---
id: 5900f40f1000cf542c50ff22
challengeType: 5
title: '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).
## Instructions
## Tests
```yml
tests:
- text: euler163() should return 343047.
testString: assert.strictEqual(euler163(), 343047, 'euler163() should return 343047.');
```
## Challenge Seed
```js
function euler163() {
// Good luck!
return true;
}
euler163();
```
## Solution
```js
// solution required
```