-- The cube, 41063625 (345^3), can be permuted to produce two other cubes:
-- 56623104 (384^3) and 66430125 (405^3). In fact, 41063625 is the smallest
-- cube which has exactly three permutations of its digits which are also cube.
--
-- Find the smallest cube for which exactly five permutations of its digits are
-- cube.

import Euler

main = print $ head $ do
   let cubes = map (^3) [1..]
   x <- cubes
   let ps = filter ((== sort (toDigits x)) . sort . toDigits)
          $ takeWhile (< 10 * x) $ dropWhile (< x) cubes
   guard $ length ps == 5
   return x