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

Abusive comment hidden.(Show it anyway.)9 x 7 = 63. 6 + 3 = 9

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

Abusive comment hidden.(Show it anyway.)Abusive comment hidden.(Show it anyway.)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.

Abusive comment hidden.(Show it anyway.)Abusive comment hidden.(Show it anyway.)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! :)

Abusive comment hidden.(Show it anyway.)Abusive comment hidden.(Show it anyway.)Abusive comment hidden.(Show it anyway.)Abusive comment hidden.(Show it anyway.)so...

4283 - 3824 = 459

954 - 459 = 495

594 - 495 = 99

99 - 99 = 0

am I missing something?

Abusive comment hidden.(Show it anyway.)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

Abusive comment hidden.(Show it anyway.)If you want to try:

http://spreadsheets.google.com/ccc?key=0AtjwtBQnQot5dC1TSDRIYVRRMnl3cDRodlpJVzFGS0E&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.

Abusive comment hidden.(Show it anyway.)if nobody's figured that out yet I'd like that to be called "Brandon's constant" please.

i.e. 4321-1234=3087 etc.

Abusive comment hidden.(Show it anyway.)Abusive comment hidden.(Show it anyway.)Abusive comment hidden.(Show it anyway.)7641 - 1467 = 6174

Weird.

Abusive comment hidden.(Show it anyway.)Abusive comment hidden.(Show it anyway.)in each step.Abusive comment hidden.(Show it anyway.)Take a few tries on my web-based calculator. It might make understanding easier if you can try different values.

Abusive comment hidden.(Show it anyway.)I added another sheet to your calculator. Hope you don't mind! Have a look. I would love to know what you think.

Abusive comment hidden.(Show it anyway.)Abusive comment hidden.(Show it anyway.)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?

Abusive comment hidden.(Show it anyway.)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.

Abusive comment hidden.(Show it anyway.)Abusive comment hidden.(Show it anyway.)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.

Abusive comment hidden.(Show it anyway.)3087 is 8730-0387=8343

Should be:

3087 is 8730-0378=8352

8352 is 8532-2358=6174

Abusive comment hidden.(Show it anyway.)Abusive comment hidden.(Show it anyway.)On the other hand: For the idiot that destroyed the first sheet... well done!

Abusive comment hidden.(Show it anyway.)Abusive comment hidden.(Show it anyway.)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.

Abusive comment hidden.(Show it anyway.)the sum of the digits in the answer always add up to nine

3x9= 27 2+7 =9

123x9= 1107 1+1+0+7 =9

Abusive comment hidden.(Show it anyway.)Abusive comment hidden.(Show it anyway.)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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