def has_property(p):
primes = [2, 3, 5, 7, 11, 13, 17]
for i in range(1, len(p) - 2):
n = get_int(p[i:i + 3])
if n % primes[i - 1]:
return False
return True
Sub-string divisibility
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 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 itertools import permutations
from euler import get_int
def has_property(p):
primes = [2, 3, 5, 7, 11, 13, 17]
for i in range(1, len(p) - 2):
n = get_int(p[i:i + 3])
if n % primes[i - 1]:
return False
return True
print sum([get_int(p) for p in permutations(range(10)) if has_property(p)])
