66 lines
2.2 KiB
Markdown
66 lines
2.2 KiB
Markdown
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---
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id: 5
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localeTitle: 5900f3861000cf542c50fe99
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challengeType: 5
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title: 'Problem 26: Reciprocal cycles'
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---
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## Description
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<section id='description'>
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Una fracción unitaria contiene 1 en el numerador. Se da la representación decimal de las fracciones unitarias con denominadores 2 a 10:
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<div style='padding-left: 4em; display: inline-grid; grid-template-rows: auto; row-gap: 7px;'><div> <sup><sub>Media</sub></sup> = 0,5 </div><div> <sup><sub>1/3</sub></sup> = 0. (3) </div><div> <sup><sub>1/4</sub></sup> = 0,25 </div><div> <sup><sub>1/5</sub></sup> = 0,2 </div><div> <sup><sub>1/6</sub></sup> = 0,1 (6) </div><div> <sup><sub>Séptima</sub></sup> = 0. (142857) </div><div> <sup><sub>1/8</sub></sup> = 0,125 </div><div> <sup><sub>1/9</sub></sup> = 0. (1) </div><div> <sup><sub>1/10</sub></sup> = 0,1 </div></div>
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Donde 0.1 (6) significa 0.166666 ..., y tiene un ciclo recurrente de 1 dígito. Puede ser visto que <sup><sub>1/7</sub></sup> tiene un ciclo recurrente de 6 dígitos.
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Encuentre el valor de <var>d</var> < <var>n</var> para el cual <sup>1</sup> / <sub>d</sub> contiene el ciclo recurrente más largo en su parte de fracción decimal.
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</section>
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## Instructions
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<section id='instructions'>
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</section>
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## Tests
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<section id='tests'>
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```yml
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tests:
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- text: <code>reciprocalCycles(700)</code> deben devolver 659.
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testString: 'assert(reciprocalCycles(700) == 659, "<code>reciprocalCycles(700)</code> should return 659.");'
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- text: <code>reciprocalCycles(800)</code> deben devolver 743.
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testString: 'assert(reciprocalCycles(800) == 743, "<code>reciprocalCycles(800)</code> should return 743.");'
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- text: <code>reciprocalCycles(900)</code> deben devolver 887.
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testString: 'assert(reciprocalCycles(900) == 887, "<code>reciprocalCycles(900)</code> should return 887.");'
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- text: <code>reciprocalCycles(1000)</code> deben devolver 983.
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testString: 'assert(reciprocalCycles(1000) == 983, "<code>reciprocalCycles(1000)</code> should return 983.");'
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```
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</section>
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## Challenge Seed
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<section id='challengeSeed'>
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<div id='js-seed'>
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```js
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function reciprocalCycles(n) {
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// Good luck!
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return n;
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}
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reciprocalCycles(1000);
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```
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</div>
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</section>
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## Solution
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<section id='solution'>
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```js
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// solution required
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```
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</section>
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