---
id: 5900f40f1000cf542c50ff22
title: 'Problem 163: Cross-hatched triangles'
challengeType: 5
forumTopicId: 301797
dashedName: problem-163-cross-hatched-triangles
---

# --description--

Consider an equilateral triangle in which straight lines are drawn from each vertex to the middle of the opposite side, such as in the size 1 triangle in the sketch below.

<img class="img-responsive center-block" alt="triangles with size 1 and size 2" src="https://cdn.freecodecamp.org/curriculum/project-euler/cross-hatched-triangles.gif" style="background-color: white; padding: 10px;">

Sixteen triangles of either different shape or size or orientation or location can now be observed in that triangle. Using size 1 triangles as building blocks, larger triangles can be formed, such as the size 2 triangle in the above sketch. One-hundred and four triangles of either different shape or size or orientation or location can now be observed in that size 2 triangle.

It can be observed that the size 2 triangle contains 4 size 1 triangle building blocks. A size 3 triangle would contain 9 size 1 triangle building blocks and a size $n$ triangle would thus contain $n^2$ size 1 triangle building blocks.

If we denote $T(n)$ as the number of triangles present in a triangle of size $n$, then

$$\begin{align}
  & T(1) = 16 \\\\
  & T(2) = 104
\end{align}$$

Find $T(36)$.

# --hints--

`crossHatchedTriangles()` should return `343047`.

```js
assert.strictEqual(crossHatchedTriangles(), 343047);
```

# --seed--

## --seed-contents--

```js
function crossHatchedTriangles() {

  return true;
}

crossHatchedTriangles();
```

# --solutions--

```js
// solution required
```