---
id: 5900f3861000cf542c50fe99
challengeType: 5
title: 'Problem 26: Reciprocal cycles'
---

## Description
<section id='description'>
A unit fraction contains 1 in the numerator. The decimal representation of the unit fractions with denominators 2 to 10 are given:
<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>
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.
Find the value of <var>d</var> < <var>n</var> for which <sup>1</sup>/<sub>d</sub> contains the longest recurring cycle in its decimal fraction part.
</section>

## Instructions
<section id='instructions'>

</section>

## Tests
<section id='tests'>

```yml
tests:
  - text: <code>reciprocalCycles(700)</code> should return 659.
    testString: 'assert(reciprocalCycles(700) == 659, ''<code>reciprocalCycles(700)</code> should return 659.'');'
  - text: <code>reciprocalCycles(800)</code> should return 743.
    testString: 'assert(reciprocalCycles(800) == 743, ''<code>reciprocalCycles(800)</code> should return 743.'');'
  - text: <code>reciprocalCycles(900)</code> should return 887.
    testString: 'assert(reciprocalCycles(900) == 887, ''<code>reciprocalCycles(900)</code> should return 887.'');'
  - text: <code>reciprocalCycles(1000)</code> should return 983.
    testString: 'assert(reciprocalCycles(1000) == 983, ''<code>reciprocalCycles(1000)</code> should return 983.'');'

```

</section>

## Challenge Seed
<section id='challengeSeed'>

<div id='js-seed'>

```js
function reciprocalCycles(n) {
  // Good luck!
  return n;
}

reciprocalCycles(1000);
```

</div>



</section>

## Solution
<section id='solution'>

```js
// solution required
```
</section>