Problem 43

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 $d_1$ be the $1$^st digit, $d_2$ be the $2$^nd digit, and so on. In this way, we note the following:

$d_2d_3d_4=406$ 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.

子串的可整除性

$1406357289$是一个$0$至$9$全数字数，因为它由$0$到$9$这十个数字排列而成；但除此之外，它还有一个有趣的性质：子串的可整除性。

记$d_1$是它的第$1$个数字，$d_2$是第$2$个数字，依此类推，注意到：

$d_2d_3d_4=406$能被$2$整除
$d_3d_4d_5=063$能被$3$整除
$d_4d_5d_6=635$能被$5$整除
$d_5d_6d_7=357$能被$7$整除
$d_6d_7d_8=572$能被$11$整除
$d_7d_8d_9=728$能被$13$整除
$d_8d_9d_{10}=289$能被$17$整除

找出所有满足同样性质的$0$至$9$全数字数，并求它们的和。