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and change all the challenges to new `md` format.
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Oliver Eyton-Williams
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curriculum/challenges/english/10-coding-interview-prep/rosetta-code/farey-sequence.md
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@ -1,58 +1,83 @@
---
title: Farey sequence
id: 59c3ec9f15068017c96eb8a3
title: Farey sequence
challengeType: 5
forumTopicId: 302266
---
## Description
<section id='description'>
The <a href="https://en.wikipedia.org/wiki/Farey sequence" title="wp: Farey sequence" target="_blank">Farey sequence</a> <code>F<sub>n</sub></code> of order <code>n</code> is the sequence of completely reduced fractions between <code>0</code> and <code>1</code> which, when in lowest terms, have denominators less than or equal to <code>n</code>, arranged in order of increasing size.
The <i>Farey sequence</i> is sometimes incorrectly called a <i>Farey series</i>.
# --description--
The [Farey sequence](<https://en.wikipedia.org/wiki/Farey sequence> "wp: Farey sequence") <code>F<sub>n</sub></code> of order `n` is the sequence of completely reduced fractions between `0` and `1` which, when in lowest terms, have denominators less than or equal to `n`, arranged in order of increasing size.
The *Farey sequence* is sometimes incorrectly called a *Farey series*.
Each Farey sequence:
<ul>
<li>starts with the value 0, denoted by the fraction $ \frac{0}{1} $</li>
<li>ends with the value 1, denoted by the fraction $ \frac{1}{1}$.</li>
</ul>
The Farey sequences of orders <code>1</code> to <code>5</code> are:
The Farey sequences of orders `1` to `5` are:
<ul>
<li style="list-style: none;">${\bf\it{F}}_1 = \frac{0}{1}, \frac{1}{1}$</li>
<li style="list-style: none;">${\bf\it{F}}_2 = \frac{0}{1}, \frac{1}{2}, \frac{1}{1}$</li>
<li style="list-style: none;">${\bf\it{F}}_3 = \frac{0}{1}, \frac{1}{3}, \frac{1}{2}, \frac{2}{3}, \frac{1}{1}$</li>
<li style="list-style: none;">${\bf\it{F}}_4 = \frac{0}{1}, \frac{1}{4}, \frac{1}{3}, \frac{1}{2}, \frac{2}{3}, \frac{3}{4}, \frac{1}{1}$</li>
<li style="list-style: none;">${\bf\it{F}}_5 = \frac{0}{1}, \frac{1}{5}, \frac{1}{4}, \frac{1}{3}, \frac{2}{5}, \frac{1}{2}, \frac{3}{5}, \frac{2}{3}, \frac{3}{4}, \frac{4}{5}, \frac{1}{1}$</li>
<li style='list-style: none;'>${\bf\it{F}}_1 = \frac{0}{1}, \frac{1}{1}$</li>
<li style='list-style: none;'>${\bf\it{F}}_2 = \frac{0}{1}, \frac{1}{2}, \frac{1}{1}$</li>
<li style='list-style: none;'>${\bf\it{F}}_3 = \frac{0}{1}, \frac{1}{3}, \frac{1}{2}, \frac{2}{3}, \frac{1}{1}$</li>
<li style='list-style: none;'>${\bf\it{F}}_4 = \frac{0}{1}, \frac{1}{4}, \frac{1}{3}, \frac{1}{2}, \frac{2}{3}, \frac{3}{4}, \frac{1}{1}$</li>
<li style='list-style: none;'>${\bf\it{F}}_5 = \frac{0}{1}, \frac{1}{5}, \frac{1}{4}, \frac{1}{3}, \frac{2}{5}, \frac{1}{2}, \frac{3}{5}, \frac{2}{3}, \frac{3}{4}, \frac{4}{5}, \frac{1}{1}$</li>
</ul>
</section>
## Instructions
<section id='instructions'>
Write a function that returns the Farey sequence of order <code>n</code>. The function should have one parameter that is <code>n</code>. It should return the sequence as an array.
</section>
# --instructions--
## Tests
<section id='tests'>
Write a function that returns the Farey sequence of order `n`. The function should have one parameter that is `n`. It should return the sequence as an array.
```yml
tests:
- text: <code>farey</code> should be a function.
testString: assert(typeof farey === 'function');
- text: <code>farey(3)</code> should return an array
testString: assert(Array.isArray(farey(3)));
- text: <code>farey(3)</code> should return <code>["1/3","1/2","2/3"]</code>
testString: assert.deepEqual(farey(3), ["1/3","1/2","2/3"]);
- text: <code>farey(4)</code> should return <code>["1/4","1/3","1/2","2/4","2/3","3/4"]</code>
testString: assert.deepEqual(farey(4), ["1/4","1/3","1/2","2/4","2/3","3/4"]);
- text: <code>farey(5)</code> should return <code>["1/5","1/4","1/3","2/5","1/2","2/4","3/5","2/3","3/4","4/5"]</code>
testString: assert.deepEqual(farey(5), ["1/5","1/4","1/3","2/5","1/2","2/4","3/5","2/3","3/4","4/5"]);
# --hints--
`farey` should be a function.
```js
assert(typeof farey === 'function');
```
</section>
`farey(3)` should return an array
## Challenge Seed
<section id='challengeSeed'>
```js
assert(Array.isArray(farey(3)));
```
<div id='js-seed'>
`farey(3)` should return `["1/3","1/2","2/3"]`
```js
assert.deepEqual(farey(3), ['1/3', '1/2', '2/3']);
```
`farey(4)` should return `["1/4","1/3","1/2","2/4","2/3","3/4"]`
```js
assert.deepEqual(farey(4), ['1/4', '1/3', '1/2', '2/4', '2/3', '3/4']);
```
`farey(5)` should return `["1/5","1/4","1/3","2/5","1/2","2/4","3/5","2/3","3/4","4/5"]`
```js
assert.deepEqual(farey(5), [
'1/5',
'1/4',
'1/3',
'2/5',
'1/2',
'2/4',
'3/5',
'2/3',
'3/4',
'4/5'
]);
```
# --seed--
## --seed-contents--
```js
function farey(n) {
@ -60,35 +85,24 @@ function farey(n) {
}
```
</div>
</section>
## Solution
<section id='solution'>
# --solutions--
```js
function farey(n){
let farSeq=[];
for(let den = 1; den <= n; den++){
for(let num = 1; num < den; num++){
farSeq.push({
str:num+"/"+den,
val:num/den});
}
}
farSeq.sort(function(a,b){
return a.val-b.val;
});
farSeq=farSeq.map(function(a){
return a.str;
});
return farSeq;
let farSeq=[];
for(let den = 1; den <= n; den++){
for(let num = 1; num < den; num++){
farSeq.push({
str:num+"/"+den,
val:num/den});
}
}
farSeq.sort(function(a,b){
return a.val-b.val;
});
farSeq=farSeq.map(function(a){
return a.str;
});
return farSeq;
}
```
</section>