Почему тут, с BufferedInputStream / BufferedOutputStream вылетает EOFException? 
File temp = File.createTempFile("my_file", "temp");
        Solution solutionSave = new Solution(6);
        Solution solutionLoad = new Solution(20);

        try (ObjectOutputStream oos = new ObjectOutputStream(new BufferedOutputStream(new FileOutputStream(temp)));
             ObjectInputStream ois = new ObjectInputStream(new BufferedInputStream(new FileInputStream(temp)))) {
            oos.writeObject(solutionSave);
            solutionLoad = (Solution) ois.readObject();
        } catch (IOException e) {
            e.printStackTrace();
        }
А тут, без BufferedInputStream / BufferedOutputStream не вылетает? 
File temp = File.createTempFile("my_file", "temp");
       Solution solutionSave = new Solution(6);
       Solution solutionLoad = new Solution(20);

       try (ObjectOutputStream oos = new ObjectOutputStream(new FileOutputStream(temp));
            ObjectInputStream ois = new ObjectInputStream(new FileInputStream(temp))) {
           oos.writeObject(solutionSave);
           solutionLoad = (Solution) ois.readObject();
       } catch (IOException e) {
           e.printStackTrace();
       }