---
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 $S(m, n) = p^2$, where $p < 100$ is prime.
How many grids does $S(m, n) = p^2$, where $p < {10}^6$ is prime?
# --hints--
`slidingGame()` should return `2057774861813004`.
```js
assert.strictEqual(slidingGame(), 2057774861813004);
```
# --seed--
## --seed-contents--
```js
function slidingGame() {
return true;
}
slidingGame();
```
# --solutions--
```js
// solution required
```