---
id: 5900f3931000cf542c50fea6
challengeType: 5
title: 'Problem 39: Integer right triangles'
---

## Description
<section id='description'>
If p is the perimeter of a right angle triangle with integral length sides, {a,b,c}, there are exactly three solutions for p = 120.
{20,48,52}, {24,45,51}, {30,40,50}
For which value of p ≤ n, is the number of solutions maximised?
</section>

## Instructions
<section id='instructions'>

</section>

## Tests
<section id='tests'>

```yml
tests:
  - text: <code>intRightTriangles(500)</code> should return 420.
    testString: assert(intRightTriangles(500) == 420, '<code>intRightTriangles(500)</code> should return 420.');
  - text: <code>intRightTriangles(800)</code> should return 420.
    testString: assert(intRightTriangles(800) == 420, '<code>intRightTriangles(800)</code> should return 420.');
  - text: <code>intRightTriangles(900)</code> should return 840.
    testString: assert(intRightTriangles(900) == 840, '<code>intRightTriangles(900)</code> should return 840.');
  - text: <code>intRightTriangles(1000)</code> should return 840.
    testString: assert(intRightTriangles(1000) == 840, '<code>intRightTriangles(1000)</code> should return 840.');

```

</section>

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

<div id='js-seed'>

```js
function intRightTriangles(n) {
  // Good luck!
  return n;
}

intRightTriangles(1000);
```

</div>



</section>

## Solution
<section id='solution'>

```js
// solution required
```

</section>