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Feat: add new Markdown parser (#39800)

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and change all the challenges to new `md` format.
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Oliver Eyton-Williams
2020-11-27 19:02:05 +01:00
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curriculum/challenges/english/10-coding-interview-prep/project-euler/problem-318-2011-nines.md
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@ -1,62 +1,55 @@
---
id: 5900f4ab1000cf542c50ffbd
challengeType: 5
title: 'Problem 318: 2011 nines'
challengeType: 5
forumTopicId: 301974
---
## Description
<section id='description'>
# --description--
Consider the real number √2+√3.
When we calculate the even powers of √2+√3
we get:
(√2+√3)2 = 9.898979485566356...
(√2+√3)4 = 97.98979485566356...
(√2+√3)6 = 969.998969071069263...
(√2+√3)8 = 9601.99989585502907...
(√2+√3)10 = 95049.999989479221...
(√2+√3)12 = 940897.9999989371855...
(√2+√3)14 = 9313929.99999989263...
(√2+√3)16 = 92198401.99999998915...
It looks like that the number of consecutive nines at the beginning of the fractional part of these powers is non-decreasing.
In fact it can be proven that the fractional part of (√2+√3)2n approaches 1 for large n.
It looks like that the number of consecutive nines at the beginning of the fractional part of these powers is non-decreasing. In fact it can be proven that the fractional part of (√2+√3)2n approaches 1 for large n.
Consider all real numbers of the form √p+√q with p and q positive integers and p&lt;q, such that the fractional part of (√p+√q)2n approaches 1 for large n.
Consider all real numbers of the form √p+√q with p and q positive integers and p<q, such that the fractional part
of (√p+√q)2n approaches 1 for large n.
Let C(p,q,n) be the number of consecutive nines at the beginning of the fractional part of (√p+√q)2n.
Let C(p,q,n) be the number of consecutive nines at the beginning of the fractional part of (√p+√q)2n.
Let N(p,q) be the minimal value of n such that C(p,q,n) ≥ 2011.
Find ∑N(p,q) for p+q ≤ 2011.
</section>
## Instructions
<section id='instructions'>
# --hints--
</section>
## Tests
<section id='tests'>
```yml
tests:
- text: <code>euler318()</code> should return 709313889.
testString: assert.strictEqual(euler318(), 709313889);
`euler318()` should return 709313889.
```js
assert.strictEqual(euler318(), 709313889);
```
</section>
# --seed--
## Challenge Seed
<section id='challengeSeed'>
<div id='js-seed'>
## --seed-contents--
```js
function euler318() {
@ -67,17 +60,8 @@ function euler318() {
euler318();
```
</div>
</section>
## Solution
<section id='solution'>
# --solutions--
```js
// solution required
```
</section>