79d9012432
* fix(curriculum): tests quotes * fix(curriculum): fill seed-teardown * fix(curriculum): fix tests and remove unneeded seed-teardown
105 lines
2.3 KiB
Markdown
105 lines
2.3 KiB
Markdown
---
|
|
id: 5900f39d1000cf542c50feb0
|
|
challengeType: 5
|
|
title: 'Problem 49: Prime permutations'
|
|
---
|
|
|
|
## Description
|
|
<section id='description'>
|
|
The arithmetic sequence, 1487, 4817, 8147, in which each of the terms increases by 3330, is unusual in two ways: (i) each of the three terms are prime, and, (ii) each of the 4-digit numbers are permutations of one another.
|
|
There are no arithmetic sequences made up of three 1-, 2-, or 3-digit primes, exhibiting this property, but there is one other 4-digit increasing sequence.
|
|
What 12-digit number do you form by concatenating the three terms in this sequence?
|
|
</section>
|
|
|
|
## Instructions
|
|
<section id='instructions'>
|
|
|
|
</section>
|
|
|
|
## Tests
|
|
<section id='tests'>
|
|
|
|
```yml
|
|
tests:
|
|
- text: <code>primePermutations()</code> should return 296962999629.
|
|
testString: assert.strictEqual(primePermutations(), 296962999629, '<code>primePermutations()</code> should return 296962999629.');
|
|
|
|
```
|
|
|
|
</section>
|
|
|
|
## Challenge Seed
|
|
<section id='challengeSeed'>
|
|
|
|
<div id='js-seed'>
|
|
|
|
```js
|
|
function primePermutations() {
|
|
// Good luck!
|
|
return true;
|
|
}
|
|
|
|
primePermutations();
|
|
```
|
|
|
|
</div>
|
|
|
|
|
|
|
|
</section>
|
|
|
|
## Solution
|
|
<section id='solution'>
|
|
|
|
|
|
```js
|
|
function primePermutations() {
|
|
function arePermutations(num1, num2) {
|
|
const numStr1 = num1.toString();
|
|
let numStr2 = num2.toString();
|
|
if (numStr1.length !== numStr2.length) {
|
|
return false;
|
|
}
|
|
|
|
for (let i = 0; i < numStr1.length; i++) {
|
|
const index = numStr2.indexOf(numStr1[i]);
|
|
if (index === -1) {
|
|
return false;
|
|
}
|
|
numStr2 = numStr2.slice(0, index) + numStr2.slice(index + 1);
|
|
}
|
|
return true;
|
|
}
|
|
|
|
function isPrime(num) {
|
|
if (num < 2) {
|
|
return false;
|
|
} else if (num === 2) {
|
|
return true;
|
|
}
|
|
const sqrtOfNum = Math.floor(num ** 0.5);
|
|
for (let i = 2; i <= sqrtOfNum + 1; i++) {
|
|
if (num % i === 0) {
|
|
return false;
|
|
}
|
|
}
|
|
return true;
|
|
}
|
|
|
|
for (let num1 = 1000; num1 <= 9999; num1++) {
|
|
const num2 = num1 + 3330;
|
|
const num3 = num2 + 3330;
|
|
if (isPrime(num1) && isPrime(num2) && isPrime(num3)) {
|
|
if (arePermutations(num1, num2) && arePermutations(num1, num3)
|
|
&& num1 !== 1487) {
|
|
// concatenate and return numbers
|
|
return (num1 * 100000000) + (num2 * 10000) + num3;
|
|
}
|
|
}
|
|
}
|
|
return 0;
|
|
}
|
|
```
|
|
|
|
</section>
|