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Answer to Riddle #12: Three Man and Red & Blue Hats
- Inside of a dark closet are
five hats: three blue and two red. Knowing this, three smart men go into
the closet, and each selects a hat in the dark and places it unseen upon
his head.
Once
outside the closet, no man can see his own hat. The first man looks at the
other two, thinks, and says, “I cannot tell what color my hat is.” The
second man hears this, looks at the other two, and says, “I cannot tell
what color my hat is either.” The third man is blind. The blind man says,
“Well, I know what color my hat is.” What color is his hat?
This is one of those problems that sort of gives
you brain ache, you can work out the answer but explaining it clearly is
more difficult...
We will call the people A, B & C in the order that they
speak.
A does not know what colour hat he is wearing. A would
only know what colour hat he was wearing if he could see that B & C were both
wearing red hats, (as there were only two
red hats in the cupboard.) This is not the case so either:-
B & C are both wearing blue hats
OR
one
of B & C is wearing
red and the other is wearing
blue
When B speaks we obviously assume he has thought of all
of this. When B looks at C if C were wearing red
then he would know that he must be wearing blue
as they can't both be wearing red. But this does
not happen so C must be wearing blue, meaning
that B doesn't know if he is wearing red or
blue:
The third person must be wearing a
BLUE hat
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