August 28, 2013

6174, 495 : beautiful Numbers & Mathematics

6174 is known as Kaprekar's constantafter 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 its fixed point, 6174, in at most 7 iterations. Once 6174 is reached, the process will continue yielding7641 – 1467 = 6174. For example, choose 3524: 

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

or 

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

495 is the three digit equivalent. 



2 comments:

  1. Did you know that these two numbers now figure in the Krutonian Mathematics of beautiful numbers!

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