OT Friday: Logic Problem
Mueller, David
college.
Bruce - your answer reminds me of one of Martin Gardner's columns many years
ago. He posed this type of question with a fork in the road and a single
native (who might be either a truth-teller or a liar). The goal was to get
to the truth teller's village (i.e. find the correct fork to take). The
standard answer was given in the next month's column, and it was along the
lines of your answer below.
A month or two later, Mr. Gardner printed a letter from a person (I don't
remember the name). This letter raised the issue of what type of liar the
native might be and gave 3 types:
-- the simple liar, who would be unable to understand the logical
convolutions of the standard answer, and would thus mislead you with a
logically-incorrect response - this is what you mention in your last
paragraph;
-- the "logical" liar, who was as logical as you were, realized that you
had him trapped, and was forced by logic to provide you with the desired
information; and
-- what the letter writer called the "artful deceiver", who was also
logically sophisticated, would know that he was 'trapped' if he answered
logically, and so (true to his higher calling of artful deception) would
mislead you by telling you the logical truth. The writer added that no
question would work with this type of liar. Supposing that beer was the
favorite native beverage, the letter writer suggested that your best bet
(fot the road-fork problem) was to say something like "I hear there is a big
beer bash in the truth-teller's village". This gave the native 3 choices:
stonewall you - "ugh, I hate beer"; run off to the truth-teller's village
leading you where you wanted to go; or commit the ultimate sacrifice for
artful deception by running off to the liar's village sacrificing possible
inclusion in the beer bash.
-----Original Message-----
From: Bruce Black [mailto:bbl...@FDRINNOVATION.COM]
Sent: Thursday, August 29, 2002 4:21 PM
To: IBM-...@BAMA.UA.EDU
Subject: Re: OT Friday: Logic Problem
The answer I recall is:
Ask either guard "If I asked you if this was the right door, would you
reply YES?".
The truthful guard will obviously answer YES for the right door and NO
for the other.
For the right door, the untruthful guard would have answered the first
part of the quesiton NO, but he has to lie to the "would you reply YES"
part, so he has to reply YES to the entire question (a lie). Conversely
for the wrong door.
So either guard will answer YES for the right door and NO for the wrong
door.
Of course this implies that the lying guard is smart enough to
understand your question, which doesn't fit the stereotype prison guard.
I wouldn't bet my life on it!
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