Green dots, red dots puzzle
Jim Allmon
or a red dot will be placed on their forehead.
Unknown to the men green dots are placed on all their foreheads.
The men are told to raise their hand if they see a green dot.
The men are told to stand if they know what color the dot on
their own forehead is.
One man stands and says I have a green dot.
How does he know??
--
--Jim
Gary Kendall
(SPOILER below)
Taking the assumption that all people in the room have a modicum
of intelligence, here's a proof by contradiction:
Assume that at least one person has a red dot. The people without
red dots will see this and will also see three hands raised. This
implies that the people who see a red dot have a green dot on their
forehead.
As noone stands up immediately, it is a pretty safe bet that they've
all got green dots. The quickest man realises this and stands up
proclaiming his green dotted forehead :-)
Gary (joint effort with rest of office)
hume smith
JA> NNTP-Posting-Host: sirius.llnl.gov
JA> Three men are placed in a room and told that either a green dot or
JA> a red dot will be placed on their forehead. Unknown to the men
JA> green dots are placed on all their foreheads. The men are told to
JA> raise their hand if they see a green dot. The men are told to
JA> stand if they know what color the dot on their own forehead is.
JA> One man stands and says I have a green dot. How does he know??
answer (almost)
this is logic/smullyan/painted.heads, in a less entertaining form.
--
Hume Smith Marge: Homer, I want to talk to you.
hume....@acadiau.ca Homer: But then I won't be watching TV!
hume....@bnr.ca You can see the bind I'm in...
Guy Cousineau
--------
Firstly, you did not say if anybody had raised their hand yet!
On that assumption, being faced with 2 green dots, it would be natural to
assume that the CONTEST would only be FAIR if I also had a green dot.
Presuming I see hands in the air, I can imagine what the others see:
A) if I have a RED dot
the other two see a red and a green dot
presuming one of them (at least) is smart, he would say
if I have a RED dot then that fella over there with the
green dot should not have his hand up, so mine must be green
B) if I have a green dot
the other two see two greens as well
presuming one of them is smarter or faster than me
he might reach the same conclusion about red above
so either the other two contestants are not-so-bright
or I have a green dot
So jump up and say green....I will be in good company, right or wrong!
Guy
--
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MAHEENDRA BABURAO KASMALKAR
>or a red dot will be placed on their forehead.
>Unknown to the men green dots are placed on all their foreheads.
>The men are told to raise their hand if they see a green dot.
>The men are told to stand if they know what color the dot on
>their own forehead is.
>One man stands and says I have a green dot.
>
Isn't this in FAQ? If not, it is time to put this one in there.
The spoiler follows:
Spoiler:
The guy assumes that he has a red dot on his head. Then he thinks to
himself " If I have a red dot and the remaining two are raising their
hands, they would immediately know that they have green dots on their own
foreheads. But that has not happened. Hence I must have a green dot on my
forehead."
The assumptions are :
The other two are not dumb and not as smart(or smarter) than the guy who
first stood up.
--
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