NetNews Usenet Archive 1993 #3/NN_1993_3.iso/spool/rec/puzzles/8505

Internet Message Format | 1993-01-22 | 2.9 KB

Path: sparky!uunet!spool.mu.edu!news.nd.edu!irishvma!rvesterm
Date: Thursday, 21 Jan 1993 12:01:38 EST
From: <[e-mail]>
Message-ID: <[e-mail]>
Newsgroups: rec.puzzles
Subject: Re: Need puzzle help: eye colour enigma
References: <[e-mail]> <[e-mail]>
 <[e-mail]> <[e-mail]>
Lines: 44

oy vey.  somebody doesn't believe me again with the ritual sacrifice
thing.  here we go again, i'll explain myself.

first, yes, no one tells anyone else their eye color, but that's under
normal circumstances.  these are hardly normal circumstances.  the rule
is in effect under normal circumstances for a very good reason: if the
rule is broken, somebody will die.  however, breaking the rule makes
very much sense in this situation: the person who dies because of it is
going to kick it anyway, and his (perhaps) premature death will (perhaps)
save the lives of additional islanders.  remember, though it was not
stated specifically in this incarnation of the puzzle, the islanders
are completely logical.  as i posted a long time ago, being logical, they
take a clue from mister spock: "the needs of the many outweigh the needs
of the few, or the one".

second, i guess i'll explain exactly how my idea goes into effect, again,
for the benefit of those people who weren't reading this board the last
time we talked about this problem.  after the guru is done talking, the
islanders are each randomly assigned a unique number from 1 to (number of
islanders).  number one gets up on stage and asks, "do i have blue eyes?"
the natives tell him, yes or no, truthfully.  if yes, everybody goes home,
and number one kills himself later that night.  if no, number one sits
down, and number two stands up; the process repeats.  this breaks the
induction that would otherwise kill half the islanders.

third, i'll address the problem that one person had before with this,
to avoid it being addressed again.  the problem he had was that he thought
there was no base case for my idea: that is, if there were exactly one
blue-eye, he would know he was a blue-eye, and so announce, "this meeting
is a waste of time.  wasting time is illogical."  thus the meeting would
never happen.  so now if there were two blue-eyes, the meeting will happen;
one dies, and the other now knows he's a blue-eye, since the meeting did
happen, and there are now no people with blue-eyes left that he can see.

my answer to this is that the meeting is NOT logically a waste of time.
a hundred years down the road, the same situation may occur, but with
more than one blue-eye.  if the current lone blue-eye does not spend
an hour or two making the base case happen, he would be responsible for
the deaths of many blue-eyes.  spending an hour or two to potentially
save the lives of your progeny and countrymen is hardly illogical.

bob vesterman.