Added solution for Project Euler problem 125 (#3073)

* Added solution for Project Euler problem 125

* Fixed typos

project_euler/problem_125/sol1.py

@@ -0,0 +1,56 @@
+"""
+Problem 125: https://projecteuler.net/problem=125
+
+The palindromic number 595 is interesting because it can be written as the sum
+of consecutive squares: 6^2 + 7^2 + 8^2 + 9^2 + 10^2 + 11^2 + 12^2.
+
+There are exactly eleven palindromes below one-thousand that can be written as
+consecutive square sums, and the sum of these palindromes is 4164. Note that
+1 = 0^2 + 1^2 has not been included as this problem is concerned with the
+squares of positive integers.
+
+Find the sum of all the numbers less than 10^8 that are both palindromic and can
+be written as the sum of consecutive squares.
+"""
+
+
+def is_palindrome(n: int) -> bool:
+    """
+    Check if an integer is palindromic.
+    >>> is_palindrome(12521)
+    True
+    >>> is_palindrome(12522)
+    False
+    >>> is_palindrome(12210)
+    False
+    """
+    if n % 10 == 0:
+        return False
+    s = str(n)
+    return s == s[::-1]
+
+
+def solution() -> int:
+    """
+    Returns the sum of all numbers less than 1e8 that are both palindromic and
+    can be written as the sum of consecutive squares.
+    """
+    LIMIT = 10 ** 8
+    answer = set()
+    first_square = 1
+    sum_squares = 5
+    while sum_squares < LIMIT:
+        last_square = first_square + 1
+        while sum_squares < LIMIT:
+            if is_palindrome(sum_squares):
+                answer.add(sum_squares)
+            last_square += 1
+            sum_squares += last_square ** 2
+        first_square += 1
+        sum_squares = first_square ** 2 + (first_square + 1) ** 2
+
+    return sum(answer)
+
+
+if __name__ == "__main__":
+    print(solution())