Created problem_43 in project_euler

project_euler/problem_43/__init__.py

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+#

project_euler/problem_43/sol1.py

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+"""
+The number, 1406357289, is a 0 to 9 pandigital number because it is made up of
+each of the digits 0 to 9 in some order, but it also has a rather interesting
+sub-string divisibility property.
+
+Let d1 be the 1st digit, d2 be the 2nd digit, and so on. In this way, we note
+the following:
+
+d2d3d4=406 is divisible by 2
+d3d4d5=063 is divisible by 3
+d4d5d6=635 is divisible by 5
+d5d6d7=357 is divisible by 7
+d6d7d8=572 is divisible by 11
+d7d8d9=728 is divisible by 13
+d8d9d10=289 is divisible by 17
+Find the sum of all 0 to 9 pandigital numbers with this property.
+"""
+
+
+from itertools import permutations
+
+
+def is_substring_divisible(num: tuple) -> bool:
+    """
+    Returns True if the pandigital number passes
+    all the divisibility tests.
+    >>> is_substring_divisible((0, 1, 2, 4, 6, 5, 7, 3, 8, 9))
+    False
+    >>> is_substring_divisible((5, 1, 2, 4, 6, 0, 7, 8, 3, 9))
+    False
+    >>> is_substring_divisible((1, 4, 0, 6, 3, 5, 7, 2, 8, 9))
+    True
+    """
+    tests = [2, 3, 5, 7, 11, 13, 17]
+    for i, test in enumerate(tests):
+        if (num[i + 1] * 100 + num[i + 2] * 10 + num[i + 3]) % test != 0:
+            return False
+    return True
+
+
+def compute_sum(n: int = 10) -> int:
+    """
+    Returns the sum of all pandigital numbers which pass the
+    divisiility tests.
+    >>> compute_sum(10)
+    16695334890
+    """
+    list_nums = [
+        int("".join(map(str, num)))
+        for num in permutations(range(n))
+        if is_substring_divisible(num)
+    ]
+
+    return sum(list_nums)
+
+
+if __name__ == "__main__":
+    print(f"{compute_sum(10) = }")