---
id: 5900f4291000cf542c50ff3c
title: 'Problem 189: Tri-colouring a triangular grid'
challengeType: 5
forumTopicId: 301825
dashedName: problem-189-tri-colouring-a-triangular-grid
---

# --description--

Consider the following configuration of 64 triangles:

We wish to colour the interior of each triangle with one of three colours: red, green or blue, so that no two neighbouring triangles have the same colour. Such a colouring shall be called valid. Here, two triangles are said to be neighbouring if they share an edge. Note: if they only share a vertex, then they are not neighbours.

For example, here is a valid colouring of the above grid:

A colouring C' which is obtained from a colouring C by rotation or reflection is considered distinct from C unless the two are identical.

How many distinct valid colourings are there for the above configuration?

# --hints--

`euler189()` should return 10834893628237824.

```js
assert.strictEqual(euler189(), 10834893628237824);
```

# --seed--

## --seed-contents--

```js
function euler189() {

  return true;
}

euler189();
```

# --solutions--

```js
// solution required
```