freeCodeCamp/curriculum/challenges/english/08-coding-interview-prep/project-euler/problem-312-cyclic-paths-on-sierpiski-graphs.english.md

---
id: 5900f4a51000cf542c50ffb7
challengeType: 5
title: 'Problem 312: Cyclic paths on Sierpiński graphs'
---

## Description
<section id='description'>
- A Sierpiński graph of order-1 (S1) is an equilateral triangle.
- Sn+1 is obtained from Sn by positioning three copies of Sn so that every pair of copies has one common corner.




Let C(n) be the number of cycles that pass exactly once through all the vertices of Sn.
For example, C(3) = 8 because eight such cycles can be drawn on S3, as shown below:




It can also be verified that :
C(1) = C(2) = 1
C(5) = 71328803586048
C(10 000) mod 108 = 37652224
C(10 000) mod 138 = 617720485

Find C(C(C(10 000))) mod 138.
</section>

## Instructions
<section id='instructions'>

</section>

## Tests
<section id='tests'>

```yml
tests:
  - text: <code>euler312()</code> should return 324681947.
    testString: assert.strictEqual(euler312(), 324681947, '<code>euler312()</code> should return 324681947.');

```

</section>

## Challenge Seed
<section id='challengeSeed'>

<div id='js-seed'>

```js
function euler312() {
  // Good luck!
  return true;
}

euler312();
```

</div>



</section>

## Solution
<section id='solution'>

```js
// solution required
```
</section>