Problem043.py

"""
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 d[1] be the 1st digit, d[2] be the 2nd digit, and so on. In this
way, we note the following:

  * d[2]d[3]d[4]=406 is divisible by 2
  * d[3]d[4]d[5]=063 is divisible by 3
  * d[4]d[5]d[6]=635 is divisible by 5
  * d[5]d[6]d[7]=357 is divisible by 7
  * d[6]d[7]d[8]=572 is divisible by 11
  * d[7]d[8]d[9]=728 is divisible by 13
  * d[8]d[9]d[10]=289 is divisible by 17

Find the sum of all 0 to 9 pandigital numbers with this property.
"""

from itertools import permutations

# TODO: This Problem could use some cleanup 


first_primes = [2, 3, 5, 7, 11, 13, 17]
digits = list(range(0, 10))
result = 0
for digits in (i for i in permutations(range(0, 10)) if i[0] != 0 and i[3] % 2 == 0 and sum(i[2:5]) % 3 == 0 and i[5] % 5 == 0):

    if all((digits[i]*100+digits[i+1]*10+digits[i+2]) % prime == 0 for prime, i in zip(first_primes, range(1, len(digits) - 2))):
        result += int("".join([str(i) for i in digits]))


print(result)