**6174**is known as

**Kaprekar's constant**

^{[1]}

^{[2]}

^{[3]}after the Indian mathematician D. R. Kaprekar. This number is notable for the following property:

- Take any four-digit number, using at least two different digits. (Leading zeros are allowed.)
- Arrange the digits in ascending and then in descending order to get two four-digit numbers, adding leading zeros if necessary.
- Subtract the smaller number from the bigger number.
- Go back to step 2.

**Kaprekar's routine**, will always reach 6174 in at most 7 iterations.

^{[4]}Once 6174 is reached, the process will continue yielding 7641 – 1467 = 6174. For example, choose 3524:

- 5432 – 2345 = 3087
- 8730 – 0378 = 8352
- 8532 – 2358 =
**6174**

- 2111 – 1112 = 0999
- 9990 – 0999 = 8991 (rather than 999 – 999 = 0)
- 9981 – 1899 = 8082
- 8820 – 0288 = 8532
- 8532 – 2358 =
**6174**

- 9831 – 1389 = 8442
- 8442 – 2448 = 5994
- 9954 – 4599 = 5355
- 5553 – 3555 = 1998
- 9981 – 1899 = 8082
- 8820 – 0288 = 8532 (rather than 882 – 288 = 594)
- 8532 – 2358 =
**6174**

495 is the equivalent constant for three-digit numbers. For five-digit numbers and above, there is no single equivalent constant; for each digit length the routine may terminate at one of several fixed values or may enter one of several loops instead.

^{[4]}

## See also

## References

**^**Mysterious number 6174**^**Kaprekar DR (1955). "An Interesting Property of the Number 6174".*Scripta Mathematica***15**: 244–245.**^**Kaprekar DR (1980). "On Kaprekar Numbers".*Journal of Recreational Mathematics***13**(2): 81–82.- ^
^{a}^{b}Weisstein, Eric W., "Kaprekar Routine" from MathWorld.

## External links

- Mysterious Number 6174 Article
- The mysterious 6174 revisited
- Kaprekar Series Generator
- Online Kaprekar script

Hey, I don't do this stuff! One of my college-aged kids showed it to me. It's from a site called www.collegehumor.com

But I think I know

*some*body who would like it .....

From the book "Not Even Wrong" (to which I give my highest recommendation) by Peter Woit:

The story behind this seems to be that particle theorist John Ellis and experimentalist Melissa Franklin were playing darts one evening at CERN in 1977, and a bet was made that would require Ellis to insert the word "penguin" somehow into his next research paper if he lost. He did lose, and was having a lot of trouble working out how he would do this. Finally, 'the answer came to him when one evening, leaving CERN, he dropped by to visit some friends where he smoked an 'illegal substance'. While working on his paper later that night 'in a moment of revelation he saw that the diagrams looked like penguins'.

*Oo-o-h, looks, I see two penquins!*

Luvz,

Heidi

Here's a video of me:

Luvz,

Heidi

Here's a video of me:

## 3 comments:

Dangit, Heidi, stop invading my posts! How do you DO that anyway? Is your middle name Feynman?

Steven,

I can remember spending hours tracing the "orbits" of numbers after reading about Kaprekar's number. I would make up rules for transforming numbers and then see how they are linked.... and that is no penguin, that is a milkshake with two straws...

Really? I never heard of that number or that problem. Yahoo or CNN, I forget which has a list of the ten strangest things in Wikipedia, that's how I found out about it. And oh yeah that's a milkshake, hmm.

I thought the list of constants at the bottom was cool, I got lost there for an hour or so.

Post a Comment