---
id: 5900f4a61000cf542c50ffb8
challengeType: 5
title: 'Problem 313: Sliding game'
---

## Description
<section id='description'>
In a sliding game a counter may slide horizontally or vertically into an empty space. The objective of the game is to move the red counter from the top left corner of a grid to the bottom right corner; the space always starts in the bottom right corner. For example, the following sequence of pictures show how the game can be completed in five moves on a 2 by 2 grid.



Let S(m,n) represent the minimum number of moves to complete the game on an m by n grid. For example, it can be verified that S(5,4) = 25.



There are exactly 5482 grids for which S(m,n) = p2, where p < 100 is prime.

How many grids does S(m,n) = p2, where p < 106 is prime?
</section>

## Instructions
<section id='instructions'>

</section>

## Tests
<section id='tests'>

```yml
tests:
  - text: <code>euler313()</code> should return 2057774861813004.
    testString: 'assert.strictEqual(euler313(), 2057774861813004, "<code>euler313()</code> should return 2057774861813004.");'

```

</section>

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

<div id='js-seed'>

```js
function euler313() {
  // Good luck!
  return true;
}

euler313();
```

</div>



</section>

## Solution
<section id='solution'>

```js
// solution required
```
</section>