freeCodeCamp/guide/english/certifications/coding-interview-prep/project-euler/problem-9-special-pythagorean-triplet/index.md

---
title: 'Problem 9: Special Pythagorean triplet'
---
# Problem 9: Special Pythagorean triplet

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## Problem Explanation
- In this challenge we need to find the pythagorean triple.
- We have the following information - `a < b < c`
- Based on this, we can make a loop starting from `a = 0` and `b = a` since `a < b` always.
- We also know that `a + b + c = n` and `a^2 + b^2 = c^2`, since we have `a`, `b` and `n`. We can find `c` and see if it satisfies the triplet theorem.


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## Solutions
<details><summary>Solution 1 (Click to Show/Hide)</summary>

```js
function specialPythagoreanTriplet(n) {
  let sumOfabc = n;
  for (let a = 1; a < n; a++) {
    for (let b = a; b < n; b++) {
      let c = n - a - b;
      if (c > 0) {
        if (c ** 2 == a ** 2 + b ** 2) {
          return a * b * c;
        }
      }
    }
  }
}

specialPythagoreanTriplet(1000);
```

#### Relevant Links
- [Wikipedia](https://en.wikipedia.org/wiki/Pythagorean_triple)

</details>