My teacher likes to give online quizzes that are about 20-30 questions long. Every student has the same questions in the same order. We are not told after taking the quiz which questions we got wrong, but the system does tell us our score.
That made me curious as to inferring the answers statistically. (Note that this is not cheating, as the teacher encourages heavy collaboration.) My idea is this: when a courageous person is confident of his answers, he submits the quiz. Each answer for each question has a fitness score. Each time someone gets the result after taking the quiz, the square of this quiz score is added to the fitness score of every answer he selected. After some tries, we will have a good prediction of the right answers for all of the questions.
Is this statistically rigorous? If not, are there better procedures?