My 100 doors problem solution

100doors.hs

data DoorState = Open | Closed deriving (Show, Eq)

switch Open = Closed
switch Closed = Open

initial = map (\n -> (n, Closed)) [1..100]

visitMult xs n = map change  xs
    where mult x y = x `mod` y == 0
          change (x, st) = (x, if x `mult` n then switch st else st)

visitUpTo xs n = if n > 0 then (xs `visitMult` n) `visitMult` (n-1) else xs

main = do
    print $ initial `visitUpTo` 100