51 lines
1.4 KiB
Markdown
51 lines
1.4 KiB
Markdown
---
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id: 5900f5081000cf542c510019
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title: 'Problem 411: Uphill paths'
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challengeType: 5
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forumTopicId: 302080
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dashedName: problem-411-uphill-paths
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---
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# --description--
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Let $n$ be a positive integer. Suppose there are stations at the coordinates $(x, y) = (2^i\bmod n, 3^i\bmod n)$ for $0 ≤ i ≤ 2n$. We will consider stations with the same coordinates as the same station.
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We wish to form a path from (0, 0) to ($n$, $n$) such that the $x$ and $y$ coordinates never decrease.
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Let $S(n)$ be the maximum number of stations such a path can pass through.
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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:
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<img class="img-responsive center-block" alt="valid path passing through 5 stations, for n = 22, with 11 distinct stations" src="https://cdn.freecodecamp.org/curriculum/project-euler/uphill-paths.png" style="background-color: white; padding: 10px;">
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It can also be verified that $S(123) = 14$ and $S(10\\,000) = 48$.
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Find $\sum S(k^5)$ for $1 ≤ k ≤ 30$.
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# --hints--
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`uphillPaths()` should return `9936352`.
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```js
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assert.strictEqual(uphillPaths(), 9936352);
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```
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# --seed--
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## --seed-contents--
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```js
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function uphillPaths() {
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return true;
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}
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uphillPaths();
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```
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# --solutions--
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```js
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// solution required
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```
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