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Sub-string Divisibility

 Published on Friday, 9th May 2003, 06:00 pm; Solved by 63773;
Difficulty rating: 5%

Problem 43

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.