eef1805fe6
* fix: clean-up Project Euler 201-220 * fix: corrections from review Co-authored-by: Tom <20648924+moT01@users.noreply.github.com> Co-authored-by: Tom <20648924+moT01@users.noreply.github.com>
47 lines
931 B
Markdown
47 lines
931 B
Markdown
---
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id: 5900f43e1000cf542c50ff50
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title: 'Problem 210: Obtuse Angled Triangles'
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challengeType: 5
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forumTopicId: 301852
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dashedName: problem-210-obtuse-angled-triangles
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---
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# --description--
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Consider the set $S(r)$ of points ($x$,$y$) with integer coordinates satisfying $|x| + |y| ≤ r$.
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Let $O$ be the point (0,0) and $C$ the point ($\frac{r}{4}$,$\frac{r}{4}$).
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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 $90°<α<180°$.
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So, for example, $N(4)=24$ and $N(8)=100$.
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What is $N(1\\,000\\,000\\,000)$?
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# --hints--
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`obtuseAngledTriangles()` should return `1598174770174689500`.
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```js
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assert.strictEqual(obtuseAngledTriangles(), 1598174770174689500);
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```
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# --seed--
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## --seed-contents--
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```js
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function obtuseAngledTriangles() {
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return true;
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}
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obtuseAngledTriangles();
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```
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# --solutions--
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```js
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// solution required
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```
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