055.py

#!/usr/bin/python
# -*- 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.

#Answer:
	#249

from time import time; t=time()

c = 0
for n in range(10000):
    x, s = n, int(str(n)[::-1])
    for i in range(50-1):
        x += s
        s = int(str(x)[::-1])
        if x == s: break
    else:
        c += 1

print(c)#, time()-t