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| Knave trial (Posted on 2011-02-03) |
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There was a trial in a land where every inhabitant is either a knight, a liar, or a knave. There were three suspects, A, B, and C.
A:I am a knight.
B:I am a liar.
C:I am a knave.
A:No knaves are guilty.
B:A is a knight.
C:At most one of us is guilty.
What are A, B, and C, and who is guilty?
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Submitted by Math Man
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Rating: 4.5000 (2 votes)
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Solution:
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B is obviously a knave because neither a knight nor a liar can claim to be a liar. Since B is a knave, B's first statement is false, so B's second statement is true. Therefore, A is a knight. C claimed to be a knave, so C is not a knight. If C is a knave, then C's first statement is true, so C's second statement is false. If C is a liar, then C's second statement is false. Either way, C's second statement is false. Therefore, at least two of them are guilty. Since A is a knight, no knaves are guilty, so B is innocent. Therefore, A and C are both guilty. Since no knaves are guilty, C is a liar.
A:guilty knight
B:innocent knave
C:guilty liar
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