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 1st digit, $d_2$ be the 2nd digit, and so on. In this way, we note the following:
$d_2d_3d_4$=406 is divisible by 2
$d_3d_4d_5$=063 is divisible by 3
$d_4d_5d_6$=635 is divisible by 5
$d_5d_6d_7=357$ is divisible by 7
$d_6d_7d_8=572$ is divisible by 11
$d_7d_8d_9=728$ is divisible by 13
$d_8d_9d_{10} =289$ is divisible by 17
Find the sum of all 0 to 9 pandigital numbers with this property.