It is a logic puzzle left by my discrete math professor. We are learning propositional logic now. Here is the puzzle:
Among all the students in our class, at most two students give the 'correct' answer. There may be multiple 'correct' answers, even if someone gives the 'correct' answer, he or she may not be right ultimately. So the question is:
What is the 'correct' answer?
Note that this question is about marking exam papers so the teacher should mark the papers in a usual, normal and real-world way, i.e. answers like randomly choosing zero or one or two students' answer as the ultimate right answer(s) are not the initial aim of the question. So before posting your answer, think twice that in real world, do teachers mark test papers in that way you suggested?
For example, I tried like this:
The 'correct' answer is: "My answer and at most one answer of all the other students are right."
First my logic is right, explanation: If no one else or someone else give the same answer as me, then as my correct answer states, we are both right; while if more than one students give the same answer as me then the answer statement itself contradicts the fact so all our answers are wrong, i.e. even if all these answers are 'correct' yet still no one is right.
But my professor said that this is still kind of weird as in real world, teachers don't take notes of the number of 'correct' answers while marking and then decide who is/are right. And he gave me a hint that the answer is about paradox. But I can't figure it out. So in your opinion, what is the 'correct' answer (not limited by the hint paradox)?