schoeller@alien.DEC (Todd Schoeller) (11/12/84)
-Newsgroups: net.puzzle
-Path: decwrl!decvax!mcnc!duke!ucf-cs!hollis
-Subject: Figure me this...
-Posted: Wed Nov 7 09:49:36 1984
-
-You are shipwrecked and wash ashore onto an island populated by
-cannibals. There are two types of cannibals on this island:
-short ones who always tell the truth and tall ones who always lie.
-
-As you crawl up the beach, one of the short ones, the chief,
-approaches you and makes you an offer you can't refuse.
-
-The chief blindfolds you and places three men from his tribe
-near you on the beach. From what they say to you, you must
-tell the chief which are short and which are tall - and prove
-your answer. If you manage to do this, you will be set free.
-Otherwise, you are invited to dinner.
-
-As the first tribesman begins to speak, a wave breaks on the
-nearby reef and drowns out his voice. Then you hear the
-second say 'The first one said he is short and he is, and so
-am I". The third one says 'The second one is lying, he is
-tall and I am short'.
-
-You have all the information I had... and I lived to tell
-about it.
-
-
-Ken Hollis
===============================================================================
Mr. Hollis,
Your not becoming dinner for those tribesmen was by luck. This riddle has 2
answers. Therefore, you must have taken a wild guess about the type of tribes-
men in front of you. The two answers are :
1) The first is short, 2) The first is tall,
the second is short, and OR the second is tall, and
the third is tall. the thirs is short.
Proof: We are given that all the tall tribesmen will always lie. We are given
that the short tribesmen will always tell the truth. We are also given
that we did not hear what the first tribesman said. From the conversa-
tion, we have this...
Case 1:
If the second person is short, then the first person must also be short
since a short tribesman must always tell the truth. Therefore, the third
person must be tall since he said that the second was lying (and in fact,
the second was not). Therefore, in this situation, one of the answers is
that the first person is short and must of said that he was short, the
second person is short, and the third person is tall.
Case 2:
If the second person is tall, then the first person must also be tall
since the second person said that the first person is short and the
second person MUST lie. Therefore, the third person must be telling the
truth since he said that the second person was lying (and the second was
indeed lying). Therefore, in this situation, the other answer is that
the first is tall, the second is tall, and the third is short.
THEREFORE...
The person had a 50-50 chance of being the main course for dinner. And in
that case, luck, NOT LOGIC, is what saved that person from being eaten. Good
puzzel. It's like saying what is 'X' if X**2 ('X' squared) equals 4. You have
a 50-50 chance of getting it right with '2' or '-2'. If there is only one
answer to this puzzel, please post it with the proof. Thank you.
Todd Schoeller.hollis@ucf-cs.UUCP (William ) (11/13/84)
Case 2 cannot be true, because if the first person is short, then
he would have said 'I am short'. If the first person is tall then he would
have said 'I am short'. If the second person was short, he would say
'The first person said he was short, and so am I' which is what he said, if
however the second person was tall, then he would have had to have said
'The first person said he was tall, and I am short' because he ALWAYS has
to lie, so therefore it must be the case of case 1.
An interesting sidelight, it has been suggested to me that if what the first
cannible said was actually something like 'The sun is blue' then the whole
thing would fall apart, but assume that in this case they all would make
a statement about thier hieghts.
Ken Hollis
William Kendall Hollis
...decvax!ucf-cs!hollis or ...duke!ucf-cs!hollis
hollis.ucf-cs@Csnet-Relaysjk@asgb.UUCP (11/14/84)
Reference: <4@decwrl.UUCP> -Subject: Figure me this... -Posted: Wed Nov 7 09:49:36 1984 - -As the first tribesman begins to speak, a wave breaks on the -nearby reef and drowns out his voice. Then you hear the -second say 'The first one said he is short and he is, and so -am I". The third one says 'The second one is lying, he is -tall and I am short'. - - -Ken Hollis > ======================================================================== > > Case 2: > If the second person is tall, then the first person must also be tall > since the second person said that the first person is short and the > second person MUST lie. Therefore, the third person must be telling the > truth since he said that the second person was lying (and the second was > indeed lying). Therefore, in this situation, the other answer is that > the first is tall, the second is tall, and the third is short. > > > Todd Schoeller. The reason this puzzle only has one answer requires careful analysis of the second tribesman's statement. If he were indeed a total liar, he would have heard the first tribesmans statement ("I am short", assuming that he is tall and therefore a liar) and inverted the statement. Thus, if he were a liar, he would have said "The first one said he is tall, but he is not, and neither am I." Therefore scenario 2 is incorrect and the only solution is short, short, tall. Scott J. Kamin ucbvax \ Burroughs Corp. ihnp4 \ Advanced Systems Group decvax - sdcsvax\ 6655 Lookout Rd. dcdwest / > bmcg!asgb!sjk Boulder, CO 80301 akgua / cepu / (303) 530-3905
rosen@sunybcs.UUCP (Jay Rosenberg) (11/21/84)
Well it does have two answers, since we have no information as to what the first one said, we don't know if it was a statement about his height. He could have said "the moon is made of cream cheese", in that case the answer would be tall, tall, short. If the first statement was anything but a self reference of height, then number 2 was lying about what number 1 said. number 3 makes no reference to number 1 statement just that he (3) is short and 2 is a liar and is tall. So my answer (to get me out of hot water would be). If number 1 made a self reference about his height then 1 and 2 are short and 3 is tall (see previous postings), if not then he (i.e. he statement concerned some other fact) then he had to lie, since 2 said "1 said he is short and he is", thus 2 lied about what 1 said, thus 2 lied that 1 was short, thus 1 is tall, thus 1 lied. So we now have 1 and 2 being tall, and therefore 3 is short. Note that if 1 talked about the height of either 2 or 3, then 1 is tall. So even if you add the constraint that they must talk about either of their respective heights, we still get two answers unless we KNOW that 1 had to explicitly mention his height.
jlg@lanl.ARPA (11/21/84)
There is only one answer. What the first native said was unintelligable, so the second native was lying (how could he know what the first one said either). The second native must be tall since he lied, the first must be tall because the secont said he was short, the third was short for reasons stated before in this exchange.
ndiamond@watdaisy.UUCP (Norman Diamond) (11/26/84)
What the first native said was unintelligible to "you", but the second native was probably standing much closer to the first native and very likely understood him. (Though of course, they might not even speak the same language as each other, etc. etc.)