---
id: 5900f4a61000cf542c50ffb8
title: 'Problem 313: Sliding game'
challengeType: 5
forumTopicId: 301969
dashedName: problem-313-sliding-game
---

# --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 &lt; 100 is prime.

How many grids does S(m,n) = p2, where p &lt; 106 is prime?

# --hints--

`euler313()` should return 2057774861813004.

```js
assert.strictEqual(euler313(), 2057774861813004);
```

# --seed--

## --seed-contents--

```js
function euler313() {

  return true;
}

euler313();
```

# --solutions--

```js
// solution required
```
