euler_043.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 utils import lazy_primes
from itertools import islice, permutations


PRIMES = list(islice(lazy_primes(), 7))


def divisible(perms):
    snum = ''.join(map(str, perms))
    return all((int(snum[idx+1:idx+4]) % prime == 0 for idx, prime in enumerate(PRIMES)))


def p43():
    return sum(int(''.join(map(str, perm)))
               for perm in filter(divisible, permutations(range(10))))