397a9f0c3e
* fix: clean-up Project Euler 462-480 * fix: missing image extension * 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
997 B
Markdown
49 lines
997 B
Markdown
---
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id: 5900f5411000cf542c510053
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title: 'Problem 469: Empty chairs'
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challengeType: 5
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forumTopicId: 302144
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dashedName: problem-469-empty-chairs
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---
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# --description--
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In a room $N$ chairs are placed around a round table.
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Knights enter the room one by one and choose at random an available empty chair.
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To have enough elbow room the knights always leave at least one empty chair between each other.
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When there aren't any suitable chairs left, the fraction $C$ of empty chairs is determined. We also define $E(N)$ as the expected value of $C$.
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We can verify that $E(4) = \frac{1}{2}$ and $E(6) = \frac{5}{9}$.
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Find $E({10}^{18})$. Give your answer rounded to fourteen decimal places in the form 0.abcdefghijklmn.
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# --hints--
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`emptyChairs()` should return `0.56766764161831`.
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```js
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assert.strictEqual(emptyChairs(), 0.56766764161831);
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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 emptyChairs() {
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return true;
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}
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emptyChairs();
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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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