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

## Description
<section id='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?
</section>

## Instructions
<section id='instructions'>

</section>

## Tests
<section id='tests'>

```yml
tests:
  - text: <code>euler189()</code> should return 10834893628237824.
    testString: assert.strictEqual(euler189(), 10834893628237824);

```

</section>

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

<div id='js-seed'>

```js
function euler189() {
  // Good luck!
  return true;
}

euler189();
```

</div>



</section>

## Solution
<section id='solution'>

```js
// solution required
```

</section>