#!/usr/bin/env python

"""
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 digits import generate_pandigitals

def has_p43_property(n):
    primes = [2, 3, 5, 7, 11, 13, 17]
    for i, offset in enumerate(range(1, 8)):
        substr = str(n)[offset:offset+3]
        if int(substr) % primes[i] != 0:
            return False
    return True

if __name__ == '__main__':
    result = filter(
        has_p43_property,
        generate_pandigitals(10, include_zero=True))
    for n in result:
        print n
    print sum(result)
