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Conference rusure::math

Title:	Mathematics at DEC

Moderator:	RUSURE::EDP

Created:	Mon Feb 03 1986
Last Modified:	Fri Jun 06 1997
Last Successful Update:	Fri Jun 06 1997
Number of topics:	2083
Total number of notes:	14613

176.0. "Shipwrecked" by HARE::STAN () Fri Nov 09 1984 16:20

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

T.R	Title	User	Date	Lines
176.1		MDVAX1::DIGNAN	`Fri Nov 09 1984 17:26`	7
	WE THINK THAT THE FIRST TWO ARE AS SHORT AS THE CHIEF; THE THIRD ONE IS TALL. REASON: NOBODY CAN SAY "I AM TALL" SO THE SECOND GUY HAS TO BE TELLING THE TRUTH, WHICH MAKES HIM SHORT; THE FIRST GUY COULD NOT HAVE SAID "I AM TALL" , SO HE MUST HAVE SAID "I AM SHORT"... YOU GET THE IDEA.... PETE (WITH ALL THE WORK DONE BY BOB TATUM AND TOM ALBERT..)
176.2		TURTLE::GILBERT	`Fri Nov 09 1984 19:36`	33
	Hmmm. Short folks tell the truth, and the others tell tall tales? First, note that regardless of a tribemans height, he'll claim to be short. The second tribesman said: 'The first one said he is short and he is, and so am I' -------------(1)-------------- -(2)- --(3)-- (3) is worthless information. (1) implies the first guy commented on his height; he must've said he's short. Thus, the second tribesman is a truth-teller (and short), and then (2) implies the first guy is short. The third one said: 'The second one is lying, he is tall and I am short' ----------(4)---------- ---(5)---- ----(6)--- (6) is worthless information. (4) and (5) mean the same thing, and both are lies; thus the third tribesman is a tall liar. Ken Hollis said: 'You have all the information I had... and I lived to tell about it' I suspect Ken's tale is a fabrication; were he a tribesman, he'd be no more. - Gilbert
176.3		TURTLE::GILBERT	`Fri Nov 09 1984 19:37`	2
	(despite the different time-stamps, the two preceding responses were written at roughly the same time).
176.4		TAV02::NITSAN	`Wed Nov 14 1984 05:26`	22
	RE: " The second tribesman said: 'The first one said he is short and he is, and so am I' -------------(1)-------------- -(2)- --(3)-- (1) implies the first guy commented on his height; he must've said he's short." *** Why ?? Maybe the 1-st guy said NOTHING about HIS own height. So there is a second solution: - Guy #1 is tall and lied about something unimportant. - Guy #2 is tall and lied about three things: * about quoting guy #1 (who said nothing of the sort...) * about saying guy #1 was short (that's how we know #1 was tall...) * about saying himself was short - Guy #3 is short and told the truth about three things: * about guy #2 lying * about guy #2 being tall * about himself being short Note this solution is the complement of the first one. NITSAN D.
176.5		MDVAX1::DIGNAN	`Wed Nov 14 1984 16:13`	8
	WELL, HOW ABOUT IT? IS THE AUTHOR GOING TO REMAIN SILENT OR EXPLAIN WHY THERE IS A UNIQUE SOLUTION (IF THERE IS ONE)? IT SEEMS THAT RESPONSE 4 ONLY WORKS IF YOU ASSUME THAT THE SPEAKERS ARE NOT BOUND TO SAY SOMETHING RELEVANT. AFTER ALL, SPEAKERS 2 AND 3 BOTH COMMENTED ON THEIR OWN HEIGHT. P.S. TO MR. NITSAN--WE CHECKED OUT SOME OF YOUR ANIMATION FROM NODE PICA'S GAMES NOTES--PERHAPS AN "R" RATING WOULD BE APPROPRIATE.
176.6		HARE::GILBERT	`Wed Nov 14 1984 21:06`	4
	Ayup, that's why I spelled out that first implication. Usually, with problems of this kind, the lies are very, very straight-forward, unlike the real world, where lies are frequently subtle and lent credence by the surrounding truths and half-truths.
176.7		TAV02::NITSAN	`Thu Nov 15 1984 00:55`	10
	re: .5,.6 1. Saying something about the other two is also relevant, but I agree we can "assume" the 1-st guy also described himself as the others did. Anyway, the real solution can be that the 3-rd guy is different. 2. The specific animation picture you refer to, was not mine, but drawn by somebody else here... sorry... (but that's for another notes file). NITSAN DUVDEVANI
176.8		TAV02::NITSAN	`Thu Nov 15 1984 07:08`	4
	...just like Benny Hill said to the girl: " Is it true that when you say 'no' you really mean 'yes' ? "