perplexus.info :: Liars and Knights : Quiz Score Settlement

Quiz Score Settlement (Posted on 2014-05-13)

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.

No Solution Yet Submitted by K Sengupta

Rating: 2.3333 (3 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)

The way I look at it

| Comment 1 of 5

Even assuming they all had different scores, I can't figure out Carl's position:

If Andy is the knight:

Bert has scored more than Andy and also more than Danny, and Danny has scored more than Carl. But if Andy is in last place then Carl is in second to last, or third, place.

If Bert is the knight:

Both Andy and Danny beat out Bert, but we can't tell about Carl.

Carl can't be the knight as he claims another is telling the truth.

If Danny is the knight, Andy beat Bert, who beat Danny, but we don't know about Carl as Carl's falsehood is assured by the first part of his statement.

Posted by Charlie on 2014-05-13 11:15:12

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