[43]SubStringDivisibility.py

"""
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 itertools import permutations
pans = ["".join(p) for p in permutations("0123456789")]

primes = [2, 3, 5, 7, 11, 13, 17]
total = 0

for pan in pans:
    for i in range(1, 8):
        test = int(pan[i:i+3:1])
        if test % primes[i-1]:
            break
        elif i == 7:
            total += int(pan)
    #if pan == "1406357289" : break
print(total)