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.

It's clear by his own statement, as well as Danny's, that Carl isn't the Knight.  But this leaves multiple interpretations.

Case 1: "Andy is telling the truth" is true, and "Danny has scored less than Carl" is false.  From this we'd know B > A, B > D, and D > C.  So C is less than B and D, but we don't know it's relation to A, so C could be 3rd or 4th. 

Case 2: "Andy is telling the truth" is false, and "Danny has scored less than Carl" is true.  From this we'd know A > B and C > D.  But we wouldn't know if Bert was telling the truth or lying, and even if we did it still wouldn't tell us where C ended up.

Case 3: Both parts of Carl's statement are false.  From this we'd know A > B and D > C.  But we wouldn't know if Bert was telling the truth or lying.  IF Bert was lying, then this would tell us that B > D, and thus C was the lowest.  But if Bert was the Knight, then D > B and we wouldn't know C's rank.

 

Posted by tomarken on 2014-05-13 11:41:07