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Baby Kingdom - 親子王國香港討論區 › 首頁 › 自由講場› 最難的邏輯問題

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最難的邏輯問題 [複製鏈接]

sonic04

水晶宮

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至尊種植勳章好媽媽勳章醒目開學勳章 2011至尊種植勳章畀面勳章環保接龍勳章爸B勳章

1^#

發表於 08-3-18 01:43 |只看該作者 |倒序瀏覽 |打印

Raymond Smullyan
有甲、乙、丙三個精靈，其中一個只說真話，另外一個只說假話，還有一個隨機地決定何時說真話，何時說假話。
你可以向這三個精靈發問三條是非題，而你的任務是從他們的答案找出誰說真話，誰說假話，誰是隨機答話。
你每次可選擇任何一個精靈問話，問的問題可以取決於上一題的答案。
這個難題困難的地方是這些精靈會以「Da」或「Ja」回答，但你並不知道它們的意思，只知道其中一個字代表「對」，另外一個字代表「錯」。
你應該問那三條問題呢？

0 0 0

錦瑟無端五十弦，一弦一柱思華年。
莊生曉夢迷蝴蝶，望帝春心託杜鵑。
滄海月明珠有淚，藍田日暖玉生煙。
此情可待成追憶？只是當時已惘然。

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heiheikwok

侯爵府

積分: 22787

BK Milk勳章

2^#

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ccps

男爵府

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3^#

發表於 08-3-18 02:27 |只看該作者

哎呀..好難ar>>>>
幾時有答案!!

原文章由 sonic04 於 2008/3/18 01:43 發表
Raymond Smullyan
有甲、乙、丙三個精靈，其中一個只說真話，另外一個只說假話，還有一個隨機地決定何時說真話，何時說假話。
你可以向這三個精靈發問三條是非題，而你的任務是從他們的答案找出誰說真話，誰說假話，誰是隨機答話。 ...

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BarryMami

大宅

積分: 1581

4^#

發表於 08-3-18 12:46 |只看該作者

甲:只說真話
乙:只說假話
丙:視乎情況

Q1:問甲是否只說真話
Q2:問乙阿甲剛才是否說真話
Q3:問丙阿乙剛才是否說真話

對不對呢?

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Pasqurell

複式洋房

積分: 485

5^#

發表於 08-3-18 13:39 |只看該作者

回覆 #4 BarryMami 的文章

The solution

Boolos states that the "first move is to find a god that you can be certain is not Random, and hence is either True or False". There are many different questions that will achieve this result. One strategy is to use complicated logical connectives in your questions (either biconditionals or some equivalent construction).

Boolos' question was:

Does 'da' mean yes if and only if you are True if and only if B is Random?

Equivalently:

Are an odd number of the following statements true: you are False, 'ja' means yes, B is Random?

The puzzle's solution can be simplified by using counterfactuals. The key to this solution is that, for any yes/no question Q, asking either True or False the question

If I asked you Q, would you say 'ja'?
results in the answer 'ja' if the truthful answer to Q is yes, and the answer 'da' if the truthful answer to Q is no. The reason this works can be seen by looking at the eight possible cases.

Assume that 'ja' means yes and 'da' means no.
True is asked and responds with 'ja'. Since he is telling the truth the truthful answer to Q is 'ja', which means yes.

True is asked and responds with 'da'. Since he is telling the truth the truthful answer to Q is 'da', which means no.

False is asked and responds with 'ja'. Since he is lying it follows that if you asked him Q he would instead answer 'da'. He would be lying, so the truthful answer to Q is 'ja', which means yes.

False is asked and responds with 'da'. Since he is lying it follows that if you asked him Q he would in fact answer 'ja'. He would be lying, so the truthful answer to Q is 'da', which means no.

Assume 'ja' means no and 'da' means yes.
True is asked and responds with 'ja'. Since he is telling the truth the truthful answer to Q is 'da', which means yes.

True is asked and responds with 'da'. Since he is telling the truth the truthful answer to Q is 'ja', which means no.

False is asked and responds with 'ja'. Since he is lying it follows that if you asked him Q he would in fact answer 'ja'. He would be lying, so the truthful answer to Q 'da', which means yes.

False is asked and responds with 'da'. Since he is lying it follows that if you asked him Q he would instead answer 'da'. He would be lying, so the truthful answer to Q is 'ja', which means no.

Using this fact, one may proceed as follows.

