The Puzzle: On a
certain island fairly far away, there live three blue-faced people.
These people have lived happily on the island for over 50 years. On
this island, however, there are two taboos: (1) If anyone knows that he
have a blue face, then he will kill himself by midnight that night, and
(2) no one can tell another that he has a blue face.
There are no
mirrors or reflecting pools or
anything that might show a reflection on the island, so none of them
know that
they have a blue face. Also, because of taboo (2), none of the three
blue-faced men on the island know that they themselves has a blue face.
Then, one day, a stranger comes to the island. He
stands up
and says: "at least one of you has a blue face." He then gets in his
boat and leaves....
So the first night after the stranger departs passes. Nothing happens.
The second night
passes and, again, nothing happens. But the third night passes, and all
three of the
guys kill themselves at midnight. Ok, so…
Question
1: What happened? Why did they all kill
themselves on the third night?
Question 2: What new info did
the stranger
tell them that they didn't already know beforehand?
Black and White Hats
The Puzzle: There are a
hundred men waiting to be lined up. They will be lined up facing one
direction, on an incline facing slightly downhill. The men do not know
what order they will be placed; any man has a chance of being placed
anywhere in the line-up. Once they have been lined up however, we will
distribute 100 hats, one for each of the men in line. We have 100 white
hats and 100 black hats. We will distribute them in whichever order we
please--e.g., 100 white hats, 100 black hats, half and half, black and
white every other guy, a white hat every third guy and black hats
otherwise, a random ordering, etc. The hats will be distributed in any
order, just as the men will be placed in any order in the line-up. Now
the men are allowed to conspire before hand and devise any code they
like, given the following restriction: when we finally line them up and
distribute the has, we will start with guy 100 and work our way down to
guy 1, asking each in turn which color hat they have. They may only say
either 'black' or 'white' and nothing else. We will take their utterance to
mean the color of the hat that they are wearing. If they get it right,
they live, and then move on to the next guy. If they get it wrong, we
obliterate them, and then move on to the next guy. They cannot vary the
cadence, or whisper or yell or vary the volume of their utterance, or
anything other trick. They may only say 'black' or 'white' in one,
normal way. Also, no one can see his own hat, yet he can see the hats
of all of the men in front of him (except for guy 1, who has no one in
front of him). Ok, so...
Question 1: What is the most number
of people that the men can guarantee
will live?
Question 2: How do they do this?
What is the strategy to guarantee the most number of lives?