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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?
看答案
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.
解析
我要編輯答：其中一個是騎士。
由於他們中只有一個是Joker，但他們都說別人是Joker，所以Joker說謊。如果Joker說的是實話，那麼他們會說他們自己就是Joker，但這三人都沒有這樣說。
由此可知，其中一人說的是實話。例如，假設Ellis是Joker，那麼Gobi是說實話。或者你可以假設Farin是Joker，在這種情況下是Ellis說實話，舉Gobi也是。
這個說實話的人不會是一個Joker，因為所有的對話都指責其他人是Joker，而且，說實話的Joker會說他們自己就是Joker。所以說真話的人必須是knight。
所以一個人是Joker，至少有一個是knight。第三個人不能是knight（他必須是一個knave），因為騎士和第三個人都說別人是Joker，而只會有一個Joker所以是不成立的。例如，如果Ellis是Joker，那麼Gobi就是在說實話（並且他是knight），而Farin正在撒謊（並且他是knave）。
所以，因為只有一個說真話的人，而他就是騎士。
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