---
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>
