63 lines
1018 B
Markdown
63 lines
1018 B
Markdown
---
|
||
id: 5900f43e1000cf542c50ff50
|
||
challengeType: 5
|
||
title: 'Problem 210: Obtuse Angled Triangles'
|
||
forumTopicId: 301852
|
||
---
|
||
|
||
## Description
|
||
<section id='description'>
|
||
Consider the set S(r) of points (x,y) with integer coordinates satisfying |x| + |y| ≤ r.
|
||
Let O be the point (0,0) and C the point (r/4,r/4).
|
||
Let N(r) be the number of points B in S(r), so that the triangle OBC has an obtuse angle, i.e. the largest angle α satisfies 90°<α<180°.
|
||
So, for example, N(4)=24 and N(8)=100.
|
||
|
||
What is N(1,000,000,000)?
|
||
</section>
|
||
|
||
## Instructions
|
||
<section id='instructions'>
|
||
|
||
</section>
|
||
|
||
## Tests
|
||
<section id='tests'>
|
||
|
||
```yml
|
||
tests:
|
||
- text: <code>euler210()</code> should return 1598174770174689500.
|
||
testString: assert.strictEqual(euler210(), 1598174770174689500);
|
||
|
||
```
|
||
|
||
</section>
|
||
|
||
## Challenge Seed
|
||
<section id='challengeSeed'>
|
||
|
||
<div id='js-seed'>
|
||
|
||
```js
|
||
function euler210() {
|
||
|
||
return true;
|
||
}
|
||
|
||
euler210();
|
||
```
|
||
|
||
</div>
|
||
|
||
|
||
|
||
</section>
|
||
|
||
## Solution
|
||
<section id='solution'>
|
||
|
||
```js
|
||
// solution required
|
||
```
|
||
|
||
</section>
|