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Knight, Knave, and Liar Party (Posted on 2005-02-14) Difficulty: 3 of 5
I went to a crazy party where there were 8 people (whose names are conveniently only one letter long). Each person is either a knight, a knave, or a liar. I didn't know any of them very well, but I didn't want to ask them what they were directly, so I asked each person about two other people. They each gave two statements. Here are their responses:

A: B is a knave. C is a knave.
B: C is a liar. D is a knave.
C: D is a liar. E is a knight.
D: E is a knave. F is a knight.
E: F is a knight. G is a knight.
F: G is a liar. H is a liar.
G: H is a knave. A is a liar.
H: A is a liar. B is a knave.

Whom can I trust?

  Submitted by Dustin    
Rating: 4.0000 (3 votes)
Solution: (Hide)
Any time you know the identities of two consecutive persons, you can work backwards and see if it checks out.

Assume A is a knight. He calls B a knave. Now, work backwards to discover that B, a knave, makes two false statements. Therefore, the assumption that A is a knight is false.
Assume A is a knave. One of his two statments is true. Assume it's the B is a knave one. Now, with two consecutive persons, work backwards to discover that knave B makes two false statements.
OK, now assume it's the C is a knave one. B is not a knave, so either a knight or a liar. Can't be a knight, because he falsely calls C a liar. Work backwards to discover knave C tells two lies.
Since A can't be a knight, a truth-lie knave, or a lie-truth knave, he must be a liar.

G and H correctly say A is a liar, so neither one of G and H is a liar. So F, saying they both are, must be lying himself. Since A lies saying B is a knave, B must not be a knave. Since H calls B a knave, he must be lying in that statement, so H is a knave.
Since A and H are consecutive, and you have already eliminated the other possibilities for A, the solution that follows from working backwards must be correct. And indeed, when you check A's and H's statements to make sure they match, they do.

Final conclusion:
Knights: B and G.
Knaves: D, E, and H.
Liars: A, C, and F.

Comments: ( You must be logged in to post comments.)
  Subject Author Date
answerK Sengupta2007-11-24 10:39:04
Whom to trustscott2005-08-02 13:44:25
Some ThoughtsSolution?Angela2005-02-15 11:30:13
SolutionAvin2005-02-14 19:52:42
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