---
id: 5900f4371000cf542c50ff49
title: 'Problem 202: Laserbeam'
challengeType: 5
forumTopicId: 301843
dashedName: problem-202-laserbeam
---

# --description--

Three mirrors are arranged in the shape of an equilateral triangle, with their reflective surfaces pointing inwards. There is an infinitesimal gap at each vertex of the triangle through which a laser beam may pass.

Label the vertices A, B and C. There are 2 ways in which a laser beam may enter vertex C, bounce off 11 surfaces, then exit through the same vertex: one way is shown below; the other is the reverse of that.

There are 80840 ways in which a laser beam may enter vertex C, bounce off 1000001 surfaces, then exit through the same vertex.

In how many ways can a laser beam enter at vertex C, bounce off 12017639147 surfaces, then exit through the same vertex?

# --hints--

`euler202()` should return 1209002624.

```js
assert.strictEqual(euler202(), 1209002624);
```

# --seed--

## --seed-contents--

```js
function euler202() {

  return true;
}

euler202();
```

# --solutions--

```js
// solution required
```