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curriculum/challenges/italian/10-coding-interview-prep/project-euler/problem-411-uphill-paths.md

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+---
+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
+```