freeCodeCamp/curriculum/challenges/english/08-coding-interview-prep/project-euler/problem-126-cuboid-layers.english.md

---
id: 5900f3ea1000cf542c50fefd
challengeType: 5
title: 'Problem 126: Cuboid layers'
---

## Description
<section id='description'>
The minimum number of cubes to cover every visible face on a cuboid measuring 3 x 2 x 1 is twenty-two.


If we then add a second layer to this solid it would require forty-six cubes to cover every visible face, the third layer would require seventy-eight cubes, and the fourth layer would require one-hundred and eighteen cubes to cover every visible face.
However, the first layer on a cuboid measuring 5 x 1 x 1 also requires twenty-two cubes; similarly the first layer on cuboids measuring 5 x 3 x 1, 7 x 2 x 1, and 11 x 1 x 1 all contain forty-six cubes.
We shall define C(n) to represent the number of cuboids that contain n cubes in one of its layers. So C(22) = 2, C(46) = 4, C(78) = 5, and C(118) = 8.
It turns out that 154 is the least value of n for which C(n) = 10.
Find the least value of n for which C(n) = 1000.
</section>

## Instructions
<section id='instructions'>

</section>

## Tests
<section id='tests'>

```yml
tests:
  - text: <code>euler126()</code> should return 18522.
    testString: assert.strictEqual(euler126(), 18522, '<code>euler126()</code> should return 18522.');

```

</section>

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

<div id='js-seed'>

```js
function euler126() {
  // Good luck!
  return true;
}

euler126();
```

</div>



</section>

## Solution
<section id='solution'>

```js
// solution required
```
</section>