2018-09-30 22:01:58 +00:00
---
id: 5900f4cf1000cf542c50ffe1
challengeType: 5
2018-10-20 18:02:47 +00:00
title: 'Problem 354: Distances in a bee''s honeycomb'
2018-09-30 22:01:58 +00:00
---
## 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.
2018-10-08 00:01:53 +00:00
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.
2018-09-30 22:01:58 +00:00
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
2018-10-04 13:37:37 +00:00
tests:
- text: < code > euler354()</ code > should return 58065134.
2018-10-20 18:02:47 +00:00
testString: assert.strictEqual(euler354(), 58065134, '< code > euler354()< / code > should return 58065134.');
2018-09-30 22:01:58 +00:00
```
< / 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 >