problem43.py

"""
Sub-string divisibility
Project Euler Problem #43
by Muaz Siddiqui

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 euler_helpers import timeit, perms

@timeit
def answer():
    pandigitals = perms(1234567890)
    sum_ = 0
    for num in pandigitals:
        next = str(num)
        if len(next)==10 and not int(next[1:4])%2 and not int(next[2:5])%3 and not int(next[3:6])%5 and not int(next[4:7])%7 and not int(next[5:8])%11 and not int(next[6:9])%13 and not int(next[7:10])%17:
            sum_ += num
    return sum_