#### Problem

*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.*

#### Solution