Ask god B, "If I asked you 'Is A Random?', would you say 'ja'?". If B answers 'ja', then either B is Random (and is answering randomly), or B is not Random and the answer indicates that A is indeed Random. Either way, C is not Random. If B answers 'da', then either B is Random (and is answering randomly), or B is not Random and the answer indicates that A is not Random. Either way, A is not Random.
Go to the god who was identified as not being Random by the previous question (either A or C), and ask him: "If I asked you 'Are you True?', would you say 'ja'?". Since he is not Random, an answer of 'ja' indicates that he is True and an answer of 'da' indicates that he is False.
Ask the same god the question: "If I asked you 'Is B Random?', would you say 'ja'?". If the answer is 'ja' then B is Random; if the answer is 'da' then the god you have not yet spoken to is Random. The remaining god can be identified by elimination.

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sonic04

水晶宮

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至尊種植勳章好媽媽勳章醒目開學勳章 2011至尊種植勳章畀面勳章環保接龍勳章爸B勳章

6^#

發表於 08-3-19 00:32 |只看該作者

先把那三位神隨意叫作A,B及C.
第一題先問A.
Q1.如果我問你B是不是鬼,你會答da,是不是?
若答da,則C非鬼.
若答ja,則B非鬼.
C非鬼和B非鬼的情況類似,所以只說一個情況.設C非鬼,則餘下兩條只問C.
Q2.da是不是yes的意思?
答da則C是神.
答ja則C是魔.
C是神:
Q3.1:如果我問你B是不是鬼,你會答da,是不是?(和Q1一樣)
da則B是鬼,所以A魔,B鬼,C神.
ja則A鬼,B魔,C神.
C是魔:
Q3.2如果我問你B是不是鬼,你會答da,是不是?(和Q1一樣)
da則B是鬼,所以A:神,B:鬼,C:魔.
ja則A:鬼,B:神,C:魔.
考慮到ABC的身份及da,ja所代表的意思.總共有12個可能.設T=神,L=魔,M=鬼,Y=是,N=非.可得:
A B C da ja
1. M T L Y N
2. M T L N Y
3. M L T Y N
4. M L T N Y
5. T M L Y N
6. T M L N Y
7 L M T Y N
8. L M T N Y
9. T L M Y N
10.T L M N Y
11.L T M Y N
12.L T M N Y
我們的問題是’ 如果我問你B是不是鬼,你會答da,是不是?’
而這問題的重點是分辨出B和C中那一個不是鬼.因此若A是鬼的話(情況1-4),B和C也不會是鬼.所以1-4可暫時不理.問題是在5-8的情況下A會答什麼呢?
例如情況5:因B是鬼,da是yes的意思及A必講真話,因此如果問A’B是不是鬼?’,他會答da,所以’ 如果我問你B是不是鬼,你會答da,是不是?’是對的,所以這問題A最後會答da.
又例如情況7:因B是鬼,A是魔及da是yes的思意,因此如果問A’B是不是鬼?’, 他會答ja,所以’如果我問你B是不是鬼,你會答da,是不是?’是錯的,但因A必講假話,因此他最後也會答da.其它情況如此類推,而最後的結論是答da則A或B是鬼,答ja則A或C是鬼.如妳還有什麼疑問就請再提出吧.

註：
神=真話精靈
魔=假話精靈
鬼=隨機精靈

錦瑟無端五十弦，一弦一柱思華年。
莊生曉夢迷蝴蝶，望帝春心託杜鵑。
滄海月明珠有淚，藍田日暖玉生煙。
此情可待成追憶？只是當時已惘然。

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purplechili

子爵府

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好媽媽勳章醒目開學勳章

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mouth:

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twins214wy

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好媽媽勳章醒目開學勳章環保接龍勳章

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1928mickey

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2018父親節勳章 2018母親節勳章 2018復活節勳章 15週年勳章親子王國15週年勳章畀面勳章 BK猜猜猜慶中秋 BK Milk勳章 hashtag影視迷勳章最關心BB問題熱投勳章美好大世界2017勳章開心吸收勳章

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BarryMami

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發表於 08-3-20 00:45 |只看該作者

原文章由 sonic04 於 08-3-19 00:32 發表
先把那三位神隨意叫作A,B及C.
第一題先問A.
Q1.如果我問你B是不是鬼,你會答da,是不是?
若答da,則C非鬼.
若答ja,則B非鬼.
C非鬼和B非鬼的情況類似,所以只說一個情況.設C非鬼,則餘下兩條只問C.
Q2.da是不是yes的 ...

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hoiching930

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叻叻勳章 wyeth冷知識勳章畀面勳章陪月勳章

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nnfonder

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發表於 08-4-18 15:10 |只看該作者

mouth:

居天下之廣居，立天下之正位，行天下之大道；得志與民由之，不得志獨行其道；富貴不能淫，貧賤不能移，威武不能屈：此之謂大丈夫。

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發表於 08-4-18 15:19 |只看該作者

我鐘意你同我講 I Love U, I Love U Too！
You are the sunshine of my life. That's why I'll always stay around. You are the apple of my eye. Forever you'll stay in my heart.

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