47 lines
2.0 KiB
Markdown
47 lines
2.0 KiB
Markdown
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---
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id: 5900f4a71000cf542c50ffb9
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title: 'Problem 314: The Mouse on the Moon'
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challengeType: 5
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forumTopicId: 301970
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dashedName: problem-314-the-mouse-on-the-moon
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---
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# --description--
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The moon has been opened up, and land can be obtained for free, but there is a catch. You have to build a wall around the land that you stake out, and building a wall on the moon is expensive. Every country has been allotted a 500 m by 500 m square area, but they will possess only that area which they wall in. 251001 posts have been placed in a rectangular grid with 1 meter spacing. The wall must be a closed series of straight lines, each line running from post to post.
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The bigger countries of course have built a 2000 m wall enclosing the entire 250 000 m2 area. The Duchy of Grand Fenwick, has a tighter budget, and has asked you (their Royal Programmer) to compute what shape would get best maximum enclosed-area/wall-length ratio.
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You have done some preliminary calculations on a sheet of paper. For a 2000 meter wall enclosing the 250 000 m2 area the enclosed-area/wall-length ratio is 125. Although not allowed , but to get an idea if this is anything better: if you place a circle inside the square area touching the four sides the area will be equal to π*2502 m2 and the perimeter will be π*500 m, so the enclosed-area/wall-length ratio will also be 125.
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However, if you cut off from the square four triangles with sides 75 m, 75 m and 75√2 m the total area becomes 238750 m2 and the perimeter becomes 1400+300√2 m. So this gives an enclosed-area/wall-length ratio of 130.87, which is significantly better.
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Find the maximum enclosed-area/wall-length ratio. Give your answer rounded to 8 places behind the decimal point in the form abc.defghijk.
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# --hints--
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`euler314()` should return 132.52756426.
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```js
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assert.strictEqual(euler314(), 132.52756426);
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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 euler314() {
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return true;
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}
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euler314();
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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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