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As simple as it gets (Posted on 2006-09-02) Difficulty: 3 of 5
In Tripleland, natives always go in trios: a knight, a knave, and a liar.

Once I met such a trio, and I asked one of the natives a simple question ("simple" meaning, "of six words or less"); he answered, and I knew what type he was. Then, I asked another of the natives a different simple question; he answered, and I knew what type he was, and therefore, the type of the third one too.

"Logical" thinking: This cannot be. The natives could be in six possible orders. Two yes-no questions allow four combinations. Thus, you cannot pick one out of six with only two questions; you need one more!

How could this be? What's wrong with the reasoning above?

  Submitted by Federico Kereki    
Rating: 4.5000 (2 votes)
Solution: (Hide)
I asked "Are you a liar?", and the first one said "Yes", showing he was a Knave. I asked the second "Is he a knave?", and depending on his answer I knew whether he was a knight or a liar.

The reasoning is wrong because the first question allowed us to discern what the first native was (a 1 in 3 probability), then leaving two cases for the second question. A yes/no question need not imply 50%/50% distribution of cases: in this problem, a "YES" answer implies only one case, while a "NO" would have implied two cases, and then I would have needed an extra question.

Comments: ( You must be logged in to post comments.)
  Subject Author Date
SolutionSolutionMath Man2012-10-20 16:35:00
re(3): Two waysDej Mar2006-09-02 22:19:28
re(2): Two waysCharlie2006-09-02 16:38:05
Hints/TipsIdea (no spoiler)Old Original Oskar!2006-09-02 16:03:38
Questionre: Two wayse.g.2006-09-02 13:06:33
SolutionTwo waysCharlie2006-09-02 11:52:38
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