From: moon@mozart.llnl.gov (Steven Moon)
Newsgroups: sci.math
Subject: Re: Problematic smurfs!
Keywords: smurfs
Date: 31 Aug 92 18:16:29 GMT
Organization: Lawrence Livermore National Laboratory

In article <94952@bu.edu>, spacefox@acs.bu.edu (Godfrey Degamo) writes:
|> -------------------------------------------------------------------------------
|>      A group of 1000 smurfs wear either a red or blue hat on their head.
|> They can only wear one color. The color hat on their head is known to all, but
|> the wearer.  The wearer of the hat has no means whatsoever for obtaining the
|> color of his hat.  It is never the case that all 1000 smurfs will wear
|> the same color hat.
|>      One day the mayor, not apart of the 1000 smurfs, decides to call a
|> town meeting.  All 1000 smurfs are gathered into the town hall.  The mayor
|> is not wearing a hat.  During the meeting, the mayor asks that all the
|> smurfs wearing red hats to stand up.
|>      There is a bit of commotion in the crowd, but no one stands up.
|>      The mayor requests the same demand a bit more sternly.
|>      Again, commotion, but no one stands up.
|>      The mayor, irate, demands the red hatted smurfs to stand up.
|>      Then, a certain amount of smurfs rise.
|> 
|> find:
|>      The exact amount of smurfs that rise.  
|>          (Hint: This number will be greater than one.)
|>      The color of the hats of the smurfs that rise.
|> 
|> more importantly,
|>      Explain how you deduced your answer.
|> -------------------------------------------------------------------------------
|> 
|> I hope that's clear enough for you.  If not, post, but all the necessary
|> information has been supplied.  I'll only answer questions about my poor
|> grammar and writing style.  Put on your smurf hats and think!
|> 
|> 
|>                                         -G. Degamo,
|>                                          spacefox@acs.bu.edu

This problem is a variation of one I heard some time ago.
It is with three individuals each wearing one of five hats, three
brown two black.  They are standing in a line and can only see 
those in front of them.  The last in line can see the color of
the hats of the two in front of him.  The second in line can see
the only the one in front of him and the first in line can't see
anyones hat.  They can't talk or leave untill they are certain what
color hat they have on.  After a long time the person first in
line leaves.  What color hat does he have on.

.steve





Spolier




- What we know -
out of 1000 hats >= 2 are red.
each Smurf can see the other 999 hats.  
since the mayor was singling these red hat wearers out we
suspect they are in the minority.
since the mayor also knew of the 'rules of hat' yet demanded
the red hatted Smurfs stand.  the red hatted Smurfs must
be able to determine who they are.

However, Smurfs are not consummate puzzle solvers and so I see several posibilities
- We all know that Papa Smurf can figure this out, so he won't stand.
- Clumsy Smurf will not figure it out, so the prob. that he'll stand is 50-50.
- Smurfet and Vanity Smurf will of course stand in order to be part of the 
prestigious red hat wearers.
At this point my Smurf knowledge fails and I can not determine the actions of the 
other 996 Smurfs.  Maybe we should let Peyo answer this puzzle.
- Thus I conclude two stand and each has on a red hat. -

since each of these Smurfs can see only one other
Smurf with a red hat.

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