Problem Archive

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.