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


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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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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...
or
7252 --> 5254 --> 3076 --> 7252...
(there may be more...these are the only ones I've found so far).
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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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