01-29-2004, 12:46 AM
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#7 (permalink)
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Junkie
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This one seems to work:
Quote:
As a contestant on the island's only TV quiz show, you face 3 residents: Tommy, Babette and Cathy. You are told that 1 is a Knight, 1 a Knave, and 1 a Normal. Tommy says, "I am a Normal." Babette says, "That is true." Cathy says, "I am not a Normal." Your job is to prove with certainty what each is. (Smullyan's #39)
Possible solutions
Tommy is a Knight.
Tommy is a Knave.
Tommy is a Normal.
Babette is a Knight.
Babette is a Knave.
Babette is a Normal.
Cathy is a Knight.
Cathy is a Knave.
Cathy is a Normal.
Fact list
Knights always tell the truth.
Knaves always lie.
Normals sometimes lie, and sometimes tell the truth.
1 contestant is a Knight, 1 a Normal, and 1 a Knave.
Tommy says, "I am a Normal."
Babette says, "That is true."
Cathy says, "I am not a Normal."
Evaluation
If Tommy is lying or telling the truth, he cannot be a Knight. Therefore he is either a truth-telling Normal, or a liar. If he is lying, he must be a Knave. For if he were a lying Normal, he would be telling the truth - an impossibility. If Babette is telling the truth, she is the Knight, and Tommy the Normal. If she is lying, she is a lying Normal, and Tommy is the Knave. If Cathy is lying, she is a Normal. If she is telling the truth, she must be a Knight. As we have shown 1 of the first 2 must be a Normal, Cathy has to be the Knight. Therefore, Babette is the Normal and Tommy the Knave.
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From here: http://www.classroomtools.com/logic2.htm
Maybe some more match, but if you replace knight with truth-teller, knave with liar, and sometimes with normal, you should get your answer. |
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