46 lines
1.2 KiB
Python
46 lines
1.2 KiB
Python
'''
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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.
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Let d1 be the 1st digit, d2 be the 2nd digit, and so on. In this 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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from itertools import permutations
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def listToNum(l):
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s = ''.join(map(str, l))
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return int(s)
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def check(l):
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primes = [2, 3, 5, 7, 11, 13, 17]
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for i in range(1, 8):
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# print(listToNum(l[i:i+3]))
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if listToNum(l[i:i+3]) % primes[i-1] != 0:
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return False
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return True
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def main():
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print("Hello this is Patrick")
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summand = 0
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# print(check(list(map(int, str(1406357289)))))
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for p in permutations(range(10)):
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if check(p):
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summand += listToNum(p)
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print(summand)
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if __name__ == "__main__":
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main() |