6147. That chances of randomly arriving at that number 1/10,000 if you took 4 slots and began injecting random numbers in them. On the surface what can you say about 6147, that it’s divisible by 3 or that it’s an odd number?

Well, 6147 was dubbed Kaprekar’s Constant in 1949 and it has a unique property in relation to nearly any other 4-digit number. This property is known as Kaperekar’s Routine.

Suppose you have a 4-digit number (with at least 2 different digits) you can perform Kaprekar’s routine.

Choosing 7238 as our test subject, I guarantee you within 7 iterations of special subtraction we will end up with 6147.

First, we take 7238 and rearrange to make the largest 4-digit number possible.

8732 right?

Now we subtract the opposite of this number — 2378 from 8732.

8732–2378 = 6354

Now repeat the step again so we get 6543 (largest number from the difference)

Reverse the order to get — 3456 and let’s do our subtraction again.

6543–3456 = 3087

By now you should understand the steps. So I will fast forward and start calculating.

8730–378 = 8352

8532–2358 = 6147

And Bingo, in less than 7 iterations we got our magic number 6147.

If you are more interested in understanding why Kaprekar’s Routine occurs check out this pdf link: I’m a pdf link

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