http://xkcd.com/c287.html import Data.Array import Control.Monad -- exactly n v -- items in v that sum to exactly n -- returns list of solutions, each solution list of items exactly :: (Real a) => a -> Array Int a -> [[a]] exactly 0 v = return [] exactly n v = do i <- indices v guard (v!i <= n) liftM (v!i :) (exactly (n - v!i) (v `without` i)) -- for solutions that use items multiple times, -- change (v `without` i) to v -- v `without` i -- new array like v except one shorter with v!i missing without :: Array Int a -> Int -> Array Int a without v i = ixmap (lo, hi-1) f v where (lo, hi) = bounds v f j | j >= i = j+1 | otherwise = j play = exactly 1505 menu menu = listArray (1,6) [215, 275, 335, 355, 420, 580] test = exactly 10 (listArray (1,5) [1,1,2,3,4]) It disappoints me that there is no solution if each item is used at most once. However, do change the code to allow multiple uses, then there are many solutions.