problem-055.py

### Problem 55 - Lychrel Numbers
###-------------------------------------------------------------------------------------------------------------------------------------------------------------------------
### 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?

### Solution

# Function to determine if number is a Lychrel number
def isLychrel(n: int) -> bool:
    iterations = 0
    old_num = n
    while True:
        if iterations > 50:
            return True

        new_num = old_num + int(str(old_num)[::-1])
        iterations += 1

        if isPalindrome(new_num):
            return False
        else:
            old_num = new_num


# Function to determine if number is a palindrome
def isPalindrome(n: int) -> bool:
    return str(n) == str(n)[::-1]


num_lychrel = 0
for i in range(1, 10000):
    if isLychrel(i):
        num_lychrel += 1

print("The number of Lychrel numbers below 10,000 is: " + str(num_lychrel))