problem043.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.

import unittest

from common_funcs import answer, is_pandigital, list_perms

def has_this_property(n):
    primes = [2,3,5,7,11,13,17]
    
    for i in range(len(primes)):
        for j in range(3):
            a = int(str(n)[i+1:i+4])
            if a % primes[i] != 0:
                return False   
    return True
    
class example(unittest.TestCase):
    def test(self):
        self.assertTrue(has_this_property(1406357289))
    
def solve():
    a = [s for s in list_perms('9876543210')] # filter out 1 to 9 pandigital
    ans = 0
    for perm in a:
        if has_this_property(perm) == True:
            ans += perm
    return ans
    
answer(solve)