55 lines
1.4 KiB
Markdown
55 lines
1.4 KiB
Markdown
---
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id: 5900f5001000cf542c510012
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title: 'Problem 404: Crisscross Ellipses'
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challengeType: 5
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forumTopicId: 302072
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dashedName: problem-404-crisscross-ellipses
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---
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# --description--
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$E_a$ is an ellipse with an equation of the form $x^2 + 4y^2 = 4a^2$.
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$E_a'$ is the rotated image of $E_a$ by $θ$ degrees counterclockwise around the origin $O(0, 0)$ for $0° < θ < 90°$.
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<img class="img-responsive center-block" alt="ellipse E_a and ellipse rotated by θ degrees E_a'" src="https://cdn.freecodecamp.org/curriculum/project-euler/crisscross-ellipses.gif" style="background-color: white; padding: 10px;">
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$b$ is the distance to the origin of the two intersection points closest to the origin and $c$ is the distance of the two other intersection points.
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We call an ordered triplet ($a$, $b$, $c$) a canonical ellipsoidal triplet if $a$, $b$ and $c$ are positive integers.
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For example, (209, 247, 286) is a canonical ellipsoidal triplet.
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Let $C(N)$ be the number of distinct canonical ellipsoidal triplets ($a$, $b$, $c$) for $a ≤ N$.
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It can be verified that $C({10}^3) = 7$, $C({10}^4) = 106$ and $C({10}^6) = 11\\,845$.
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Find $C({10}^{17})$.
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# --hints--
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`crisscrossEllipses()` should return `1199215615081353`.
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```js
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assert.strictEqual(crisscrossEllipses(), 1199215615081353);
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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 crisscrossEllipses() {
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return true;
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}
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crisscrossEllipses();
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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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