freeCodeCamp/curriculum/challenges/english/10-coding-interview-prep/project-euler/problem-52-permuted-multiples.md

---
id: 5900f3a01000cf542c50feb3
challengeType: 5
title: 'Problem 52: Permuted multiples'
forumTopicId: 302163
---

## Description
<section id='description'>

It can be seen that the number, 125874, and its double, 251748, contain exactly the same digits, but in a different order.

Find the smallest positive integer, <var>x</var>, such that <var>2x</var>, <var>3x</var>, <var>4x</var>, <var>5x</var>, and <var>6x</var>, contain the same digits.

</section>

## Instructions
<section id='instructions'>

</section>

## Tests
<section id='tests'>

```yml
tests:
  - text: <code>permutedMultiples()</code> should return a number.
    testString: assert(typeof permutedMultiples() === 'number');
  - text: <code>permutedMultiples()</code> should return 142857.
    testString: assert.strictEqual(permutedMultiples(), 142857);

```

</section>

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

<div id='js-seed'>

```js
function permutedMultiples() {

  return true;
}

permutedMultiples();
```

</div>



</section>

## Solution
<section id='solution'>


```js
function permutedMultiples() {
    const isPermutation = (a, b) =>
        a.length !== b.length
            ? false
            : a.split('').sort().join() === b.split('').sort().join();


    let start = 1;
    let found = false;
    let result = 0;

    while (!found) {
        start *= 10;
        for (let i = start; i < start * 10 / 6; i++) {
            found = true;
            for (let j = 2; j <= 6; j++) {
                if (!isPermutation(i + '', j * i + '')) {
                    found = false;
                    break;
                }
            }
            if (found) {
                result = i;
                break;
            }
        }
    }

    return result;
}
```

</section>