1. Write a function that, given a sequence of either positive or negative integers, returns true if any subset of the list sums up to zero. Eg: find-solutions ([-7 4 3 8 -5]) => true find-solutions ([-6 2 3]) => false 2. Make it work with any number, not just zero. Eg: find-solutions (0, [-7 4 3 8 -5]) => true find-solutions (13, [-7 4 3 8 -5]) …

FuncPuzzle4.fsx

let initMask length = List.init length (fun i -> if i = length - 1 then 1 else 0)
let addOne mask = List.foldBack (fun t (resList, c) -> (if (t = 1 && c = 1) then (0::resList, 1) elif (t = 0 && c= 0) then (0::resList, 0) else (1::resList, 0))) mask ([], 1) |> fst
let subsetsWhosSumsSatisfiesPredicate lst pred = 
    let rec work mask = seq{
        let sum, subSet = List.fold2 (fun (accSum, subSet) m l -> if m = 0 then (accSum, subSet) else (accSum + l, l::subSet)) (0, []) mask lst
        if pred sum then
            yield (List.rev subSet)
        if List.exists (fun t -> t = 0) mask then
            yield! work (addOne mask)
        }
    work (initMask (List.length lst))

//Tests in repl
> subsetsWhosSumsSatisfiesPredicate [-7;4;3;8;-5] ((=)0);;
> let isEven s = s / 2 = 0;;
> let isOdd s = s % 2 <> 0;;
> subsetsWhosSumsSatisfiesPredicate [-7;4;3;8;-5] (isEven);;
> subsetsWhosSumsSatisfiesPredicate [-7;4;3;8;-5] (isOdd);;