Count all solutions on the chessboard

nqueens3.fs

    member x.safe(row) =
        not (rows.[row] || fwDiagonals.[row + col] 
                        || bwDiagonals.[row - col + size - 1])

    member x.placeQueen(row) =
        rows.[row] <- true
        fwDiagonals.[row + col] <- true
        bwDiagonals.[row - col + size - 1] <- true
        col <- col+1
        
    member x.removeQueen(row) =
        col <- col-1
        rows.[row] <- false
        fwDiagonals.[row + col] <- false
        bwDiagonals.[row - col + size - 1] <- false

    member x.countSolutions() =
        if col = size then 1
        else
            let mutable answer = 0
            for row in 0..size-1 do
                if x.safe(row) then
                    x.placeQueen(row)
                    answer <- answer + x.countSolutions()
                    x.removeQueen(row)
            answer