p043.py

# -*- coding: utf-8 -*-
"""
Created on Thu Jul  2 08:52:47 2020

@author: zhixia liu
"""

"""
Project Euler 43: Sub-string divisibility

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.

"""

#%% naive

from itertools import permutations

results = []
for n in permutations('0123456789',10):
    if n[0] == 0:
        continue
    n = ''.join(n)
    for i in range(1,8):
        if int(n[i:i+3])%([2,3,5,7,11,13,17][i-1]) != 0:
            break
    else:
        results.append(int(n))
print(results)
print(sum(results))