Puzzle.hs

module Puzzle where

import Data.List (permutations)
import Control.Monad (guard)

solution = do
  [a,b,c,d,e,f] <- permutations "123456"
  guard $ multiple 6 [a,b,c,d,e,f]
  guard $ multiple 5 [a,b,c,d,e]
  guard $ multiple 4 [a,b,c,d]
  guard $ multiple 3 [a,b,c]
  guard $ multiple 2 [a,b]
  return [a,b,c,d,e,f]
  where multiple n digits = mod (read digits) n == 0

A six digit number "abcdef" is formed using each of the digits 1,2,3,4,5,6 once and only once so that "abcdef" is a multiple of 6, "abcde" is a multiple of 5, "abcd" is a multiple of 4, "abc" is a multiple of 3 and "ab" is a multiple of 2.
a) Find a solution for "abcdef"
b) Is the solution you find unique?