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Know Who Your Friends Are (Posted on 2003-09-05) Difficulty: 3 of 5
A traveler passing through the land of liars and knights stops in at a pub, where he meets a group of six friendly locals. Their stories all are funny, but he doesn't know which ones to believe, so he asks them (tactfully) who the liars and knights are in the group. They make one statement each:

Amery: Cuthbert and Fredo are both liars.
Brant: Everard and Fredo are both knights.
Cuthbert: Brant is a liar and Everard is a knight.
Derek: Amery and Brant are both liars.
Everard: Cuthbert and Derek are both knights.
Fredo: Derek is a liar and Amery is a knight.

Which of the men are liars, and which are knights?
Remember: only part of a logical AND statement needs to be false for the entire statement to be false.

  Submitted by Bryan    
Rating: 2.9000 (10 votes)
Solution: (Hide)
Amery, Brant, and Fredo are liars, while Cuthbert, Derek, and Everard are knights.

Number the six statements 1-6 and nickname the men A-F. Start by assuming E is a liar. Then statements 2 and 3 are false, making B and C liars.

If D is a knight, statement 4 is true, making A a liar and statement 1 false. Since C is a liar, F must be a knight, making statement 6 true, making A a knight, which contradicts an earlier assumption. Therefore D is not a knight.

If D is a liar, statement 4 is false, and since B is a liar, A must be a knight, so statement 1 is true, making F a liar, so statement 6 is false, and since A is a knight, D must be a knight, which contradicts the original assumption.

Since D can be neither a liar nor a knight when starting from the assumption that E is a liar, this assumption must be wrong. Therefore E is a knight and statement 5 is true, so C and D are also knights. From statement 4, A and B are both liars, so from statement 2, F must be a liar.

In summary: the liars are Amery, Brant, and Fredo, and the knights are Cuthbert, Derek, and Everard.

Comments: ( You must be logged in to post comments.)
  Subject Author Date
SolAndre2010-06-02 18:13:06
answerK Sengupta2007-10-20 00:27:21
possible solutionDetti2004-10-06 17:30:44
Possible solutionratsnstuff2003-10-02 07:19:39
And the winner is ...Lawrence2003-09-05 22:21:39
SolutionSolutionDJ2003-09-05 15:28:15
SolutionsolutionCharlie2003-09-05 14:41:39
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