72 lines
1.2 KiB
Markdown
72 lines
1.2 KiB
Markdown
---
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id: 5900f4a31000cf542c50ffb6
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challengeType: 5
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title: 'Problem 311: Biclinic Integral Quadrilaterals'
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forumTopicId: 301967
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---
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## Description
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<section id='description'>
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ABCD is a convex, integer sided quadrilateral with 1 ≤ AB < BC < CD < AD.
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BD has integer length. O is the midpoint of BD. AO has integer length.
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We'll call ABCD a biclinic integral quadrilateral if AO = CO ≤ BO = DO.
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For example, the following quadrilateral is a biclinic integral quadrilateral:
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AB = 19, BC = 29, CD = 37, AD = 43, BD = 48 and AO = CO = 23.
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Let B(N) be the number of distinct biclinic integral quadrilaterals ABCD that satisfy AB2+BC2+CD2+AD2 ≤ N.
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We can verify that B(10 000) = 49 and B(1 000 000) = 38239.
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Find B(10 000 000 000).
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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>euler311()</code> should return 2466018557.
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testString: assert.strictEqual(euler311(), 2466018557);
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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 euler311() {
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// Good luck!
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return true;
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}
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euler311();
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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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