---
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.

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.

# --hints--

`euler354()` should return 58065134.

```js
assert.strictEqual(euler354(), 58065134);
```

# --seed--

## --seed-contents--

```js
function euler354() {

  return true;
}

euler354();
```

# --solutions--

```js
// solution required
```