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Visiting Day at the Asylum (Posted on 2004-10-27) Difficulty: 3 of 5
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.

See The Solution Submitted by Brian Smith    
Rating: 3.0000 (2 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
Solution Solution, but does Frank even need to ask a question? | Comment 1 of 7

(P.S. I am going to use the first letters of their names.)

Suppose A is the patient.  From their first responses, B, C, and D are all knights, and E is a liar.  However, C calls D a liar, which is not true. Contradiction.  That means A is not the patient.

Suppose B is the patient.  From their first responses, A, C, and D are all knights, and E is a liar.  However, C calls D a liar, which is not true.  Contradiction.  That means B is not the patient.

Suppose C is the patient.  From their first responses, A, B, and E are liars, and D is a knight.  All of their second responses check out.  So C could be the patient.

Suppose D is the patient.  From their first responses, B, C, and E are all knights, and A is a liar.  However, C calls D a liar, which is not true.  Contradiction.  That means D is not the patient.

Suppose E is the patient.  From their first responses, B, C, and D are all knights, and A is a liar.  However C calls D a liar, which is not true.  Contradiction.  That means E is not the patient.

So C is the patient, D is a knight, and A, B, and E are liars, which is ironic because "Honest ABE" would never lie.

My only concern is Frank's last question he can ask.  I seemed to get everything without needing another question.  This leads me to believe that either Brian Smith is trying to throw us off, or I did something wrong.  Either way, this was fun.


  Posted by Dustin on 2004-10-27 17:07:59
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