1af6e7aa5a
* fix: clean-up Project Euler 321-340 * fix: typo * fix: corrections from review Co-authored-by: Sem Bauke <46919888+Sembauke@users.noreply.github.com> * fix: corrections from review Co-authored-by: Tom <20648924+moT01@users.noreply.github.com> Co-authored-by: Sem Bauke <46919888+Sembauke@users.noreply.github.com> Co-authored-by: Tom <20648924+moT01@users.noreply.github.com>
45 lines
1.5 KiB
Markdown
45 lines
1.5 KiB
Markdown
---
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id: 5900f4c01000cf542c50ffd2
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title: 'Problem 339: Peredur fab Efrawg'
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challengeType: 5
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forumTopicId: 301997
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dashedName: problem-339-peredur-fab-efrawg
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---
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# --description--
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"And he came towards a valley, through which ran a river; and the borders of the valley were wooded, and on each side of the river were level meadows. And on one side of the river he saw a flock of white sheep, and on the other a flock of black sheep. And whenever one of the white sheep bleated, one of the black sheep would cross over and become white; and when one of the black sheep bleated, one of the white sheep would cross over and become black." - Peredur the Son of Evrawc
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Initially, each flock consists of $n$ sheep. Each sheep (regardless of color) is equally likely to be the next sheep to bleat. After a sheep has bleated and a sheep from the other flock has crossed over, Peredur may remove a number of white sheep in order to maximize the expected final number of black sheep. Let $E(n)$ be the expected final number of black sheep if Peredur uses an optimal strategy.
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You are given that $E(5) = 6.871346$ rounded to 6 places behind the decimal point.
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Find $E(10\\,000)$ and give your answer rounded to 6 places behind the decimal point.
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# --hints--
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`peredurFabEfrawg()` should return `19823.542204`.
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```js
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assert.strictEqual(peredurFabEfrawg(), 19823.542204);
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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 peredurFabEfrawg() {
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return true;
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}
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peredurFabEfrawg();
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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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