P055.py

# -*- coding: utf-8 -*-
"""
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.
"""

def isPalindrome(n):
    s=str(n)
    return s==s[::-1]
    
def lychrel(n, niter=0):
    if (niter>50):
        return -1
    s=str(n)
    sly = n + int(s[::-1])
    #print sly, niter
    if isPalindrome(sly):
        return niter
    else:
        return lychrel(sly, niter+1)

nlych = 0

for n in range(10001):
    l = lychrel(n)
    if l == -1:
        nlych += 1
        
print nlych #249