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Only One Question (Posted on 2005-02-16) Difficulty: 3 of 5
The following two facts are known about Adam, Bert, and Carl:

1) Of Adam, Bert, and Carl, there is one knight, one knave, and one liar.
2) Adam said once, "Bert said that Carl isn't a knight."

Can you ask one yes/no question to one person and figure out who is who? If not, how many questions must you ask?

See The Solution Submitted by Dustin    
Rating: 4.0000 (8 votes)

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Solution re: part one | Comment 2 of 23 |
(In reply to part one by Charlie)

My previous post established that you couldn't get by with less than three yes/no questions, but did not prove that you could do it with just three.  Here's a strategy for asking three yes/no questions.  The third question (if a third is necessary) depends on the answers to the first two.  I don't know if it's possible to make up all three questions in advance.

If we ask Carl if Adam is a Knave, and then ask Carl if Bert is a Liar, then, depending on their answers:

If the answer to both is No, then Adam is a Liar, Bert is a Knave and Carl is a Knight.

If the answers are Yes and No respectively, then Adam is a Liar, Bert is a Knight and Carl is a Knave.

If the answers are No and Yes respectively, it may still be true that Adam is a Liar, Bert is a Knight and Carl is a Knave, but it's also possible that  Adam is a Knave, Bert is a Knight and Carl is a Liar.  But since at this time you know Bert is a Knight, you can ask him, as your third question, whether Carl is the Liar.

If the answers to the first two questions were both Yes, then it might be that Adam is the Knight, Bert the Knave and Carl the Liar or that Adam is the Knave, Bert the Liar and Carl the Knight. If this is the case then ask Carl if Adam is the Liar. If he says Yes, you know Carl is the Liar, and if he says No you know he's the Knight, since you already know that Adam is not the Liar and that Carl is either the Liar or the Knight.


  Posted by Charlie on 2005-02-16 20:20:46
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