Created problem_55 in project_euler (#2354)

* Create __init__.py

* Add files via upload

* Update sol1.py

project_euler/problem_55/__init__.py

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+#

project_euler/problem_55/sol1.py

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+"""
+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)
+    33
+    """
+    return int(n) + int(str(n)[::-1])
+
+
+def compute_lychrel_nums(limit: int) -> int:
+    """
+    Returns the count of all lychrel numbers below limit.
+    >>> compute_lychrel_nums(10000)
+    249
+    >>> compute_lychrel_nums(5000)
+    76
+    >>> compute_lychrel_nums(1000)
+    13
+    """
+    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"{compute_lychrel_nums(10000) = }")