p043.py

# Steve Beal
# Project Euler problem 43 solution
# 3/11/15

# 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 utils import permutations

def sum_prime_subdivisible_pandigitals():
    perms = permutations("0123456789")

    s = 0
    for p in perms:
        if int(p[7:]) % 17 == 0 and int(p[6:9]) % 13 == 0 and \
           int(p[5:8]) % 11 == 0 and int(p[4:7]) % 7 == 0 and \
           int(p[3:6]) % 5 == 0 and int(p[2:5]) % 3 == 0 and \
           int(p[1:4]) % 2 == 0:
            s += int(p)
    return s

print(sum_prime_subdivisible_pandigitals())