-- Take the number 192 and multiply it by each of 1, 2, and 3:
--
--   192 × 1 = 192
--   192 × 2 = 384
--   192 × 3 = 576
--
-- By concatenating each product we get the 1 to 9 pandigital, 192384576. We
-- will call 192384576 the concatenated product of 192 and (1,2,3).
--
-- What is the largest 1 to 9 pandigital 9-digit number that can be formed as
-- the concatenated product of an integer with (1,2, ... , n) where n > 1?

import Euler

pandigital n = sort (toDigits n) == [1..9]

concatProduct n = fromDigits $ concat $ zipWith const products upTo9
   where
      products = map (toDigits . (n*)) [1..]
      lengths  = map length products
      totals   = scanl1 (+) lengths
      upTo9    = takeWhile (<= 9) totals

main = print $ maximum $ [ n | n <- map concatProduct [1..9999]
                             , n >= 100000000
                             , pandigital n ]