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curriculum/challenges/english/10-coding-interview-prep/project-euler/problem-41-pandigital-prime.md

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+---
+id: 5900f3951000cf542c50fea8
+challengeType: 5
+title: 'Problem 41: Pandigital prime'
+forumTopicId: 302078
+---
+
+## Description
+<section id='description'>
+
+We shall say that an <var>n</var>-digit number is pandigital if it makes use of all the digits 1 to <var>n</var> 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?
+
+</section>
+
+## Instructions
+<section id='instructions'>
+
+</section>
+
+## Tests
+<section id='tests'>
+
+```yml
+tests:
+  - text: <code>pandigitalPrime(4)</code> should return a number.
+    testString: assert(typeof pandigitalPrime(4) === 'number');
+  - text: <code>pandigitalPrime(4)</code> should return 4231.
+    testString: assert(pandigitalPrime(4) == 4231);
+  - text: <code>pandigitalPrime(7)</code> should return 7652413.
+    testString: assert(pandigitalPrime(7) == 7652413);
+
+```
+
+</section>
+
+## Challenge Seed
+<section id='challengeSeed'>
+
+<div id='js-seed'>
+
+```js
+function pandigitalPrime(n) {
+
+  return n;
+}
+
+pandigitalPrime(7);
+```
+
+</div>
+
+
+
+</section>
+
+## Solution
+<section id='solution'>
+
+
+```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;
+}
+```
+
+</section>