## Sub-string divisibility

### Problem 43

Published on Friday, 9th May 2003, 06:00 pm; Solved by 34497; Difficulty rating: 5%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 *d*_{1} be the 1^{st} digit, *d*_{2} be the 2^{nd} digit, and so on. In this way, we note the following:

*d*_{2}*d*_{3}*d*_{4}=406 is divisible by 2*d*_{3}*d*_{4}*d*_{5}=063 is divisible by 3*d*_{4}*d*_{5}*d*_{6}=635 is divisible by 5*d*_{5}*d*_{6}*d*_{7}=357 is divisible by 7*d*_{6}*d*_{7}*d*_{8}=572 is divisible by 11*d*_{7}*d*_{8}*d*_{9}=728 is divisible by 13*d*_{8}*d*_{9}*d*_{10}=289 is divisible by 17

Find the sum of all 0 to 9 pandigital numbers with this property.