---
id: 5900f5081000cf542c510019
title: 'Problem 411: Uphill paths'
challengeType: 5
forumTopicId: 302080
dashedName: problem-411-uphill-paths
---

# --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.

# --hints--

`euler411()` should return 9936352.

```js
assert.strictEqual(euler411(), 9936352);
```

# --seed--

## --seed-contents--

```js
function euler411() {

  return true;
}

euler411();
```

# --solutions--

```js
// solution required
```