Add solution for problem 43.

Problem043.hs

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+-- 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)