msg@drutx.UUCP (GrahamM) (12/31/85)
Stop yourself if you've heard this one:
Here's the situation:
You're walking along a road and you come to a fork where the road splits
into two paths, one to the right and one to the left. You don't know
which way to go, but you must find out.
You see two people nearby, and you find out that one of them always lies,
and the other always tells the truth. They know which way to go.
You can find out which way to go by asking either one of them ONE certain
question. What is the ONE question?
Matt Graham
ihnp4!drutx!msghopp@nbs-amrf.UUCP (Ted Hopp) (01/01/86)
> Here's the situation: > > You're walking along a road and you come to a fork where the road splits > into two paths, one to the right and one to the left. You don't know > which way to go, but you must find out. > > You see two people nearby, and you find out that one of them always lies, > and the other always tells the truth. They know which way to go. > > You can find out which way to go by asking either one of them ONE certain > question. What is the ONE question? Point at one of the roads and ask either one, "If I were to ask you if this is the road to Xanadu [that's where you're going, right?], would you say 'yes'?" If the answer is "yes", that's the road to Xanadu, regardless of whether you asked the truth-teller or the liar. An interesting philosophical point concerns the nature of a lie. If a "lie" is something that is logically false, then the above answer works. On the other hand, a "lie" can be any deceptive answer, in which case the "liar" could answer "no", even if that is the truth (i.e., the liar WOULD answer "no" if you asked the antecedent question). I don't know how to solve the puzzle for liars of the deceptive sort. -- Ted Hopp {seismo,umcp-cs}!nbs-amrf!hopp
hsu@eneevax.UUCP (Dave Hsu) (01/02/86)
In article <100@nbs-amrf.UUCP> hopp@nbs-amrf.UUCP (Ted Hopp) writes: >> You're walking along a road and you come to a fork where the road splits >> into two paths, one to the right and one to the left. You don't know >> which way to go, but you must find out. >> You see two people nearby, and you find out that one of them always lies, >> and the other always tells the truth. They know which way to go. >> You can find out which way to go by asking either one of them ONE certain >> question. What is the ONE question? > >Point at one of the roads and ask either one, "If I were to ask you if this >is the road to Xanadu [that's where you're going, right?], would you say >'yes'?" If the answer is "yes", that's the road to Xanadu, regardless of >whether you asked the truth-teller or the liar. > >An interesting philosophical point concerns the nature of a lie. ... >... I don't know how to solve the >puzzle for liars of the deceptive sort. > >Ted Hopp {seismo,umcp-cs}!nbs-amrf!hopp I believe the deceptive solution is: 1) ask "Which road will the other tell me to take" 2) don't take that one. -dave -- David Hsu Communication & Signal Processing Lab, EE Department <disclaimer> University of Maryland, College Park, MD 20742 hsu@eneevax.umd.edu {seismo,allegra}!umcp-cs!eneevax!hsu CF522@UMDD.BITNET And then there were none.
grady@cad.UUCP (Steven Grady) (01/02/86)
In article <470@eneevax.UUCP> hsu@eneevax.UUCP (Dave Hsu) writes: >In article <100@nbs-amrf.UUCP> hopp@nbs-amrf.UUCP (Ted Hopp) writes: >>> You're walking along a road and you come to a fork where the road splits >>> into two paths, one to the right and one to the left. You don't know >>> which way to go, but you must find out. >>> You see two people nearby, and you find out that one of them always lies, >>> and the other always tells the truth. They know which way to go. >>> You can find out which way to go by asking either one of them ONE certain >>> question. What is the ONE question? >> >>An interesting philosophical point concerns the nature of a lie. ... >>... I don't know how to solve the >>puzzle for liars of the deceptive sort. >> >I believe the deceptive solution is: >1) ask "Which road will the other tell me to take" >2) don't take that one. > There's no way to get past a "deceptive" liar. If his intention is to avoid giving you information, he can simply resolve that he will answer the same way no matter what question you ask. (For that matter, he could choose not to respond at all). Steven
gwyn@brl-tgr.ARPA (Doug Gwyn <gwyn>) (01/02/86)
> I don't know how to solve the puzzle for liars of the deceptive sort.
