79d9012432
* fix(curriculum): tests quotes * fix(curriculum): fill seed-teardown * fix(curriculum): fix tests and remove unneeded seed-teardown
68 lines
1.3 KiB
Markdown
68 lines
1.3 KiB
Markdown
---
|
|
id: 5900f5081000cf542c510019
|
|
challengeType: 5
|
|
title: 'Problem 411: Uphill paths'
|
|
---
|
|
|
|
## Description
|
|
<section id='description'>
|
|
Let n be a positive integer. Suppose there are stations at the coordinates (x, y) = (2i mod n, 3i mod n) for 0 ≤ i ≤ 2n. We will consider stations with the same coordinates as the same station.
|
|
|
|
We wish to form a path from (0, 0) to (n, n) such that the x and y coordinates never decrease.
|
|
Let S(n) be the maximum number of stations such a path can pass through.
|
|
|
|
For example, if n = 22, there are 11 distinct stations, and a valid path can pass through at most 5 stations. Therefore, S(22) = 5.
|
|
The case is illustrated below, with an example of an optimal path:
|
|
|
|
|
|
|
|
It can also be verified that S(123) = 14 and S(10000) = 48.
|
|
|
|
Find ∑ S(k5) for 1 ≤ k ≤ 30.
|
|
</section>
|
|
|
|
## Instructions
|
|
<section id='instructions'>
|
|
|
|
</section>
|
|
|
|
## Tests
|
|
<section id='tests'>
|
|
|
|
```yml
|
|
tests:
|
|
- text: <code>euler411()</code> should return 9936352.
|
|
testString: assert.strictEqual(euler411(), 9936352, '<code>euler411()</code> should return 9936352.');
|
|
|
|
```
|
|
|
|
</section>
|
|
|
|
## Challenge Seed
|
|
<section id='challengeSeed'>
|
|
|
|
<div id='js-seed'>
|
|
|
|
```js
|
|
function euler411() {
|
|
// Good luck!
|
|
return true;
|
|
}
|
|
|
|
euler411();
|
|
```
|
|
|
|
</div>
|
|
|
|
|
|
|
|
</section>
|
|
|
|
## Solution
|
|
<section id='solution'>
|
|
|
|
```js
|
|
// solution required
|
|
```
|
|
</section>
|