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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.

  Submitted by Brian Smith    
Rating: 3.0000 (2 votes)
Solution: (Hide)
Let K='Knight', L='Liar', and P=Patient. After Frank's first question there are 5 scenarios:
  A B C D E
1.P K K K L
2.K P K K L
3.L L P K L
4.L K K P K
5.L K K K P
The responses to Frank's second question leaves only scenarios 3 and 4.

Since either Carl or Dave is the Patient, Frank should ask one of Alex, Bert or Eddy.

Frank could ask Alex "Is Bert a 'Liar'?" If Alex says yes, then Dave is the Patient, otherwise Carl is the Patient.

Frank could ask Bert or Eddy "Does two plus two equal four?" If the answer is yes then Dave is the Patient, otherwise Carl is the Patient.

Comments: ( You must be logged in to post comments.)
  Subject Author Date
Some ThoughtsPuzzle Thoughts K Sengupta2023-06-29 13:44:21
re: Did I do this right?Terence2005-10-12 10:12:16
SolutionDid I do this right?Lisa2005-05-09 16:19:21
Solutionyet another version of same solutionSteveH2004-10-27 19:25:20
SolutionNo SubjectPenny2004-10-27 18:14:32
SolutionSolution if I misunderstood the Mr. X thingDustin2004-10-27 17:22:33
SolutionExtra infonikki2004-10-27 17:10:22
SolutionSolution, but does Frank even need to ask a question?Dustin2004-10-27 17:07:59
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