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Simple Logic Questions 3 - TRUTH-SEEKING邏輯謎題

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Simple Logic Questions 3
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      Suppose you are visiting an island with knights who always tell the truth, 
      knaves who always lie, and jokers who can do either.
      
      You meet three islanders named Ellis, Farin, and Gobi.
      They all know what each other is (a knight, knave or joker)
      and make the following statements:
 
      
      If exactly one of them is a joker, how many of them are knights?
 
TRUE2018-04-29提供(2018-04-29修改)
來源:BRILLIANT
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      Answer: One of them is a knight.
      
  • Since exactly one of them is a joker, and they all accuse different people of being jokers, then the joker is lying. If the joker were telling the truth, then they would claim that they themselves are the joker, which none of these three are doing.
 
  • Given this, one of them is telling the truth. For instance, suppose that Ellis is the Joker, then Gobi is telling the truth. Or you can suppose that Farin is the joker, in which case Ellis is telling the truth. Same thing with Gobi.
 
  • This person telling the truth can't be a joker since all the statements accuse other people of being jokers and, again, a joker telling the truth this one would say that they, themselves, are the joker. So the truth-teller must be a knight.
 
  • So one person is a joker, and at least one is a knight. The third person can't be a knight (they must be a knave) because the knight and the third person are saying that different people are jokers, which is impossible with only one joker. For instance, if Ellis is the joker, then Gobi is telling the truth (and is a knight), and Farin is lying (and is a knave.
 
  • So, since there is only one truth-teller there must be only one knight.
 
  • Note: "None of them are knights" is incorrect because one of them is a joker, and all of them point to another person as the joker. One of them has to be telling the truth, and it's not the joker.

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作者:TRUE | 歷史版本

      這道題目的英文比較多,如果有大大有興趣的話可以翻譯一下。
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      以上。
 
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