Special Numbers: 6174

Try this:

  1. Take any four-digit number, using at least two different digits. Repdigits, such as 1111, will not work, because you will just end up with 0 after step 3.
  2. Arrange the digits in ascending and then in descending order, adding leading zeros if necessary. Add leading zeros if necessary – for example, 4560 in ascending order is 0456 and 6540.
  3. Subtract the smaller number from the bigger number.
  4. Go back to step 2 and repeat the process.

This process, known as the Kaprekar routine, will always reach the number 6174, within 7 iterations. Once 6174 is reached, the process will continue yielding 6174 because 7641 – 1467 = 6174.

For example, choose 6532:

6532 – 2356 = 4176

7641 – 1467 = 6174

Another example, choose 4905:

9640 – 0469 = 9171

9711 – 1179 = 8532

8532 – 2358 = 6174

7641 – 1467 = 6174

6174 is known as Kaprekar’s constant, named after Indian mathematician D. R. Kaprekar.

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