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世界上最难的逻辑题

已有 2816 次阅读| 2008-1-8 20:59

世界最难逻辑题

The puzzle: Three gods A, B, and C are called, in some order, True, False, and　Random. True always speaks truly, False always speaks falsely, but whether Random speaks truly or falsely is a completely random matter. Your task is to determine the　identities of A, B, and C by asking three yes-no questions; each question must be put to exactly one god. The gods understand English, but will answer all questions in their own language, in which the words for “yes” and “no” are “da” and “ja,” in some order. You do not know which word means which.

有甲、乙、丙三个精灵，其中一个只说真话，另外一个只说假话。还有一个随机地决定何时说真话，何时说假话。你可以向这三个精灵发问三条是非题，而你的任务是从他们的答案找出谁说真话，谁说假话，谁是随机答话。这个难题困难的地方是这些精灵会以“Da”或“Ja”回答，但你并不知道它们的意思，只知道其中一个字代表“对”，另外一个字代表“错”。你应该问那三条问题呢？

《补充说明》

SOME YEARS AGO, THE LOGICIAN AND PUZZLE-MASTER Raymond Smullyan devised a logical puzzle that has no challengers I know of for the title of Hardest Logical Puzzle Ever. I’ll set out the puzzle here, give the solution, and then briefly discuss one of its more interesting aspects.

（相对该文章）几年前，逻辑学家和难题制作大师Raymond Smullyan制作了一道就该文章作者所知无人挑战的逻辑难题，叫迄今最难的逻辑题。

The extra twist of not knowing which are the gods"" words for "yes" and "no" is due to the computer scientist John McCarthy.

而有人还进一步加大该题的难度；计算机科学家 John McCarthy 将该题“扭”得更难：精灵的语言中哪个词表示“是”，哪个词表示“否”是未知的。

GEORGE BOOLOS IS Professor of Philosophy at MIT and one of the founders of the field of “Provability Logic.＂He is the author of The Logic of Provability (Cambridge, 1993) and, with Richard Jeffrey, Computability and Logic (Cambridge, 1974). SPRING 1996 THE HARVARD REVIEW OF PHILOSOPHY

George Boolos 是麻省理工学院哲学教授和“Provability Logic”的创始人之一，《The Logic of Provability》一书的作者。上述文章出现在1996年春的哈佛哲学评论.

you can find the solution in chapter 29 of Boolos""s book Logic, Logic, Logic, published in 1998 by the Harvard University Press.

文章的内容在Boolos的书《逻辑，逻辑，逻辑》的第29章。（1998年哈佛大学出版社出版）.

[ 本帖最后由 genghis 于 2007-12-30 11:31 编辑 ]

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