69 lines
1.7 KiB
Markdown
69 lines
1.7 KiB
Markdown
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---
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id: 5900f3861000cf542c50fe99
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title: 'Problem 26: Reciprocal cycles'
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challengeType: 5
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forumTopicId: 301908
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dashedName: problem-26-reciprocal-cycles
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---
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# --description--
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A unit fraction contains 1 in the numerator. The decimal representation of the unit fractions with denominators 2 to 10 are given:
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<div style='padding-left: 4em; display: inline-grid; grid-template-rows: auto; row-gap: 7px;'><div><sup>1</sup>/<sub>2</sub> = 0.5</div><div><sup>1</sup>/<sub>3</sub> = 0.(3)</div><div><sup>1</sup>/<sub>4</sub> = 0.25</div><div><sup>1</sup>/<sub>5</sub> = 0.2</div><div><sup>1</sup>/<sub>6</sub> = 0.1(6)</div><div><sup>1</sup>/<sub>7</sub> = 0.(142857)</div><div><sup>1</sup>/<sub>8</sub> = 0.125</div><div><sup>1</sup>/<sub>9</sub> = 0.(1)</div><div><sup>1</sup>/<sub>10</sub> = 0.1</div></div>
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Where 0.1(6) means 0.166666..., and has a 1-digit recurring cycle. It can be seen that <sup>1</sup>/<sub>7</sub> has a 6-digit recurring cycle.
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Find the value of `d` < `n` for which <sup>1</sup>/<sub>d</sub> contains the longest recurring cycle in its decimal fraction part.
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# --hints--
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`reciprocalCycles(700)` should return a number.
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```js
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assert(typeof reciprocalCycles(700) === 'number');
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```
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`reciprocalCycles(700)` should return 659.
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```js
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assert(reciprocalCycles(700) == 659);
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```
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`reciprocalCycles(800)` should return 743.
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```js
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assert(reciprocalCycles(800) == 743);
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```
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`reciprocalCycles(900)` should return 887.
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```js
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assert(reciprocalCycles(900) == 887);
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```
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`reciprocalCycles(1000)` should return 983.
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```js
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assert(reciprocalCycles(1000) == 983);
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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 reciprocalCycles(n) {
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return n;
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}
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reciprocalCycles(1000);
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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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