47 lines
1.3 KiB
Markdown
47 lines
1.3 KiB
Markdown
---
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id: 5900f4371000cf542c50ff49
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title: 'Problem 202: Laserbeam'
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challengeType: 5
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forumTopicId: 301843
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dashedName: problem-202-laserbeam
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---
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# --description--
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Three mirrors are arranged in the shape of an equilateral triangle, with their reflective surfaces pointing inwards. There is an infinitesimal gap at each vertex of the triangle through which a laser beam may pass.
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Label the vertices $A$, $B$ and $C$. There are 2 ways in which a laser beam may enter vertex $C$, bounce off 11 surfaces, then exit through the same vertex: one way is shown below; the other is the reverse of that.
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<img class="img-responsive center-block" alt="one way in which laser beam may enter vertex C, bounce off 11 surfaces and exit through the same vertex" src="https://cdn.freecodecamp.org/curriculum/project-euler/laserbeam.gif" style="background-color: white; padding: 10px;">
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There are 80840 ways in which a laser beam may enter vertex $C$, bounce off 1000001 surfaces, then exit through the same vertex.
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In how many ways can a laser beam enter at vertex $C$, bounce off 12017639147 surfaces, then exit through the same vertex?
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# --hints--
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`laserbeam()` should return `1209002624`.
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```js
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assert.strictEqual(laserbeam(), 1209002624);
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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 laserbeam() {
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return true;
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}
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laserbeam();
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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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