49 lines
1.5 KiB
Markdown
49 lines
1.5 KiB
Markdown
---
|
|
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.
|
|
|
|
<img class="img-responsive center-block" alt="completing game in five moves on grid 2x2" src="https://cdn.freecodecamp.org/curriculum/project-euler/sliding-game-1.gif" style="background-color: white; padding: 10px;">
|
|
|
|
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 $S(5, 4) = 25$.
|
|
|
|
<img class="img-responsive center-block" alt="initial grid state and final grid state for game on grid 5x4" src="https://cdn.freecodecamp.org/curriculum/project-euler/sliding-game-2.gif" style="background-color: white; padding: 10px;">
|
|
|
|
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
|
|
```
|