---
id: 5900f4a31000cf542c50ffb6
challengeType: 5
title: 'Problem 311: Biclinic Integral Quadrilaterals'
---

## Description
<section id='description'>
ABCD is a convex, integer sided quadrilateral with 1 ≤ AB < BC < CD < AD.
BD has integer length. O is the midpoint of BD. AO has integer length.
We'll call ABCD a biclinic integral quadrilateral if AO = CO ≤ BO = DO.

For example, the following quadrilateral is a biclinic integral quadrilateral:
AB = 19, BC = 29, CD = 37, AD = 43, BD = 48 and AO = CO = 23.




Let B(N) be the number of distinct biclinic integral quadrilaterals ABCD that satisfy AB2+BC2+CD2+AD2 ≤ N.
We can verify that B(10 000) = 49 and B(1 000 000) = 38239.


Find B(10 000 000 000).
</section>

## Instructions
<section id='instructions'>

</section>

## Tests
<section id='tests'>

```yml
tests:
  - text: <code>euler311()</code> should return 2466018557.
    testString: assert.strictEqual(euler311(), 2466018557, '<code>euler311()</code> should return 2466018557.');

```

</section>

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

<div id='js-seed'>

```js
function euler311() {
  // Good luck!
  return true;
}

euler311();
```

</div>



</section>

## Solution
<section id='solution'>

```js
// solution required
```

</section>