This is the whole Haskell code

haskell-solution.hs

import qualified Data.MultiSet as MultiSet
import qualified Data.Set as Set

limit :: Int
limit = 100

products :: MultiSet.MultiSet Int
products = MultiSet.fromList [ x * y | x <- [2..limit], y <- [x+1..limit-x] ]

sums_with_unambiguous_products :: Set.Set Int
sums_with_unambiguous_products = Set.fromList [ x + y | x <- [2..limit], y <- [x+1..limit-x], MultiSet.occur (x * y) products == 1 ]

products_causing_S_not_to_know :: MultiSet.MultiSet Int
products_causing_S_not_to_know = MultiSet.fromList [ p | s <- [2..limit], Set.notMember s sums_with_unambiguous_products, x <- [2..(s `div` 2)+1], let p = x * (s - x), MultiSet.occur p products > 1 ]

ambiguous_sums :: MultiSet.MultiSet Int
ambiguous_sums = MultiSet.fromList [ s | s <- [2..limit], Set.notMember s sums_with_unambiguous_products, x <- [2..(s `div` 2)+1], let p = x * (s - x), MultiSet.occur p products_causing_S_not_to_know == 1 ]

solutions :: [(Int, Int)]
solutions = [ (x, y) | s <- [2..limit], x <- [2..(s `div` 2)+1], let y = s - x ]

main :: IO ()
main = mapM_ print solutions