freeCodeCamp/curriculum/challenges/english/10-coding-interview-prep/project-euler/problem-414-kaprekar-constant.md

---
id: 5900f50b1000cf542c51001d
challengeType: 5
title: 'Problem 414: Kaprekar constant'
forumTopicId: 302083
---

## Description
<section id='description'>
6174 is a remarkable number; if we sort its digits in increasing order and subtract that number from the number you get when you sort the digits in decreasing order, we get 7641-1467=6174.
Even more remarkable is that if we start from any 4 digit number and repeat this process of sorting and subtracting, we'll eventually end up with 6174 or immediately with 0 if all digits are equal.
This also works with numbers that have less than 4 digits if we pad the number with leading zeroes until we have 4 digits.
E.g. let's start with the number 0837:
8730-0378=8352
8532-2358=6174


6174 is called the Kaprekar constant. The process of sorting and subtracting and repeating this until either 0 or the Kaprekar constant is reached is called the Kaprekar routine.


We can consider the Kaprekar routine for other bases and number of digits.
Unfortunately, it is not guaranteed a Kaprekar constant exists in all cases; either the routine can end up in a cycle for some input numbers or the constant the routine arrives at can be different for different input numbers.
However, it can be shown that for 5 digits and a base b = 6t+3≠9, a Kaprekar constant exists.
E.g. base 15: (10,4,14,9,5)15
base 21: (14,6,20,13,7)21

Define Cb to be the Kaprekar constant in base b for 5 digits.
Define the function sb(i) to be
 0 if i = Cb or if i written in base b consists of 5 identical digits
 the number of iterations it takes the Kaprekar routine in base b to arrive at Cb, otherwise

Note that we can define sb(i) for all integers i < b5. If i written in base b takes less than 5 digits, the number is padded with leading zero digits until we have 5 digits before applying the Kaprekar routine.


Define S(b) as the sum of sb(i) for 0 < i < b5.
E.g. S(15) = 5274369
S(111) = 400668930299


Find the sum of S(6k+3) for 2 ≤ k ≤ 300.
Give the last 18 digits as your answer.
</section>

## Instructions
<section id='instructions'>

</section>

## Tests
<section id='tests'>

```yml
tests:
  - text: <code>euler414()</code> should return 552506775824935500.
    testString: assert.strictEqual(euler414(), 552506775824935500);

```

</section>

## Challenge Seed
<section id='challengeSeed'>

<div id='js-seed'>

```js
function euler414() {

  return true;
}

euler414();
```

</div>



</section>

## Solution
<section id='solution'>

```js
// solution required
```

</section>