---
id: 5900f40f1000cf542c50ff22
challengeType: 5
title: 'Problem 163: Cross-hatched triangles'
---

## Description
<section id='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.

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 n2 size 1 triangle building blocks.
If we denote T(n) as the number of triangles present in a triangle of size n, then
T(1) = 16
T(2) = 104
Find T(36).
</section>

## Instructions
<section id='instructions'>

</section>

## Tests
<section id='tests'>

```yml
tests:
  - text: <code>euler163()</code> should return 343047.
    testString: assert.strictEqual(euler163(), 343047, '<code>euler163()</code> should return 343047.');

```

</section>

## Challenge Seed
<section id='challengeSeed'>

<div id='js-seed'>

```js
function euler163() {
  // Good luck!
  return true;
}

euler163();
```

</div>



</section>

## Solution
<section id='solution'>

```js
// solution required
```
</section>
