Project Euler, 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 1st digit, $d_{2}$ be the 2nd digit, and so on. In this way, we note the following:

$d_{2} d_{3} d_{4} = 406$ is divisible by 2
$d_{3} d_{4} d_{5} = 063$ is divisible by 3
$d_{4} d_{5} d_{6} = 635$ is divisible by 5
$d_{5} d_{6} d_{7} = 357$ is divisible by 7
$d_{6} d_{7} d_{8} = 572$ is divisible by 11
$d_{7} d_{8} d_{9} = 728$ is divisible by 13
$d_{8} d_{9} d_{10} = 289$ is divisible by 17

Find the sum of all 0 to 9 pandigital numbers with this property.

Runtime: 0

Average: 0 Runs: 0

SD: 0 ms

Max: 0

Min: 1000

To solve this I checked all the pandigital numbers from 1,023,456,789 to 9,876,543,210 to see if they fit this pattern. I used the Pandita algorithm to permute through the numbers and made a batch of functions to do all the steps for solving it.

I want to find a faster solution though. This one relies on checking 10! - 9! numbers and takes over 2 seconds...

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