---
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--
`triangularGridColoring()` should return `10834893628237824`.
```js
assert.strictEqual(triangularGridColoring(), 10834893628237824);
```
# --seed--
## --seed-contents--
```js
function triangularGridColoring() {
return true;
}
triangularGridColoring();
```
# --solutions--
```js
// solution required
```