55 lines
1.6 KiB
Python
55 lines
1.6 KiB
Python
#!/usr/bin/env python3
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"""
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Created on 03 Aug 2021
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@author: David Doblas Jiménez
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@email: daviddoji@pm.me
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Solution for problem 43 of Project Euler
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https://projecteuler.net/problem=43
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"""
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from itertools import permutations
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from utils import timeit
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@timeit("Problem 43")
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def compute():
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"""
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The number, 1406357289, is a 0 to 9 pandigital number because
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it is made up of each of the digits 0 to 9 in some order, but
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it also has a rather interesting sub-string divisibility property.
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Let d1 be the 1st digit, d2 be the 2nd digit, and so on. In this
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way, we note 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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ans = []
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pandigital = ['0', '1', '2', '3', '4', '5', '6', '7', '8', '9']
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for n in permutations(pandigital):
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n_ = "".join(n)
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if n_[0] != "0" and sorted("".join(n_)) == pandigital:
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if int(n_[7:]) % 17 == 0:
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if int(n_[6:9]) % 13 == 0:
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if int(n_[5:8]) % 11 == 0:
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if int(n_[4:7]) % 7 == 0:
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if int(n_[3:6]) % 5 == 0:
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if int(n_[2:5]) % 3 == 0:
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if int(n_[1:4]) % 2 == 0:
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ans.append(int(n_))
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return sum(ans)
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if __name__ == "__main__":
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print(f"Result for Problem 43: {compute()}") |