32dbe23f5e
* fix: clean-up Project Euler 301-320 * fix: corrections from review Co-authored-by: Tom <20648924+moT01@users.noreply.github.com> Co-authored-by: Tom <20648924+moT01@users.noreply.github.com>
57 lines
1.6 KiB
Markdown
57 lines
1.6 KiB
Markdown
---
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id: 5900f4a51000cf542c50ffb7
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title: 'Problem 312: Cyclic paths on Sierpiński graphs'
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challengeType: 5
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forumTopicId: 301968
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dashedName: problem-312-cyclic-paths-on-sierpiski-graphs
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---
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# --description--
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- A Sierpiński graph of order-1 ($S_1$) is an equilateral triangle.
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- $S_{n + 1}$ is obtained from $S_n$ by positioning three copies of $S_n$ so that every pair of copies has one common corner.
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<img class="img-responsive center-block" alt="Sierpinski graphs of order-1 to order-5" src="https://cdn.freecodecamp.org/curriculum/project-euler/cyclic-paths-on-sierpinski-graphs-1.gif" style="background-color: white; padding: 10px;">
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Let $C(n)$ be the number of cycles that pass exactly once through all the vertices of $S_n$. For example, $C(3) = 8$ because eight such cycles can be drawn on $S_3$, as shown below:
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<img class="img-responsive center-block" alt="eight cycles that pass exactly once through all vertices of S_3" src="https://cdn.freecodecamp.org/curriculum/project-euler/cyclic-paths-on-sierpinski-graphs-2.gif" style="background-color: white; padding: 10px;">
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It can also be verified that:
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$$\begin{align}
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& C(1) = C(2) = 1 \\\\
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& C(5) = 71\\,328\\,803\\,586\\,048 \\\\
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& C(10 000)\bmod {10}^8 = 37\\,652\\,224 \\\\
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& C(10 000)\bmod {13}^8 = 617\\,720\\,485 \\\\
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\end{align}$$
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Find $C(C(C(10\\,000)))\bmod {13}^8$.
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# --hints--
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`pathsOnSierpinskiGraphs()` should return `324681947`.
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```js
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assert.strictEqual(pathsOnSierpinskiGraphs(), 324681947);
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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 pathsOnSierpinskiGraphs() {
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return true;
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}
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pathsOnSierpinskiGraphs();
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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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