Kaprekar's Constant:'495 and 6174'

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In this post, I am going to prove Kaprekar's Constant. Now let us prove this by taking some examples.

3-Digit Number Rule:


Example 1: I'm taking a three-digit number '658'. You can assume any 3-digit number.

Condition: You should not assume the same numbers as 999,111,222, etc. Because if you take in the form a Descending number - Ascending number, you will get 111-111=000. But you can assume 3-digit numbers like this: 665, 991,344.
For this number, the Descending number is '865' and the Ascending number is '568'. Subtract the Ascending number from Descending number.


Next, take the number 297. For this number, the Descending number is '972' and the Ascending number is '279'. Subtract the Ascending number from Descending number.

Next, take the number 693. For this number, the Descending number is '963' and the Ascending number is '369'. Subtract the Ascending number from Descending number.

Next, take the number 594. For this number, the Descending number is '954' and the Ascending number is '459'. Subtract the Ascending number from Descending number.

Finally, we got the result of 495.

Hence, it is proved that for any three-digit number if we subtract in the form of an Ascending order from Descending order after repeating steps somewhere you will get 495.

You can try your own examples.

4-Digit Number Rule:

Example 2: I'm taking a four-digit number '1285'. You can assume any four-digit number.

Condition: You should not assume the same numbers as 9999,1111,2222, etc. Because if you take in the form a Descending number - Ascending number, you will get 9999-9999=0000. But you can assume 4-digit numbers like this: 6655, 9923,3444.

For this number, the Descending number is '8521' and the Ascending number is '1258'. Subtract Ascending number from Descending number.


Next, take the number 7263. For this number, the Descending number is '7632' and the Ascending number is '2367'. Subtract the Ascending number from Descending number.

Next, take the number 5265. For this number, the Descending number is '6552' and the Ascending number is '2556'. Subtract the Ascending number from Descending number.

Next, take the number 3996. For this number, the Descending number is '9963' and the Ascending number is '3699'. Subtract the Ascending number from Descending number.

Next, take the number 6264. For this number, the Descending number is '6642' and the Ascending number is '2466'. Subtract the Ascending number from Descending number.

Next, take the number 4176. For this number, the Descending number is '7641' and the Ascending number is '1467'. Subtract the Ascending number from Descending number.

Hence, it is proved that for any four-digit number if we subtract in the form of an Ascending order from Descending order after repeating steps somewhere you will get 6174.

You can try your own examples.

If you have any doubts related to this concept, post in the comment box.

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