2018-10-10 22:03:03 +00:00
---
id: 5900f3951000cf542c50fea8
2021-02-06 04:42:36 +00:00
title: 'Problem 41: Pandigital prime'
2018-10-10 22:03:03 +00:00
challengeType: 5
2021-02-06 04:42:36 +00:00
forumTopicId: 302078
2021-01-13 02:31:00 +00:00
dashedName: problem-41-pandigital-prime
2018-10-10 22:03:03 +00:00
---
2020-12-16 07:37:30 +00:00
# --description--
2018-10-10 22:03:03 +00:00
2021-02-06 04:42:36 +00:00
We shall say that an `n` -digit number is pandigital if it makes use of all the digits 1 to `n` exactly once. For example, 2143 is a 4-digit pandigital and is also prime.
What is the largest `n` -length digit pandigital prime that exists?
2018-10-10 22:03:03 +00:00
2020-12-16 07:37:30 +00:00
# --hints--
2018-10-10 22:03:03 +00:00
2021-02-06 04:42:36 +00:00
`pandigitalPrime(4)` should return a number.
```js
assert(typeof pandigitalPrime(4) === 'number');
```
`pandigitalPrime(4)` should return 4231.
2018-10-10 22:03:03 +00:00
```js
2020-12-16 07:37:30 +00:00
assert(pandigitalPrime(4) == 4231);
2018-10-10 22:03:03 +00:00
```
2021-02-06 04:42:36 +00:00
`pandigitalPrime(7)` should return 7652413.
2018-10-10 22:03:03 +00:00
```js
2020-12-16 07:37:30 +00:00
assert(pandigitalPrime(7) == 7652413);
2018-10-10 22:03:03 +00:00
```
2020-08-13 15:24:35 +00:00
2021-01-13 02:31:00 +00:00
# --seed--
## --seed-contents--
```js
function pandigitalPrime(n) {
return n;
}
pandigitalPrime(7);
```
2020-12-16 07:37:30 +00:00
# --solutions--
2021-01-13 02:31:00 +00:00
```js
function pandigitalPrime(n) {
function isPrime(num) {
for (let i = 2, s = Math.sqrt(num); i < = s; i++) {
if (num % i === 0) {
return false;
}
}
return num !== 1;
}
function getPermutations(n) {
if (n === 1) {
permutations.push(digitsArr.join(''));
} else {
for (let i = 0; i < n - 1 ; i + + ) {
getPermutations(n - 1);
// swap(n % 2 === 0 ? i : 0, n - 1);
if (n % 2 === 0) {
swap(i, n - 1);
} else {
swap(0, n - 1);
}
}
getPermutations(n - 1);
}
}
function swap(x, y) {
let temp = digitsArr[x];
digitsArr[x] = digitsArr[y];
digitsArr[y] = temp;
}
let max = 0;
let permutations = [];
let digitsArr;
let pandigitalNum = '';
for (let max = n; max > 0; max--) {
pandigitalNum += max;
}
for (let i = 0; i < pandigitalNum.length ; i + + ) {
if (max > 0) {
break;
} else {
permutations = [];
const currMax = pandigitalNum.slice(i);
digitsArr = currMax.split('');
getPermutations(digitsArr.length);
// sort permutations in descending order
permutations.sort(function(a, b) {
return b - a;
});
for (let perm of permutations) {
const thisPerm = parseInt(perm);
if (isPrime(thisPerm)) {
max = thisPerm;
break;
}
}
}
}
return max;
}
```