47 lines
1.1 KiB
Markdown
47 lines
1.1 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) = (2i mod n, 3i mod 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. 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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It can also be verified that S(123) = 14 and S(10000) = 48.
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Find ∑ S(k5) for 1 ≤ k ≤ 30.
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# --hints--
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`euler411()` should return 9936352.
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```js
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assert.strictEqual(euler411(), 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 euler411() {
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return true;
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}
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euler411();
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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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