47 lines
1.3 KiB
Markdown
47 lines
1.3 KiB
Markdown
---
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id: 5900f4cf1000cf542c50ffe1
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title: 'Problem 354: Distances in a bee''s honeycomb'
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challengeType: 5
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forumTopicId: 302014
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dashedName: problem-354-distances-in-a-bees-honeycomb
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---
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# --description--
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Consider a honey bee's honeycomb where each cell is a perfect regular hexagon with side length 1.
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<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;">
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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.
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For example, $B(\sqrt{3}) = 6$, $B(\sqrt{21}) = 12$ and $B(111\\,111\\,111) = 54$.
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Find the number of $L ≤ 5 \times {10}^{11}$ such that $B(L) = 450$.
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# --hints--
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`distancesInHoneycomb()` should return `58065134`.
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```js
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assert.strictEqual(distancesInHoneycomb(), 58065134);
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```
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# --seed--
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## --seed-contents--
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```js
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function distancesInHoneycomb() {
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return true;
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}
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distancesInHoneycomb();
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```
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# --solutions--
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```js
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// solution required
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```
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