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.

``````

In [1]:

def has_property(s):
p = [2,3,5,7,11,13,17]

for i in range(2,9):
if int(s[i-1: i+2]) % p[i-2] != 0:
return False

return True

assert has_property('1406357289')

import itertools

pandigitals = []
for s in itertools.permutations([str(i) for i in range(10)]):
n = ''.join(s)

if has_property(n):
pandigitals.append(int(n))

print pandigitals
print sum(pandigitals)

``````
``````

[1406357289, 1430952867, 1460357289, 4106357289, 4130952867, 4160357289]
16695334890

``````
``````

In [ ]:

``````