FF13-2 Clock Puzzle Solver

import Data.List

----- the numbers on the clock are [3,2,1,1,2,1] and their orders are [0..5] correspondingly
testdata1 :: [Int]
testdata1 = [3,2,1,1,2,1]


----- convert the order of the elements to a list of possible next moves
----- 1 (order) -> [3,2,1,1,2,1] (list of numbers) -> [3,5] (list of orders)
getSRoutine :: Int -> [Int] -> [Int]
getSRoutine a ls = nub [fd, sd]
                   where len = length ls
                         fd = (a + ls!!a) `mod` len
                         sd = (a - ls!!a) `mod` len

----- a naive backtrack solver to show the orders of all possible routes
----- REMARK: the orders are of [0..], not [1..]
tokSolver :: [Int] -> [[Int]]
tokSolver [] = []
tokSolver ls = concat [ tokSolver' len [[a]] | a <- [0..len-1] ]
               where len = length ls
                     tokSolver' :: Int -> [[Int]] -> [[Int]]
                     tokSolver' 1 routes = routes
                     tokSolver' len routes = tokSolver' (len-1) (concatMap nextMove routes)
                                             where nextMove route = [ route ++ [s] | s <- filter (\x -> x `notElem` route) $ getSRoutine (last route) ls ]