5a52c229f5
* fix: clean-up Project Euler 181-200 * fix: corrections from review Co-authored-by: Tom <20648924+moT01@users.noreply.github.com> * fix: missing delimiter Co-authored-by: Tom <20648924+moT01@users.noreply.github.com>
47 lines
1.6 KiB
Markdown
47 lines
1.6 KiB
Markdown
---
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id: 5900f4241000cf542c50ff37
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title: 'Problem 184: Triangles containing the origin'
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challengeType: 5
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forumTopicId: 301820
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dashedName: problem-184-triangles-containing-the-origin
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---
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# --description--
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Consider the set $I_r$ of points $(x,y)$ with integer coordinates in the interior of the circle with radius $r$, centered at the origin, i.e. $x^2 + y^2 < r^2$.
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For a radius of 2, $I_2$ contains the nine points (0,0), (1,0), (1,1), (0,1), (-1,1), (-1,0), (-1,-1), (0,-1) and (1,-1). There are eight triangles having all three vertices in $I_2$ which contain the origin in the interior. Two of them are shown below, the others are obtained from these by rotation.
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<img class="img-responsive center-block" alt="circle with radius 2, centered at the origin, with nine marked points and two triangles - (-1,0), (0,1), (1,-1) and (-1,1), (0,-1), (1,1)" src="https://cdn.freecodecamp.org/curriculum/project-euler/triangles-containing-the-origin.gif" style="background-color: white; padding: 10px;">
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For a radius of 3, there are 360 triangles containing the origin in the interior and having all vertices in $I_3$ and for $I_5$ the number is 10600.
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How many triangles are there containing the origin in the interior and having all three vertices in $I_{105}$?
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# --hints--
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`trianglesConttainingOrigin()` should return `1725323624056`.
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```js
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assert.strictEqual(trianglesConttainingOrigin(), 1725323624056);
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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 trianglesContainingOrigin() {
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return true;
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}
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trianglesContainingOrigin();
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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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