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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-391-hopping-game.md
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@ -1,63 +1,39 @@
---
id: 5900f4f31000cf542c510006
challengeType: 5
title: 'Problem 391: Hopping Game'
challengeType: 5
forumTopicId: 302056
---
## Description
<section id='description'>
Let sk be the number of 1’s when writing the numbers from 0 to k in binary.
For example, writing 0 to 5 in binary, we have 0, 1, 10, 11, 100, 101. There are seven 1’s, so s5 = 7.
The sequence S = {sk : k ≥ 0} starts {0, 1, 2, 4, 5, 7, 9, 12, ...}.
# --description--
Let sk be the number of 1’s when writing the numbers from 0 to k in binary.
For example, writing 0 to 5 in binary, we have 0, 1, 10, 11, 100, 101. There are seven 1’s, so s5 = 7.
The sequence S = {sk : k ≥ 0} starts {0, 1, 2, 4, 5, 7, 9, 12, ...}.
A game is played by two players. Before the game starts, a number n is chosen. A counter c starts at 0. At each turn, the player chooses a number from 1 to n (inclusive) and increases c by that number. The resulting value of c must be a member of S. If there are no more valid moves, the player loses.
For example:
Let n = 5. c starts at 0.
Player 1 chooses 4, so c becomes 0 + 4 = 4.
Player 2 chooses 5, so c becomes 4 + 5 = 9.
Player 1 chooses 3, so c becomes 9 + 3 = 12.
etc.
Note that c must always belong to S, and each player can increase c by at most n.
For example: Let n = 5. c starts at 0. Player 1 chooses 4, so c becomes 0 + 4 = 4. Player 2 chooses 5, so c becomes 4 + 5 = 9. Player 1 chooses 3, so c becomes 9 + 3 = 12. etc. Note that c must always belong to S, and each player can increase c by at most n.
Let M(n) be the highest number the first player can choose at her first turn to force a win, and M(n) = 0 if there is no such move. For example, M(2) = 2, M(7) = 1 and M(20) = 4.
Given Σ(M(n))3 = 8150 for 1 ≤ n ≤ 20.
Find Σ(M(n))3 for 1 ≤ n ≤ 1000.
</section>
## Instructions
<section id='instructions'>
# --hints--
</section>
## Tests
<section id='tests'>
```yml
tests:
- text: <code>euler391()</code> should return 61029882288.
testString: assert.strictEqual(euler391(), 61029882288);
`euler391()` should return 61029882288.
```js
assert.strictEqual(euler391(), 61029882288);
```
</section>
# --seed--
## Challenge Seed
<section id='challengeSeed'>
<div id='js-seed'>
## --seed-contents--
```js
function euler391() {
@ -68,17 +44,8 @@ function euler391() {
euler391();
```
</div>
</section>
## Solution
<section id='solution'>
# --solutions--
```js
// solution required
```
</section>