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problem43.py
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problem43.py
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#! -*- utf-8 -*-
from itertools import permutations as perm
import time
"""
========================
Project Euler Problem 43
========================
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.
"""
def problem43():
nums=set(int(''.join(i)) for i in perm("0987654321")if i[5]=='5' and int(''.join(i[1:4]))%2==0 and int(''.join(i[7:]))%17==0
and int(''.join(i[6:9]))%13==0 and int(''.join(i[5:8]))%11==0 and int(''.join(i[4:7]))%7==0
and int(''.join(i[2:5]))%3==0)
return sum(nums)
if __name__=='__main__':
time1=time.time()
print problem43()
time2=time.time()
print time2-time1