Kaprekar's constant

There's a very cool mathematical constant discovered by Indian mathematician Dattatreya Ramchandra Kapreka - it's 6174.

You can read about it here, but Kaprekar discovered that if you followed a certain pattern of calculations you would always end up on the same that same number...

Here are the rules:

• Think about a four digit number, just make ensure that they are all the same. 1111 is not ok, but 2020 is ok. Let's choose 1495, since that is what the Wikipedia page uses
  • Now rearrange the digits in descending order; 9541.
  • Then rearrange the digits in ascending order; 1459.
  • Subtract these two number from each other; 9541-1459, giving the result 8082
    • Note that you will need to fill out the end of the number with zeros. 999 should be 9990 for example. 88 turns to 8800.
• Then repeat that calculations with the new number.
• Keep doing that and ... viola you'll end up in 6174

At this point you probably think what I think... How, of all things holy, did he discover that. I mean, the number of calculations he must have made before he realized that. Who, in their right mind, would ever...

Let's prove it

But this is a perfect thing to work with for people like us, developers that does test-driven development.

Let's write a program that lists all the calculations that is made from any number to Kaprekars constant. Like this:

9541 – 1459 = 8082
8820 – 0288 = 8532
8532 – 2358 = 6174

Here are some cases that you can use to get started:

• 6174

  7641 - 1467 = 6174
  

• 8532

  8532 - 2358 = 6174
  

• 8082

  8820 - 0288 = 8532
  8532 - 2358 = 6174
  

• 1495

  9541 - 1459 = 8082
  8820 - 0288 = 8532
  8532 - 2358 = 6174
  

• 8273

  8732 - 2378 = 6354
  6543 - 3456 = 3087
  8730 - 0378 = 8352
  8532 - 2358 = 6174