不如試解一道邏輯難題:藍眼島民

 

The Question: There is an island upon which a tribe resides. The tribe consists of 1000 people, 100 of which are blue-eyed and 900 of which are brown-eyed. Yet, their religion forbids them to know their own eye color, or even to discuss the topic; thus, one resident can see the eye colors of all other residents but has no way of discovering his own (there are no reflective surfaces). If a tribesperson does discover his or her own eye color, then their religion compels them to commit ritual suicide at noon the following day in the village square for all to witness. All the tribespeople are highly logical, highly devout, and they all know that each other is also highly logical and highly devout.  One day, a blue-eyed foreigner visits to the island and wins the complete trust of the tribe.  One evening, he addresses the entire tribe to thank them for their hospitality.  However, not knowing the customs, the foreigner makes the mistake of mentioning eye color in his address, mentioning in his address “how unusual it is to see another blue-eyed person like myself in this region of the world”.  What effect, if anything, does this faux pas have on the tribe?

Argument I: The foreigner has no effect, because his comments do not tell the tribe anything that they do not already know (everyone in the tribe can already see that there are several blue-eyed people in their tribe). 

Argument II: 100 days after the address, all the blue eyed people commit suicide. 

問:上面哪一个 argument 正確?

 

 

 

 

 

所有跟帖: 

未見過此題又自認邏輯强的網友可先試解。否則,答案在這兒: -中间小谢- 给 中间小谢 发送悄悄话 (278 bytes) () 11/09/2023 postreply 00:43:12

艾马,你这个太抽象了。不如俺楼上的现实:) -stonebench- 给 stonebench 发送悄悄话 stonebench 的博客首页 (167 bytes) () 11/09/2023 postreply 06:45:49

呵呵,这些问题,考GRE的时候,逻辑部分用得上。想多了,觉得会出青春痘。:) -dhyang_wxc- 给 dhyang_wxc 发送悄悄话 dhyang_wxc 的博客首页 (0 bytes) () 11/09/2023 postreply 07:41:25

这个题有意思,值得仔细研究。从大类上应该属于Modal Logics。下面链接,SEP比较专业,Wiki可以参考一下。 -露重烟微- 给 露重烟微 发送悄悄话 (256 bytes) () 11/09/2023 postreply 09:33:34

我决定站Argument I对,谢同学要不要来battle一下? -露重烟微- 给 露重烟微 发送悄悄话 (0 bytes) () 11/09/2023 postreply 19:46:00

Why do you think argument II is incorrect? -中间小谢- 给 中间小谢 发送悄悄话 (0 bytes) () 11/09/2023 postreply 20:15:22

我觉得这个题要能成立,首先这个tribe建立了要少于100天。这个foreigner来不来无所谓。 -露重烟微- 给 露重烟微 发送悄悄话 (0 bytes) () 11/09/2023 postreply 20:21:00

等到了100天大家的information也够了,就可以行动了。 -露重烟微- 给 露重烟微 发送悄悄话 (0 bytes) () 11/09/2023 postreply 20:30:00

Interesting. Your reasoning? -中间小谢- 给 中间小谢 发送悄悄话 (0 bytes) () 11/09/2023 postreply 20:37:14

接着用答案II的reasoning就可以了。每个人都知道最少有一个蓝眼晴,且每个人都知道每个人都知道……。 -露重烟微- 给 露重烟微 发送悄悄话 (0 bytes) () 11/09/2023 postreply 21:43:00

满足了common knowledge的要求。 -露重烟微- 给 露重烟微 发送悄悄话 (0 bytes) () 11/09/2023 postreply 21:44:00

"每个人都知道最少有一个蓝眼晴" isn't given in the problem, -中间小谢- 给 中间小谢 发送悄悄话 (121 bytes) () 11/09/2023 postreply 21:52:02

因为可以看到呀。一眼看过去,不管蓝眼棕眼都看到不止一个蓝眼晴。就像答案I里说的,这个visitor 并没有带来任何新信息。 -露重烟微- 给 露重烟微 发送悄悄话 (0 bytes) () 11/09/2023 postreply 21:59:00

如果题目里只有两个人,确实需要一个visitor。 -露重烟微- 给 露重烟微 发送悄悄话 (0 bytes) () 11/09/2023 postreply 21:59:00

其实I对还可以有另外的解释,不过我还没想好,看看这周能不能想明白了。 -露重烟微- 给 露重烟微 发送悄悄话 (0 bytes) () 11/09/2023 postreply 21:47:41

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