Each of the four students Andy, Bert, Carl and Danny appeared in a quiz. The following are four statements made by them on their scores in the exam.
Andy: Bert has scored more than me.
Bert: I have scored less than Danny.
Carl: Andy is telling the truth and Danny has scored less than Carl.
Danny: Both Andy and Bert are telling lies.
If precisely one of the friends is the knight who always speak the truth and the remaining three are liars who always speak falsely, then what is Carl’s score placed?
Is it highest, or 2nd highest, or 3rd highest or the lowest? Give reasons for your answer.
(In reply to ....HOWEVER
by Ady TZIDON)
This was the "Case 3" I outlined in my post.
Even if we assume that both of Carl's statements are false, we still don't know the answer. All that tells us is:
1) Andy is NOT telling the truth.
2) Danny has NOT scored less than Carl.
From 1 we know:
3) Bert has NOT scored more than Andy.
So we have A > B, and D > C.
IF Danny is the Knight and Bert is a Liar, then we learn that B > D, and thus (as you point out) we'd have the order ABDC.
HOWEVER, we don't know if Danny is the Knight. Alternately, Bert could be the Knight and Danny could be the Liar. In that case we have A > B, D > C, and D > B, and there is no way to conclude where C is ranked.
So even if we assume that the author intended for the negation of X&Y to be (notX)&(notY), we still don't have a unique solution.
Posted by tomarken
on 2014-05-13 18:00:48