Project Euler Problem 043

# Statement

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.

# Solution

Self explanatory solution.

from itertools import permutations index = [0, 2, 3, 5, 7, 11, 13, 17] def has_divisibility_property(n): str_n = str(n) for i in range(1,8): num = str_n[i:i+3] if int(num) % index[i] != 0: return False return True if __name__ == '__main__': digits = set(str(x) for x in range(0, 10)) result = 0 for x in range(1,10): tmp = digits.copy() tmp.remove(str(x)) result += sum(int(str(x) + ''.join(i)) for i in permutations(tmp) if has_divisibility_property(str(x) + ''.join(i))) print("The result is:", result)

The Python fiel is available for download here.