32dbe23f5e
* fix: clean-up Project Euler 301-320 * fix: corrections from review Co-authored-by: Tom <20648924+moT01@users.noreply.github.com> Co-authored-by: Tom <20648924+moT01@users.noreply.github.com>
49 lines
1.5 KiB
Markdown
49 lines
1.5 KiB
Markdown
---
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id: 5900f4a61000cf542c50ffb8
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title: 'Problem 313: Sliding game'
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challengeType: 5
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forumTopicId: 301969
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dashedName: problem-313-sliding-game
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---
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# --description--
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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.
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<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;">
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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 $S(5, 4) = 25$.
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<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;">
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There are exactly 5482 grids for which $S(m, n) = p^2$, where $p < 100$ is prime.
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How many grids does $S(m, n) = p^2$, where $p < {10}^6$ is prime?
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# --hints--
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`slidingGame()` should return `2057774861813004`.
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```js
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assert.strictEqual(slidingGame(), 2057774861813004);
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```
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# --seed--
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## --seed-contents--
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```js
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function slidingGame() {
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return true;
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}
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slidingGame();
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```
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# --solutions--
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```js
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// solution required
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```
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