45 lines
1.1 KiB
Markdown
45 lines
1.1 KiB
Markdown
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---
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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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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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There are exactly 5482 grids for which S(m,n) = p2, where p < 100 is prime.
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How many grids does S(m,n) = p2, where p < 106 is prime?
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# --hints--
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`euler313()` should return 2057774861813004.
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```js
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assert.strictEqual(euler313(), 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 euler313() {
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return true;
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}
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euler313();
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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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