---
id: 5900f4cb1000cf542c50ffde
title: 'Problem 351: Hexagonal orchards'
challengeType: 5
forumTopicId: 302011
dashedName: problem-351-hexagonal-orchards
---

# --description--

A hexagonal orchard of order $n$ is a triangular lattice made up of points within a regular hexagon with side $n$. The following is an example of a hexagonal orchard of order 5:

<img class="img-responsive center-block" alt="hexagonal orchard of order 5, with highlighted in green points, which are hidden from the center by a point closer to it" src="https://cdn.freecodecamp.org/curriculum/project-euler/hexagonal-orchards.png" style="background-color: white; padding: 10px;">

Highlighted in green are the points which are hidden from the center by a point closer to it. It can be seen that for a hexagonal orchard of order 5, 30 points are hidden from the center.

Let $H(n)$ be the number of points hidden from the center in a hexagonal orchard of order $n$.

$H(5) = 30$. $H(10) = 138$. $H(1\\,000)$ = $1\\,177\\,848$.

Find $H(100\\,000\\,000)$.

# --hints--

`hexagonalOrchards()` should return `11762187201804552`.

```js
assert.strictEqual(hexagonalOrchards(), 11762187201804552);
```

# --seed--

## --seed-contents--

```js
function hexagonalOrchards() {

  return true;
}

hexagonalOrchards();
```

# --solutions--

```js
// solution required
```
