Add Project Euler Problem 092 (#5091)

* adde solution to problem 092

* added solution to problem 092

* fixed the pre-comit shebang issue

project_euler/problem_092/sol1.py

@@ -0,0 +1,93 @@
+"""
+Project Euler Problem 092: https://projecteuler.net/problem=92
+Square digit chains
+A number chain is created by continuously adding the square of the digits in
+a number to form a new number until it has been seen before.
+For example,
+44 → 32 → 13 → 10 → 1 → 1
+85 → 89 → 145 → 42 → 20 → 4 → 16 → 37 → 58 → 89
+Therefore any chain that arrives at 1 or 89 will become stuck in an endless loop.
+What is most amazing is that EVERY starting number will eventually arrive at 1 or 89.
+How many starting numbers below ten million will arrive at 89?
+"""
+
+
+def next_number(number: int) -> int:
+    """
+    Returns the next number of the chain by adding the square of each digit
+    to form a neww number.
+    For example if number = 12, next_number() will return 1^2 + 2^2 = 5.
+    Therefore 5 is the next number of the chain.
+    >>> next_number(44)
+    32
+    >>> next_number(10)
+    1
+    >>> next_number(32)
+    13
+    """
+    num = 0
+    for i in range(len(str(number))):
+        num += int(str(number)[i]) ** 2
+
+    return num
+
+
+def chain(number: int) -> bool:
+    """
+    Generates the chain of numbers until the nest number generated is 1 0r 89.
+    for example, if starting number is 44, then the function generates the
+    following chain of  numbers.
+    chain: 44 → 32 → 13 → 10 → 1 → 1
+    once the next number generated is 1 or 89, the function
+    Returns True if the next number generated by next_number() if 1.
+    Returns False if the next number generated by next_number() is 89.
+    >>> chain(10)
+    True
+    >>> chain(58)
+    False
+    >>> chain(1)
+    True
+    """
+    while number != 1 and number != 89:
+        number = next_number(number)
+
+    if number == 1:
+        return True
+
+    elif number == 89:
+        return False
+
+
+def solution(number: int = 10000000) -> int:
+    """
+    The function returns the total numbers that end up in 89 after the chain generation.
+    The function accepts a range number and the function checks all the values
+    under value number.
+    if the chain generation leads to the end number as 1 or 89. If the chain()
+    returns True, then total is incremented, implying that the number we
+    started with ended up with 1 else total2 is incremented, implying that
+    the number we started with ended up in 89 after chain generation.
+    But the function returns total2 as the requirement of question is
+    to find out how many ended up in 89.
+
+    >>> solution(100)
+    80
+    >>> solution(10000000)
+    8581146
+    """
+    total = 0
+    total2 = 0
+    for i in range(1, number):
+        val = chain(i)
+
+        if val is True:
+            total += 1
+
+        elif val is False:
+            total2 += 1
+
+    return total2
+
+
+if __name__ == "__main__":
+    print(f"{solution() = }")