Few people know there is an asylum in the land of Knights and Liars. The asylum houses mental deviants called 'Patients' who randomly tell the truth or lie.

Its visiting day and Frank has just started the evening shift. There is only one group of visitors left. Unfortuneately, the previous guard forgot to tell Frank which one of the five people seated at the table is the Patient. (There is exactly one Patient at the table. There are no Knaves.) Frank asks the group "Which one of you is the Patient here?" He got the following responses:

Alex:Bert is the Patient.
Bert:Carl is not the Patient.
Carl:I am not the Patient.
Dave:I am not the Patient.
Eddy:Dave is the Patient.

This left Frank puzzled, so he asks "Who amongst you can I believe?" This time the responses were:

Bert:Carl is a 'Knight'.
Carl:Dave is a 'Liar'.
Dave:Alex is a 'Liar'.
Eddy:I am a 'Knight'.
Alex did not say anything this time.

Wanting to get a straight answer, Frank decides he should pull one member of the group aside to ask one last question.

Who should Frank choose and what question should he ask?

NOTE: If Mr X is the Patient, then the statements "Mr X is a 'Knight'" and "Mr X is a 'Liar'" are both false.

Anyone who says they are not the Patient is either a Knight or the Patient – they cannot be a Liar. So neither Carl nor Dave can be a Liar, they can only be a Knight or the Patient.

This means that Carl’s second statement is False since we know Dave can’t be a Liar. Therefore Carl isn’t a Knight.  So Carl must be the Patient.

Checking everyone else’s statements, Alex is a Liar, Bert is a Liar, Carl is the Patient, Dave is a Knight, and Eddy is a Liar. No contradictions.

So here's my question.  If there was so much extra information to begin with, why does Frank need even more?  But if he wants he can ask Dave who is the Patient, but he’ll just tell you it’s Carl.

Posted by nikki on 2004-10-27 17:10:22