problem055.py

# 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?

from common_funcs import answer, reverse_digits, is_palindrome
    
def is_lychrel(n):
    for _ in range(50):
        n += reverse_digits(n)
        if is_palindrome(n):
            return False
    return True
    
def solve():
    count = 0
    for x in range(10,10000):
        if is_lychrel(x):
            count += 1
    return count

        
answer(solve)