---
id: 5900f5351000cf542c510047
challengeType: 5
title: 'Problem 456: Triangles containing the origin II'
forumTopicId: 302130
---

## Description
<section id='description'>
Define:xn = (1248n mod 32323) - 16161yn = (8421n mod 30103) - 15051
Pn = {(x1, y1), (x2, y2), ..., (xn, yn)}


For example, P8 = {(-14913, -6630), (-10161, 5625), (5226, 11896), (8340, -10778), (15852, -5203), (-15165, 11295), (-1427, -14495), (12407, 1060)}.

Let C(n) be the number of triangles whose vertices are in Pn which contain the origin in the interior.


Examples:
C(8) = 20
C(600) = 8950634
C(40 000) = 2666610948988


Find C(2 000 000).
</section>

## Instructions
<section id='instructions'>

</section>

## Tests
<section id='tests'>

```yml
tests:
  - text: <code>euler456()</code> should return 333333208685971500.
    testString: assert.strictEqual(euler456(), 333333208685971500);

```

</section>

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

<div id='js-seed'>

```js
function euler456() {
  // Good luck!
  return true;
}

euler456();
```

</div>



</section>

## Solution
<section id='solution'>

```js
// solution required
```

</section>