---
id: 5900f37b1000cf542c50fe8e
challengeType: 5
title: 'Problem 15: Lattice paths'
---

## Description
<section id='description'>
Starting in the top left corner of a 2×2 grid, and only being able to move to the right and down, there are exactly 6 routes to the bottom right corner.

<img class="img-responsive center-block" alt="a diagram of 6 2 by 2 grids showing all the routes to the bottom right corner" src="https://i.imgur.com/1Atixoj.gif">

How many such routes are there through a given <code>gridSize</code>?
</section>

## Instructions
<section id='instructions'>

</section>

## Tests
<section id='tests'>

```yml
- text: <code>latticePaths(4)</code> should return 70.
  testString: 'assert.strictEqual(latticePaths(4), 70, ''<code>latticePaths(4)</code> should return 70.'');'
- text: <code>latticePaths(9)</code> should return 48620.
  testString: 'assert.strictEqual(latticePaths(9), 48620, ''<code>latticePaths(9)</code> should return 48620.'');'
- text: <code>latticePaths(20)</code> should return 137846528820.
  testString: 'assert.strictEqual(latticePaths(20), 137846528820, ''<code>latticePaths(20)</code> should return 137846528820.'');'

```

</section>

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

<div id='js-seed'>

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

latticePaths(4);
```

</div>



</section>

## Solution
<section id='solution'>


```js
function latticePaths(gridSize) {
  let paths = 1;

  for (let i = 0; i < gridSize; i++) {
    paths *= (2 * gridSize) - i;
    paths /= i + 1;
  }
  return paths;
}
```

</section>