---
id: 5900f4cf1000cf542c50ffe1
challengeType: 5
title: 'Problem 354: Distances in a bee''s 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.
## Instructions
## Tests
```yml
tests:
- text: euler354() should return 58065134.
testString: assert.strictEqual(euler354(), 58065134, 'euler354() should return 58065134.');
```
## Challenge Seed
```js
function euler354() {
// Good luck!
return true;
}
euler354();
```