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邏輯難題,解
送交者: nanweishui 2005年08月22日15:38:20 於 [靈機一動] 發送悄悄話
There are three people in front of you. You know that: One of them is God. He knows everything, and always tells the truth. One of them is the Devil. He also knows everything, but lies. The third person knows nothing, but answers questions as if he knows the answers. His answers, however, are completely useless and could be right or wrong. You can ask a total of three questions that can clearly be answered with yes or no, each to one of the persons. You may choose whom to ask first. Determine who is who... 解:

Call these 3 persons A, B and C. Let’s ask A the first question:

Question 1: Let’s say human is worse than God and Devil is worse than human. Is person B worse than person C?

Without the loss of generality, we can assume the answer is “Yes” (otherwise we only need to switch person B and C). This gave us three possibilities: 1) A is human; 2) A is God and he answered truthfully (so B is Devil and C is human). 3) A is Devil and he lied (so B is God and C is human).

That is, we have following 4 scenarios:
(1) A = Human, B = Devil, C = God
(2) A = Human, B = God, C = Devil
(3) A = God, B = Devil, C = Human
(4) A = Devil, B = God, C = Human.

We can see that person B is definitely NOT human (and this is the purpose of Question 1). The remaining part is much easier:

Ask the following questions to B:

Question 2: Do you know who is God?
If Yes, person B is God and we are in scenario (2) or (4).
If No, person B is Devil and we are in scenario (1) or (3).

Question 3: Is person A human:
If Yes, we are in scenario (2) or (3);
If No, we are in scenario (1) or (4).

Combining the answers to Question 2 and 3, we can figure out who is who.

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