---
id: 5900f4cf1000cf542c50ffe1
title: 'Problem 354: Distances in a bee''s honeycomb'
challengeType: 5
forumTopicId: 302014
dashedName: problem-354-distances-in-a-bees-honeycomb
---

# --description--

Consider a honey bee's honeycomb where each cell is a perfect regular hexagon with side length 1.

<img class="img-responsive center-block" alt="honeycomb with hexagon sides of length 1" src="https://cdn.freecodecamp.org/curriculum/project-euler/distances-in-a-bees-honeycomb.png" style="background-color: white; padding: 10px;">

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, $B(\sqrt{3}) = 6$, $B(\sqrt{21}) = 12$ and $B(111\\,111\\,111) = 54$.

Find the number of $L ≤ 5 \times {10}^{11}$ such that $B(L) = 450$.

# --hints--

`distancesInHoneycomb()` should return `58065134`.

```js
assert.strictEqual(distancesInHoneycomb(), 58065134);
```

# --seed--

## --seed-contents--

```js
function distancesInHoneycomb() {

  return true;
}

distancesInHoneycomb();
```

# --solutions--

```js
// solution required
```