Three convicts are brought into the warden's office. He says he can p

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Question

Three convicts are brought into the warden's office. He says
he can parole one of them and to decide which one he will
parole he takes out 5 hats (3 red and 2 white). He stands
behind them and places a hat on each one of their heads and
puts the other two remaining hats in a drawer. 

He tells the prisioners they can look at the others hats and
if they can tell which hat they have on they will be the one
who is paroled. 

The first man looks at the other two and says, "I don't know." 

The second man looks at the others hats and says, "I don't
know." 

The third man who is blind says, "Even though I have not the
gift of sight I can tell by what the others have said that
the color of my hat is..." 

What color is the blind mans hat and how does he know?

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Re: Three convicts are brought into the warden's office. He says he can parole one of them and to decide which one he will parole he takes out 5 hats (3 red and 2 white). He stands behind them and places a hat on each one of their heads and puts the other two remaining hats in a drawer. He tells the prisioners they can look at the others hats and if they can tell which hat they have on they will be the one who is paroled. The first man looks at the other two and says, "I don't know." The second man looks at the others hats and says, "I don't know." The third man who is blind says, "Even though I have not the gift of sight I can tell by what the others have said that the color of my hat is..." What color is the blind mans hat and how does he know?

Answer
# 1

The color of blind man's hat is Red. 

It is sure that the first man saw either both Red hats or
one White hat and one Red hat. There are 6 such possibilities: 

         1)  R  R  R

         2)  R  R  W

         3)  R  W  R

         4)  W  R  R

         5)  W  R  W

         6)  W  W  R

In all above possibilities, the first man won't be sure of
the color of his hat. 

Now, the second man knows that the first man saw either both
Red hats or one White hat and one Red hat. And, he also
knows that its one of the above 6 possibilities. (like we
know ;)) But he says, "I don't know". That means that (2)
and (5) are not the possibilities as in either case he would
be sure of the color of his hat (Red) by just looking at the
third man's color of hat (White). 

Now, the blind man knows that there are just 4 possibilities
- (1), (3), (4), (6) - and in all, the color of his hat is Red.

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Guest

Answer
# 2

Let the three be A, B , C
1. A sees the other two as either Two Red or One Red and One White
2. B knows that B's and C's Hats are as in #1. Had C been White B would have 
surely said his Hat is Red. Hence by contradiction C is Red.

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Anurag

Question	Asked @	Answers
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