65 lines
1.2 KiB
Markdown
65 lines
1.2 KiB
Markdown
|
---
|
||
|
id: 5900f4fa1000cf542c51000d
|
||
|
challengeType: 5
|
||
|
title: 'Problem 398: Cutting rope'
|
||
|
---
|
||
|
|
||
|
## Description
|
||
|
<section id='description'>
|
||
|
Inside a rope of length n, n-1 points are placed with distance 1 from each other and from the endpoints. Among these points, we choose m-1 points at random and cut the rope at these points to create m segments.
|
||
|
|
||
|
|
||
|
Let E(n, m) be the expected length of the second-shortest segment.
|
||
|
For example, E(3, 2) = 2 and E(8, 3) = 16/7.
|
||
|
Note that if multiple segments have the same shortest length the length of the second-shortest segment is defined as the same as the shortest length.
|
||
|
|
||
|
|
||
|
Find E(107, 100).
|
||
|
Give your answer rounded to 5 decimal places behind the decimal point.
|
||
|
</section>
|
||
|
|
||
|
## Instructions
|
||
|
<section id='instructions'>
|
||
|
|
||
|
</section>
|
||
|
|
||
|
## Tests
|
||
|
<section id='tests'>
|
||
|
|
||
|
```yml
|
||
|
tests:
|
||
|
- text: <code>euler398()</code> should return 2010.59096.
|
||
|
testString: 'assert.strictEqual(euler398(), 2010.59096, ''<code>euler398()</code> should return 2010.59096.'');'
|
||
|
|
||
|
```
|
||
|
|
||
|
</section>
|
||
|
|
||
|
## Challenge Seed
|
||
|
<section id='challengeSeed'>
|
||
|
|
||
|
<div id='js-seed'>
|
||
|
|
||
|
```js
|
||
|
function euler398() {
|
||
|
// Good luck!
|
||
|
return true;
|
||
|
}
|
||
|
|
||
|
euler398();
|
||
|
```
|
||
|
|
||
|
</div>
|
||
|
|
||
|
|
||
|
|
||
|
</section>
|
||
|
|
||
|
## Solution
|
||
|
<section id='solution'>
|
||
|
|
||
|
```js
|
||
|
// solution required
|
||
|
```
|
||
|
</section>
|