-0378=8352
8352 is 8532-2358=(you know it) 6174.

Mind = Blown

Why is it that you can write down any four digit number containg four different digits, then write down a second four digit number containg same digits in any different order..subtract the lower number from higher one, you always obtain a multiple of 9??? how does this always work for any four digit number, need an explanation please