freeCodeCamp/curriculum/challenges/english/10-coding-interview-prep/project-euler/problem-161-triominoes.md

---
id: 5900f40d1000cf542c50ff20
title: 'Problem 161: Triominoes'
challengeType: 5
forumTopicId: 301795
dashedName: problem-161-triominoes
---

# --description--

A triomino is a shape consisting of three squares joined via the edges.

There are two basic forms:

<img class="img-responsive center-block" alt="two basic triominoes forms" src="https://cdn.freecodecamp.org/curriculum/project-euler/triominoes-1.gif" style="background-color: white; padding: 10px;">

If all possible orientations are taken into account there are six:

<img class="img-responsive center-block" alt="triominoes forms including orientation" src="https://cdn.freecodecamp.org/curriculum/project-euler/triominoes-2.gif" style="background-color: white; padding: 10px;">

Any n by m grid for which nxm is divisible by 3 can be tiled with triominoes. If we consider tilings that can be obtained by reflection or rotation from another tiling as different there are 41 ways a 2 by 9 grid can be tiled with triominoes:

<img class="img-responsive center-block" alt="animation showing 41 ways of filling 2x9 grid with triominoes" src="https://cdn.freecodecamp.org/curriculum/project-euler/triominoes-3.gif" style="background-color: white; padding: 10px;">

In how many ways can a 9 by 12 grid be tiled in this way by triominoes?

# --hints--

`triominoes()` should return `20574308184277972`.

```js
assert.strictEqual(triominoes(), 20574308184277972);
```

# --seed--

## --seed-contents--

```js
function triominoes() {

  return true;
}

triominoes();
```

# --solutions--

```js
// solution required
```