PyPE solution to PE problem 55

    ProjectEuler.net 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.

    Solution
    --------

    We employ a brute-force recursion approach. We pass each starting number
    into the isLychrel function, counting how many return True. Within the
    function, we keep a depth counter (which starts at 0). We are told that
    a number may still be a Lychrel number even if it is palindromic, so if
    our depth is 0 (we haven't started yet), we don't worry about palindromicity.

    If the current depth passes the limit case (here, 50), then we return True,
    otherwise we reverse and add the number, increment the depth counter, and
    call isLychrel on the resulting number.

    Answer
    ------

    249