Few days back I posted an article based on the interesting properties of 153. Lot of people got very excited to know about similar other numbers with such interesting properties. Today I will be discussing about another such interesting number: **6174**

**Kaprekar’s Constant**

6174 is known as Kaprekar’s constant named after the Indian recreational mathematician D. R. Kaprekar. I’ve written about D.R.Kaprekar and contribution of other Indian mathematicians. 6174 has got a very interesting property. To know what that mysterious property is take any four-digit number. Arrange the digits in ascending and then in descending order to get two four-digit numbers. Then subtract the bigger number from the smaller number. If we keep on repeating this process we will end up in 6174. This process is called **Kaprekar’s** **routine**. All the numbers will yield 6174 in 7 or less than 7 iterations.

**Example**

Let’s randomly choose any number, say 4518:

Now, arranging the digits in ascending and then in descending order to get two four-digit numbers.

8541-1458 = 7083

8730-0378 = 8352

8532-2358 = 6174

Hence we get 6174 in 3 iterations.

**4651 reaches 6174 after 7 iterations**

6541-1456 = 5085

8550-558 = 7992

9972-2799 = 7173

7731-1377 = 6354

6543-3456 = 3087

8730-378 = 8352

8532-2358 = 6174

Try it for any 4-digit number yourself and see if it works.

**Questions**

- For a specific set of numbers Kaprekar’s routine will not work. Can you tell me what numbers will those be?
- If you follow Kaprekar routine with any 3 digit number it will also result in one specific number. Can you find out that 3 digit equivalent constant?
- The result of each iteration of Kaprekar’s routine is a multiple of 9. Can you explain why?

Hint: you have seen the application of similar mathematical logic in the earlier post – mind reading trick.

Leave your answers in the comments below.

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