THE UNBELIEVABLE NUMBER 6174

Take any four digit number. But one condition, all digits should not be the same like 1111 or 3333. But 2 or 3 digits can be same. Let us consider the number 2017.

STEPS
1.Arrange the digits of the number in descending order. that is , make biggest number out of four digits. We get 7210.
2. Next, arrange the digit in ascending order, making smallest number out of the same four digits. It is 0127 or 127.
3. Subtract the small number from the big one.
7210 - 127 = 7083.

Now repeat the above three steps with 7083.
1. 8730
2. 0378
3. 8730-378 = 8352
Repeat the process few more times.
2017
1. 7210-0127 = 7083
2. 8730-0378 = 8352
3. 8532-2358 = 6174
4. 7641-1467 = 6174

within 3 iterations, the result stuck at 6174. It does not change further. 6174 is called kaprekar's constant or kernel of the 4 digit numbers. The process is known as keprekar's operation.

All the 4 digit numbers end up at 6174 within 7 iterations. Now we can understand why we cannot include numbers like 3333 because small number and big number cannot be constructed using them.

I will end this articles with some open questions for your personal research.
1. What about 3 digits or 5 digits numbers etc.,?
2. Can it be applicable to numbers with other bases?
3. Any practical use for keprakar's constant? Can you devise one?
4. Can you design a operation similar to keprekar's?

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