Try This and Prepare to be Amazed

If someone ever told you that the answer to the ultimate question of life, the universe and everything is "42", tell them that is wrong. The answer is "6174" and here's why (and prepare to get your mind blown):

Take any number with 4 non-repeating digits. Say 1562.

Step 1: Arrange the number in ascending and then descending order
Step 2: Subtract the smaller number from the bigger number

6521 - 1256 = 5265

Repeat the steps:

6552 - 2556 = 3996
9963 - 3699 = 6264
6642 - 2466 = 4176
7641 - 1467 = 6174

Try any 4-digit number with non-repeating digits, and you'll *always* get 6174.

Pretty cool, huh?

6174 is known as Kaprekar's constant. The math operation above, discovered by Indian mathematician D.R. Kaprekar, will reach 6174 after at most 7 steps (if you did more than 7 iterations, check your arithmetics).

See also: Math T-shirts at the NeatoShop

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.
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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.
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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! :)
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Yola - so, 3824:

8432 - 2348 = 6084
8640 - 0468 = 8172
8721 - 1278 = 7443
7443 - 3447 = 3996
9963 - 3699 = 6264
6642 - 2466 = 4176
7641 - 1467 = 6174

Your first step was incorrect
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I've created a little spreadsheet to try it out. It's really funny.
If you want to try:

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.
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also noticed that any 4 digit number that becomes sequential when rearranged, will always result in 3087 when this pattern is applied.

if nobody's figured that out yet I'd like that to be called "Brandon's constant" please.

i.e. 4321-1234=3087 etc.
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@oli nope. The reason, why this stuff works is, that we sort the digits of the result after each step. Once in descending order (biggest number to be reached with four given digits) and ascending order (smallest number to be reached) and take the difference.

Take a few tries on my web-based calculator. It might make understanding easier if you can try different values.
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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:

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?
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9876 is 9876-6789=3087
3087 is 8730-0387=8343
8343 is 8433-3348=5085
5085 is 8550-0558=7992
7992 is 9972-2799=7173
7173 is 7731-1377=6354
6354 is 6543-3456=3087

Yeah... About that whole *ANY* number thing.
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@D.B. Cooper
If you look on the left, it goes 24-12-6-3-10. 3 is odd, but 3x3 is 9, not 10.

And yeah, that's the first thing that popped into my mind too.
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This is similar to where you can take any number, put it in word form (e.g. 500 becomes 'five hundred') and count the letters, (five hundred = 11 letters). Now take that number and do the same (eleven). Repeat the process (eleven = 6 letters), six = 3 letters, three = 5 letters, five = 4 letters. No matter what number you choose, you will Always get 4 in the end.
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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!
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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.
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Clyde mentions that the result of the procedure is not amazing because its constraints mean it will eventually settle somewhere, however it is somewhat amazing that it settles on a single number and not a group of numbers... If you apply the technique to numbers in base 9 there at least two possible attractive triplets of numbers you could end up in:
7072 --> 7432 --> 5074 --> 7072...
7252 --> 5254 --> 3076 --> 7252...
(there may be more...these are the only ones I've found so far).
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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
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