**Problem 55:**

If we take 47, reverse and add, 47 + 74 = 121, which is palindromic.

Not all numbers produce palindromes so quickly. For example,

349 + 943 = 1292,

1292 + 2921 = 4213

4213 + 3124 = 7337

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 ten-thousand?

NOTE: Wording was modified slightly on 24 April 2007 to emphasise the theoretical nature of Lychrel numbers.

**Idea:**

This is a pretty straight forward problem: reverse the number via method of choice, add it to the original number, check to see if it’s a palindrome, and repeat up to 49 more times if it’s not.

Since I already have a palindrome method from Problem 4, the only hurdle is reversing the number. I chose to convert it to a string and reverse it that way since I’m using BigIntegers (never can be too careful with these problems). Once I made the “isLychrel(int)” method, I was practically done.

int answer = 0; for(int i = 1; i < 10000; i++) { if(EulerUtils.isLychrel(i)) { answer++; } }