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68 lines
1.8 KiB
Python
68 lines
1.8 KiB
Python
"""
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Problem 43: https://projecteuler.net/problem=43
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The number, 1406357289, is a 0 to 9 pandigital number because it is made up of
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each of the digits 0 to 9 in some order, but it also has a rather interesting
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sub-string divisibility property.
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Let d1 be the 1st digit, d2 be the 2nd digit, and so on. In this way, we note
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the following:
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d2d3d4=406 is divisible by 2
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d3d4d5=063 is divisible by 3
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d4d5d6=635 is divisible by 5
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d5d6d7=357 is divisible by 7
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d6d7d8=572 is divisible by 11
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d7d8d9=728 is divisible by 13
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d8d9d10=289 is divisible by 17
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Find the sum of all 0 to 9 pandigital numbers with this property.
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"""
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from itertools import permutations
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def is_substring_divisible(num: tuple) -> bool:
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"""
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Returns True if the pandigital number passes
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all the divisibility tests.
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>>> is_substring_divisible((0, 1, 2, 4, 6, 5, 7, 3, 8, 9))
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False
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>>> is_substring_divisible((5, 1, 2, 4, 6, 0, 7, 8, 3, 9))
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False
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>>> is_substring_divisible((1, 4, 0, 6, 3, 5, 7, 2, 8, 9))
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True
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"""
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if num[3] % 2 != 0:
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return False
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if (num[2] + num[3] + num[4]) % 3 != 0:
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return False
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if num[5] % 5 != 0:
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return False
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tests = [7, 11, 13, 17]
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for i, test in enumerate(tests):
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if (num[i + 4] * 100 + num[i + 5] * 10 + num[i + 6]) % test != 0:
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return False
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return True
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def solution(n: int = 10) -> int:
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"""
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Returns the sum of all pandigital numbers which pass the
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divisibility tests.
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>>> solution(10)
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16695334890
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"""
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return sum(
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int("".join(map(str, num)))
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for num in permutations(range(n))
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if is_substring_divisible(num)
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)
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if __name__ == "__main__":
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print(f"{solution() = }")
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