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.
Please correct me if I err:
a. The puzzle, using normal Boolean reasoning is unsolvable.
b, To find what the author intended and assuming a minor error on
his part, I tried the "reverse engineering" leading to possible solution":
Danny is telling the truth - all other lie and the order is ABDC.
c, Whoever composed the puzzle assumed that Carl is an avid liar
and the negation of his 2 statements X&Y must be
( notX)&(notY); while the Boolean negation is ( notX)&(Y) OR(inclusive) ( X)&(notY).
d. So if we assume (not implied by the text)that Carl lied on both counts (like 2 statements) there is a solution