世界上最难的趣味逻辑题

作者 TombCrow, 2004 八月 28, 21:04:50

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TombCrow


subaru

我接着想
站长,把你手机号给我,有事要问你

TombCrow

发了,我漫游,不要给我打电话呀!

TombCrow

爱因斯坦确实够弓虽!
我发现三个人的确需要互相认识才有解

爱因斯坦


TombCrow

你的就是正确答案啊:P

答案在
Boolos (1998) Logic, Logic, and Logic Harvard University Press, 第29章

我没有这本书,但是我觉得你的推理没有问题,顶多是换几个问题,思路是一样的。

首先用一个问题确定JA和MA哪个是是,哪个是不是,这就要保证说真话的和说假话的回答一致,问题可以是:
你说的是真话吗?/ 你说的是假话吗?......
这样的问题,必然有两个以上答案是一致的(因为说真话的和说假话的回答必定相同),从而判断出哪个是是,哪个是不是。

第二个问题用来确定出其中一个精灵的身份,问题可以是:
你是随机的吗?
回答出现两个是的,那么唯一说不是的就是说真话的;如果回答中出现两个不是,唯一说是的就是说假话的。

当然也可以是更加直观的问题:
你是人吗?/ 你还活着吗?......
如果两个回答是,一个回答不是,那么唯一回答是或不是的那个精灵的身份可以马上判断出来。(例如对"你还活着吗"这样的问题,唯一回答不是的必然是说假话的,如果唯一的回答是是,那么它就是说真话的)

此时需要再用一个是非题搞清楚剩下两个精灵的身份。由于其中一个是随机的,根本不可能靠那两个精灵的回答来判断它们,只能利用已经辨别出来的那位来确定剩余两个的身份(问:X是那位随机的吗?由于你已经知道它会说真话还是假话,那么X的身份可以辨认,则剩下那位的身份也能推知)。

推理过程仍然是爱因斯坦的思路,我觉得如果它们不认识的话此题不可能有解。前几天一直没有想过这道题,今天在长途车上打发了一下时间,发现你果然厉害呀,呵呵......


rainbow


TombCrow

老外不是一般的罗索阿~

Your first move is to find a god who you can be certain is not Random, and hence is either True or False.

To do so, turn to A and ask Question 1:  Does da mean yes iff, you are True iff B is Random?  If A is True or False and you get the answer da, then as we have seen,B is Random, and therefore C is either True or False; but if A is True or False and you get the answer ja, then B is not Random, therefore B is either True or False.

But what if A is Random?

If A is Random, then neither B nor C is Random!

So if A is Random and you get the answer da, C is not Random (neither is B,but that's irrelevant), and therefore C is either True or False; and if A is Random and you get the answer ja, B is not random (neither is C, irrelevantly), and therefore B is either True or False. Thus, no matter whether A is True, False, or Random, if you get the answer da to Question 1, C is either True or False, and if you get the answer ja, B is either True or False!

Now turn to whichever of B and C you have just discovered is either True or False — let us suppose that it is B (if it is C, just interchange the names B and C in what follows) — and ask Question 2: Does da mean yes iff Rome is in Italy? True will answer da, and False will answer ja.  Thus, with two questions, you have either identified B as True or identified B as False.

For our third and last question, turn again to B, whom you have now either identified as True or identified as False, and ask Question 3: Does da mean yes iff A is Random?

Suppose B is True.  Then if you get the answer da, then A is Random, and therefore A is Random, B is True, C is False, and you are done; but if you get the answer ja, then A is not Random, so A is False, B is true, C is Random, and you are again done.

Suppose B is False.  Then if you get the answer da, then since B speaks falsely,A is not Random, and therefore A is True, B is False, C is Random, and you are done; but if we get ja, then A is Random, and thus B is False, and C is True, and you are again done.

爱因斯坦

老大这个都可以翻译,果真够弓虽

TombCrow


爱因斯坦

我晕,难道是正确答案?

TombCrow

对呀,就是那本书(Boolos (1998) Logic, Logic, and Logic Harvard University Press, 第29章)上面的

爱因斯坦


TombCrow

对的,正确答案不是绝对的,思路对就能求解了~

爱因斯坦

果真是强人啊,可惜我看外语头大