---
id: 5900f4cf1000cf542c50ffe1
challengeType: 5
title: 'Problem 354: Distances in a bee''s honeycomb'
---

## Description
<section id='description'>
Consider a honey bee's honeycomb where each cell is a perfect regular hexagon with side length 1.






One particular cell is occupied by the queen bee.
For a positive real number L, let B(L) count the cells with distance L from the queen bee cell (all distances are measured from centre to centre); you may assume that the honeycomb is large enough to accommodate for any distance we wish to consider.
For example, B(√3) = 6, B(√21) = 12 and B(111 111 111) = 54.

Find the number of L ≤ 5·1011 such that B(L) = 450.
</section>

## Instructions
<section id='instructions'>

</section>

## Tests
<section id='tests'>

```yml
tests:
  - text: <code>euler354()</code> should return 58065134.
    testString: assert.strictEqual(euler354(), 58065134, '<code>euler354()</code> should return 58065134.');

```

</section>

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

<div id='js-seed'>

```js
function euler354() {
  // Good luck!
  return true;
}

euler354();
```

</div>



</section>

## Solution
<section id='solution'>

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