problem55.py

"""
Lychrel Numbers
Project Euler Problem #55
by Muaz Siddiqui

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 euler_helpers import timeit, is_palindrome, is_palindrome2

def is_lychrel(n):
    count = 0
    num = n
    while count < 51:
        next = num+int(str(num)[::-1])
        if is_palindrome2(next):
            return False
        num = next
        count += 1
    return True

@timeit
def answer():
    count = 0
    for x in range(2, 10001):
        if is_lychrel(x):
            count += 1
    return count