22afc2a0ca
Co-authored-by: Oliver Eyton-Williams <ojeytonwilliams@gmail.com> Co-authored-by: Kristofer Koishigawa <scissorsneedfoodtoo@gmail.com> Co-authored-by: Beau Carnes <beaucarnes@gmail.com>
94 lines
2.2 KiB
Markdown
94 lines
2.2 KiB
Markdown
---
|
|
id: 5900f3891000cf542c50fe9c
|
|
challengeType: 5
|
|
isHidden: false
|
|
title: 'Problem 29: Distinct powers'
|
|
forumTopicId: 301941
|
|
---
|
|
|
|
## Description
|
|
<section id='description'>
|
|
|
|
Consider all integer combinations of ab for 2 ≤ a ≤ 5 and 2 ≤ b ≤ 5:
|
|
|
|
<div style='padding-left: 4em;'>
|
|
2<sup>2</sup>=4, 2<sup>3</sup>=8, 2<sup>4</sup>=16, 2<sup>5</sup>=32 <br>
|
|
3<sup>2</sup>=9, 3<sup>3</sup>=27, 3<sup>4</sup>=81, 3<sup>5</sup>=243 <br>
|
|
4<sup>2</sup>=16, 4<sup>3</sup>=64, 4<sup>4</sup>=256, 4<sup>5</sup>=1024 <br>
|
|
5<sup>2</sup>=25, 5<sup>3</sup>=125, 5<sup>4</sup>=625, 5<sup>5</sup>=3125 <br>
|
|
</div>
|
|
|
|
If they are then placed in numerical order, with any repeats removed, we get the following sequence of 15 distinct terms:
|
|
|
|
<div style='padding-left: 4em;'>
|
|
4, 8, 9, 16, 25, 27, 32, 64, 81, 125, 243, 256, 625, 1024, 3125
|
|
</div>
|
|
|
|
How many distinct terms are in the sequence generated by <var>a<sup>b</sup></var> for 2 ≤ <var>a</var> ≤ <var>`n`</var> and 2 ≤ <var>b</var> ≤ <var>`n`</var>?
|
|
|
|
</section>
|
|
|
|
## Instructions
|
|
<section id='instructions'>
|
|
|
|
</section>
|
|
|
|
## Tests
|
|
<section id='tests'>
|
|
|
|
```yml
|
|
tests:
|
|
- text: <code>distinctPowers(15)</code> should return a number.
|
|
testString: assert(typeof distinctPowers(15) === 'number');
|
|
- text: <code>distinctPowers(15)</code> should return 177.
|
|
testString: assert.strictEqual(distinctPowers(15), 177);
|
|
- text: <code>distinctPowers(20)</code> should return 324.
|
|
testString: assert.strictEqual(distinctPowers(20), 324);
|
|
- text: <code>distinctPowers(25)</code> should return 519.
|
|
testString: assert.strictEqual(distinctPowers(25), 519);
|
|
- text: <code>distinctPowers(30)</code> should return 755.
|
|
testString: assert.strictEqual(distinctPowers(30), 755);
|
|
|
|
```
|
|
|
|
</section>
|
|
|
|
## Challenge Seed
|
|
<section id='challengeSeed'>
|
|
|
|
<div id='js-seed'>
|
|
|
|
```js
|
|
function distinctPowers(n) {
|
|
// Good luck!
|
|
return n;
|
|
}
|
|
|
|
distinctPowers(30);
|
|
```
|
|
|
|
</div>
|
|
|
|
|
|
|
|
</section>
|
|
|
|
## Solution
|
|
<section id='solution'>
|
|
|
|
|
|
```js
|
|
const distinctPowers = (n) => {
|
|
let list = [];
|
|
for (let a=2; a<=n; a++) {
|
|
for (let b=2; b<=n; b++) {
|
|
let term = Math.pow(a, b);
|
|
if (list.indexOf(term)===-1) list.push(term);
|
|
}
|
|
}
|
|
return list.length;
|
|
};
|
|
```
|
|
|
|
</section>
|