"Would you like to have your arms broken, because that's
what I'll do if you don't lead me to my destination?"das@ucla-cs.UUCP (01/03/86)
In article <114@drutx.UUCP> msg@drutx.UUCP (GrahamM) writes: >You're walking along a road and you come to a fork where the road splits >into two paths, one to the right and one to the left. You don't know >which way to go, but you must find out. > >You see two people nearby, and you find out that one of them always lies, >and the other always tells the truth. They know which way to go. > >You can find out which way to go by asking either one of them ONE certain >question. What is the ONE question? Here's the classic NO-question solution: Say: "I'm going to X [where X is your destination]. They're serving free beer, all you can drink." Then follow them both. -- David Smallberg, das@locus.ucla.edu, {ihnp4,ucbvax}!ucla-cs!das
gordon@cae780.UUCP (Brian Gordon) (01/07/86)
In article <100@nbs-amrf.UUCP> hopp@nbs-amrf.UUCP (Ted Hopp) writes: >An interesting philosophical point concerns the nature of a lie. If a "lie" >is something that is logically false, then the above answer works. On the >other hand, a "lie" can be any deceptive answer, in which case the "liar" >could answer "no", even if that is the truth (i.e., the liar WOULD answer >"no" if you asked the antecedent question). I don't know how to solve the >puzzle for liars of the deceptive sort. In one of his many puzzle discussion books, Martin Gardner attacks exactly this problem. Two roads, one question to one "native", who could be a truth-teller, a liar, or an artful liar (who gives whichever answer he believes will be worse for you). The question MG proposes is, "Did you know they were giving away free beer in Xanadu?" A truth-teller will say "No", and head down the road to Xanadu -- just follow him. The (normal) liar will say "Yes", and again head down the correct road -- follow him. The artful liar will answer either Yes or No, as seems appropriate, and then head down the right road -- follow him. The worst case is the one where the artful liar figures out what you are doing and, after answering either Yes or No, deliberately goes down the wrong road, in order to "lie" with his feet! Even in that case, you at least have the satisfaction that the artful liar will never be sure that he didn't miss out on the free beer ... FROM: Brian G. Gordon, CAE Systems Division of Tektronix, Inc. UUCP: tektronix!teklds!cae780!gordon {ihnp4, decvax!decwrl}!amdcad!cae780!gordon {hplabs, resonex, qubix, leadsv}!cae780!gordon USNAIL: 5302 Betsy Ross Drive, Santa Clara, CA 95054 AT&T: (408)727-1234
jeff@rtech.UUCP (Jeff Lichtman) (01/07/86)
> > > > You see two people nearby, and you find out that one of them always lies, > > and the other always tells the truth. They know which way to go. > > > > You can find out which way to go by asking either one of them ONE certain > > question. What is the ONE question? > > Point at one of the roads and ask either one, "If I were to ask you if this > is the road to Xanadu [that's where you're going, right?], would you say > 'yes'?" If the answer is "yes", that's the road to Xanadu, regardless of > whether you asked the truth-teller or the liar. > > An interesting philosophical point concerns the nature of a lie. If a "lie" > is something that is logically false, then the above answer works. On the > other hand, a "lie" can be any deceptive answer, in which case the "liar" > could answer "no", even if that is the truth (i.e., the liar WOULD answer > "no" if you asked the antecedent question). I don't know how to solve the > puzzle for liars of the deceptive sort. > > -- > > Ted Hopp {seismo,umcp-cs}!nbs-amrf!hopp Someone once wrote Martin Gardner a letter discussing the problem of the nature of lying. It appears in the book "Mathematical Puzzles & Diversions" by Martin Gardner. It comes to the conclusion that the most general solution is to ask the question: "Did you know that they are serving free beer in the village?" (or wherever it is that you want to go). The truth-teller will say "no" and head for the village. The non-deceptive liar will say "yes" and head for the village. The deceptive liar will say, "Ugh! I hate beer!", and also head for the village. It's really worth it to get a buy a copy of this book, if only to have the letter. It's the funniest response to a logic problem I have ever read. -- Jeff Lichtman at rtech (Relational Technology, Inc.) "Saints should always be judged guilty until they are proved innocent..." {amdahl, sun}!rtech!jeff {ucbvax, decvax}!mtxinu!rtech!jeff
gwyn@brl-tgr.ARPA (Doug Gwyn <gwyn>) (01/09/86)
> Someone once wrote Martin Gardner a letter discussing the problem of the nature > of lying. It appears in the book "Mathematical Puzzles & Diversions" by Martin > Gardner. It comes to the conclusion that the most general solution is to ask > the question: "Did you know that they are serving free beer in the village?" > (or wherever it is that you want to go). The truth-teller will say "no" and > head for the village. The non-deceptive liar will say "yes" and head for the > village. The deceptive liar will say, "Ugh! I hate beer!", and also head for > the village. > > It's really worth it to get a buy a copy of this book, if only to have the > letter. It's the funniest response to a logic problem I have ever read. Another reason people should read all the Martin Gardner collections from the Scientific American "Mathematical Games" column is that it would cut down on rehashing of old, well-known puzzles in this news group.