Truth-tellers, liars and ambiguous, solution verification
Solution 1:
In general you got the logic just fine, but I still have two comments:
- You have to be careful when using ‘truth-teller’… or at least make clear what you mean by it. Is A being a ‘truth-teller’ the same as A being a worker? Or do you mean to say that in that particular instance A was telling the truth ( and so A could be a worker or a student)? Same goes for your use of ‘liar’.
Indeed, in the case of A answering ‘Yes’ to the first question, you seem to use ‘liar’ to cover both the case where A is a businessman and the case where A is a student. But in the case where the answer is ‘No’, you use ‘truth-teller’ for just the case where A is a worker. So… for a clearer proof, this needs to be cleared up.
- The proof shows that with that first question you can figure out whether B is a student or not. But you also said that the overall strategy was to first figure out who the student is. But if you find that B is not a student after the first question, that does not mean that you know who the student is. So … maybe the overall strategy us not such a clear ‘first figure out the student and then…’ strategy.
In fact, while I understand that you are really only asking to see if you understand the logic of the first half of the proof (dealing with the first question), I would encourage you to work out the second half (dealing with the second question) as well. And note: that second question involves the use of ‘truth-teller’ … so again: what exactly is meant by that? Since the first question refers to ‘worker’, I am inclined to think that the use of ‘truth-teller’ in the second question means ‘worker or student-who-currently-tells-the-truth’ … but I am not sure. But if you analyze the logic, you should probably be able to tell how this meant. Again, in general you are doing a good job with the logic, so I think you’ll be able to get this. Good luck!