6174 is known as Kaprekar's constant after the Indian mathematician D. R. Kaprekar. This number is notable for the following property:
1. Take any four-digit number, using at least two different digits. (Leading zeros are allowed.)
2. Arrange the digits in ascending and then in descending order to get two four-digit numbers, adding leading zeros if necessary.
3. Subtract the smaller number from the bigger number.
4. Go back to step 2.
The above process, known as Kaprekar's routine, will always reach 6174 in at most 7 iterations. 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
Friday, January 14, 2011
How Would Someone Figure This Out?
What would possess someone even to think of studying this, much less come up with Kaprekar's Constant?