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 1^st digit, d₂ be the 2^nd 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.

Written by gamwe6 who lives and works in San Francisco building useful things. You should follow him on Twitter