---
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.

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).

# --hints--

`euler163()` should return 343047.

```js
assert.strictEqual(euler163(), 343047);
```

# --seed--

## --seed-contents--

```js
function euler163() {

  return true;
}

euler163();
```

# --solutions--

```js
// solution required
```