-- 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.

import Euler

main = print $ sum $ do
  digits <- permutations [0..9]
  guard $ (digits!!0) /= 0
  guard $ (fromDigits $ map (digits!!) [7,8,9]) `mod` 17 == 0
  guard $ (fromDigits $ map (digits!!) [6,7,8]) `mod` 13 == 0
  guard $ (fromDigits $ map (digits!!) [5,6,7]) `mod` 11 == 0
  guard $ (fromDigits $ map (digits!!) [4,5,6]) `mod`  7 == 0
  guard $ (fromDigits $ map (digits!!) [3,4,5]) `mod`  5 == 0
  guard $ (fromDigits $ map (digits!!) [2,3,4]) `mod`  3 == 0
  guard $ (fromDigits $ map (digits!!) [1,2,3]) `mod`  2 == 0
  return (fromDigits digits)