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---
id: 5900f3761000cf542c50fe88
challengeType: 5
title: 'Problem 9: Special Pythagorean triplet'
---
## Description
< section id = 'description' >
A Pythagorean triplet is a set of three natural numbers, < var > a< / var > < < var > b< / var > < < var > c< / var > , for which,
< div style = 'text-align: center;' > < var > a< / var > < sup > 2< / sup > + < var > b< / var > < sup > 2< / sup > = < var > c< / var > < sup > 2< / sup > < / div >
For example, 3< sup > 2< / sup > + 4< sup > 2< / sup > = 9 + 16 = 25 = 5< sup > 2< / sup > .
There exists exactly one Pythagorean triplet for which < var > a< / var > + < var > b< / var > + < var > c< / var > = 1000. Find the product < var > abc< / var > such that < var > a< / var > + < var > b< / var > + < var > c< / var > = < code > n< / code > .
< / section >
## Instructions
< section id = 'instructions' >
< / section >
## Tests
< section id = 'tests' >
```yml
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tests:
- text: < code > specialPythagoreanTriplet(1000)</ code > should return 31875000.
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testString: assert.strictEqual(specialPythagoreanTriplet(1000), 31875000, '< code > specialPythagoreanTriplet(1000)< / code > should return 31875000.');
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- text: < code > specialPythagoreanTriplet(24)</ code > should return 480.
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testString: assert.strictEqual(specialPythagoreanTriplet(24), 480, '< code > specialPythagoreanTriplet(24)< / code > should return 480.');
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- text: < code > specialPythagoreanTriplet(120)</ code > should return 49920.
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testString: assert.strictEqual(specialPythagoreanTriplet(120), 49920, '< code > specialPythagoreanTriplet(120)< / code > should return 49920.');
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```
< / section >
## Challenge Seed
< section id = 'challengeSeed' >
< div id = 'js-seed' >
```js
function specialPythagoreanTriplet(n) {
let sumOfabc = n;
// Good luck!
return true;
}
specialPythagoreanTriplet(1000);
```
< / div >
< / section >
## Solution
< section id = 'solution' >
```js
const specialPythagoreanTriplet = (n)=>{
let sumOfabc = n;
let a,b,c;
for(a = 1; a< =sumOfabc/3; a++){
for(b = a+1; b< =sumOfabc/2; b++){
c = Math.sqrt(a*a+b*b);
if((a+b+c) == sumOfabc){
return a*b*c;
}
}
}
}
```
< / section >