type Cell =
    | Assigned of char
    | Undecided of char list

let assign row col value board =
    List.mapi (fun i cell ->
        match (i / 9, i % 9, cell) with
        | (r, c, _) when r = row && c = col -> Assigned value
        | (r, c, Undecided xs) when
            r = row ||
            c = col ||
            (r / 3 = row / 3 && c / 3 = col / 3) ->
                Undecided (List.filter ((<>) value) xs)
        | (_, _, cell) -> cell) board

let rec solve board =
    let rec solve' index board' =
        match board' with
        | []                   -> Some board    // Solved
        | (Undecided []) :: _  -> None          // Impossible to solve
        | (Assigned _) :: tail ->
            solve' (index + 1) tail
        | (Undecided xs) :: _ ->
            List.tryPick (fun c ->
                solve (assign (index / 9) (index % 9) c board)) xs
    solve' 0 board

server = new Socket(serverIP, Integer.valueOf(serverPort));
input = new BufferedReader(new InputStreamReader(server.getInputStream()));
response = input.readLine();