71 lines
1.4 KiB
Markdown
71 lines
1.4 KiB
Markdown
---
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id: 5900f51a1000cf542c51002d
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challengeType: 5
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title: 'Problem 430: Range flips'
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---
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## Description
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<section id='description'>
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N disks are placed in a row, indexed 1 to N from left to right.
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Each disk has a black side and white side. Initially all disks show their white side.
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At each turn, two, not necessarily distinct, integers A and B between 1 and N (inclusive) are chosen uniformly at random.
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All disks with an index from A to B (inclusive) are flipped.
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The following example shows the case N = 8. At the first turn A = 5 and B = 2, and at the second turn A = 4 and B = 6.
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Let E(N, M) be the expected number of disks that show their white side after M turns.
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We can verify that E(3, 1) = 10/9, E(3, 2) = 5/3, E(10, 4) ≈ 5.157 and E(100, 10) ≈ 51.893.
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Find E(1010, 4000).
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Give your answer rounded to 2 decimal places behind the decimal point.
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</section>
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## Instructions
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<section id='instructions'>
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</section>
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## Tests
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<section id='tests'>
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```yml
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tests:
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- text: <code>euler430()</code> should return 5000624921.38.
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testString: assert.strictEqual(euler430(), 5000624921.38, '<code>euler430()</code> should return 5000624921.38.');
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```
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</section>
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## Challenge Seed
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<section id='challengeSeed'>
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<div id='js-seed'>
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```js
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function euler430() {
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// Good luck!
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return true;
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}
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euler430();
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```
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</div>
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</section>
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## Solution
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<section id='solution'>
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```js
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// solution required
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```
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</section>
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