73 lines
1.1 KiB
Markdown
73 lines
1.1 KiB
Markdown
---
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id: 5900f5351000cf542c510047
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challengeType: 5
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title: 'Problem 456: Triangles containing the origin II'
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forumTopicId: 302130
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---
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## Description
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<section id='description'>
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Define:xn = (1248n mod 32323) - 16161yn = (8421n mod 30103) - 15051
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Pn = {(x1, y1), (x2, y2), ..., (xn, yn)}
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For example, P8 = {(-14913, -6630), (-10161, 5625), (5226, 11896), (8340, -10778), (15852, -5203), (-15165, 11295), (-1427, -14495), (12407, 1060)}.
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Let C(n) be the number of triangles whose vertices are in Pn which contain the origin in the interior.
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Examples:
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C(8) = 20
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C(600) = 8950634
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C(40 000) = 2666610948988
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Find C(2 000 000).
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</section>
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## Instructions
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<section id='instructions'>
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</section>
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## Tests
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<section id='tests'>
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```yml
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tests:
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- text: <code>euler456()</code> should return 333333208685971500.
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testString: assert.strictEqual(euler456(), 333333208685971500);
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```
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</section>
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## Challenge Seed
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<section id='challengeSeed'>
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<div id='js-seed'>
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```js
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function euler456() {
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// Good luck!
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return true;
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}
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euler456();
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```
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</div>
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</section>
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## Solution
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<section id='solution'>
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```js
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// solution required
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```
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</section>
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