Solving http://www.rubyquiz.com/quiz60.html with the power of list monad

numeric_maze.hs

import Control.Monad (guard)

double :: Int -> Int
double = (2 *)

add_two :: Int -> Int
add_two = (2 +)

halve :: Int -> Int
halve n = n `div` 2
  
paths :: Int -> Int -> [[Int]]
paths start target = map reverse $ search [start]
  where
    search :: [Int] -> [[Int]]
    search path@(x:xs) = do
      guard $ length path < 10
      op <- if even x then [double, add_two, halve] else [double, add_two]
      let new = op x
      guard $ new `notElem` path
      if new == target
        then return $ new:path 
        else search $ new:path

Example :

*Main> paths 9 2
[[9,18,20,22,24,12,6,8,4,2],[9,18,20,10,12,14,16,8,4,2],[9,18,20,10,12,6,8,4,2],[9,11,22,24,12,14,16,8,4,2],[9,11,22,24,12,6,8,4,2],[9,11,13,26,28,14,16,8,4,2],[9,11,13,15,30,32,16,8,4,2]]