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curriculum/challenges/espanol/10-coding-interview-prep/project-euler/problem-55-lychrel-numbers.md

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+---
+id: 5900f3a31000cf542c50feb6
+title: 'Problem 55: Lychrel numbers'
+challengeType: 5
+forumTopicId: 302166
+dashedName: problem-55-lychrel-numbers
+---
+
+# --description--
+
+If we take 47, reverse and add, 47 + 74 = 121, which is palindromic.
+
+Not all numbers produce palindromes so quickly. For example,
+
+<div style="margin-left: 4em;">
+  349 + 943 = 1292,<br>
+  1292 + 2921 = 4213<br>
+  4213 + 3124 = 7337<br>
+</div>
+
+That is, 349 took three iterations to arrive at a palindrome.
+
+Although no one has proved it yet, it is thought that some numbers, like 196, never produce a palindrome. A number that never forms a palindrome through the reverse and add process is called a Lychrel number. Due to the theoretical nature of these numbers, and for the purpose of this problem, we shall assume that a number is Lychrel until proven otherwise. In addition you are given that for every number below ten-thousand, it will either (i) become a palindrome in less than fifty iterations, or, (ii) no one, with all the computing power that exists, has managed so far to map it to a palindrome. In fact, 10677 is the first number to be shown to require over fifty iterations before producing a palindrome: 4668731596684224866951378664 (53 iterations, 28-digits).
+
+Surprisingly, there are palindromic numbers that are themselves Lychrel numbers; the first example is 4994.
+
+How many Lychrel numbers are there below `num`?
+
+**Note:** Wording was modified slightly on 24 April 2007 to emphasize the theoretical nature of Lychrel numbers.
+
+# --hints--
+
+`countLychrelNumbers(1000)` should return a number.
+
+```js
+assert(typeof countLychrelNumbers(1000) === 'number');
+```
+
+`countLychrelNumbers(1000)` should return 13.
+
+```js
+assert.strictEqual(countLychrelNumbers(1000), 13);
+```
+
+`countLychrelNumbers(3243)` should return 39.
+
+```js
+assert.strictEqual(countLychrelNumbers(3243), 39);
+```
+
+`countLychrelNumbers(5000)` should return 76.
+
+```js
+assert.strictEqual(countLychrelNumbers(5000), 76);
+```
+
+`countLychrelNumbers(7654)` should return 140.
+
+```js
+assert.strictEqual(countLychrelNumbers(7654), 140);
+```
+
+`countLychrelNumbers(10000)` should return 249.
+
+```js
+assert.strictEqual(countLychrelNumbers(10000), 249);
+```
+
+# --seed--
+
+## --seed-contents--
+
+```js
+function countLychrelNumbers(num) {
+
+  return true;
+}
+
+countLychrelNumbers(10000);
+```
+
+# --solutions--
+
+```js
+const countLychrelNumbers = (size) => {
+  const numReverse = (num) => {
+    return Number(num.toString().split('').reverse().join(''));
+  };
+  const isPalin = (num) => {
+    if (numReverse(num) === num) {
+      return true;
+    }
+    return false;
+  };
+  let total = 0;
+  for (let i = 1; i < size; i++) {
+    let loopCount = 1;
+    let sum = i;
+    while (loopCount < 50) {
+      sum = sum + numReverse(sum);
+      if (isPalin(sum)) {
+        break;
+      } else {
+        loopCount++;
+      }
+    }
+    if (loopCount === 50) {
+      total++;
+    }
+  }
+  return total;
+}
+```