---
id: 5900f4291000cf542c50ff3c
challengeType: 5
title: '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?
## Instructions
## Tests
```yml
tests:
- text: euler189() should return 10834893628237824.
testString: 'assert.strictEqual(euler189(), 10834893628237824, "euler189() should return 10834893628237824.");'
```
## Challenge Seed
```js
function euler189() {
// Good luck!
return true;
}
euler189();
```