#! /usr/bin/env python3

description = '''
Lychrel numbers
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?
'''

def lychrel(x):
  for i in range(0, 50):
    reversedigits = int(str(x)[::-1])
    x = x + reversedigits
    isPalendrome = str(x) == str(x)[::-1]
    if isPalendrome: return False
  return True
  
assert(not lychrel(47))
assert(not lychrel(349))
assert(lychrel(4994))

print(sum(1 for x in range(0, 10000) if lychrel(x)))

#! /usr/bin/env python3

description = '''
Lychrel numbers
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?
'''

def lychrel(x):
  for i in range(0, 50):
    reversedigits = int(str(x)[::-1])
    x = x + reversedigits
    isPalendrome = str(x) == str(x)[::-1]
    if isPalendrome: return False
  return True
  
assert(not lychrel(47))
assert(not lychrel(349))
assert(lychrel(4994))

print(sum(1 for x in range(0, 10000) if lychrel(x)))

#! /usr/bin/env python3 Lychrel numbers 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?