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"""

Lychrel numbers

Problem 55: https://projecteuler.net/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 is_palindrome(n: int) -> bool:

"""

Returns True if a number is palindrome.

>>> is_palindrome(12567321)

False

>>> is_palindrome(1221)

True

>>> is_palindrome(9876789)

True

"""

return str(n) == str(n)[::-1]

def sum_reverse(n: int) -> int:

"""

Returns the sum of n and reverse of n.

>>> sum_reverse(123)

444

>>> sum_reverse(3478)

12221

>>> sum_reverse(12)

"""

return int(n) + int(str(n)[::-1])

def solution(limit: int = 10000) -> int:

"""

Returns the count of all lychrel numbers below limit.

>>> solution(10000)

249

>>> solution(5000)

>>> solution(1000)

"""

lychrel_nums = []

for num in range(1, limit):

iterations = 0

a = num

while iterations < 50:

num = sum_reverse(num)

iterations += 1

if is_palindrome(num):

break

else:

lychrel_nums.append(a)

return len(lychrel_nums)

if __name__ == "__main__":

print(f"{solution() = }")

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