Question 1127971: inside a dark closet are 5 hats;3 blue and 2 red. knowing this 3 mengo into the closet and each select a hat in the dark and places it unseen upon his head. once outside the closet,no men can see his hat.The first man looks at other 2 and thinks, and says, "I cannot tell what colour my hat is." the second man hears this, looks at the other two and says,"I cannot tell what colour my hat is either.".The 3rd man is blind and says,"well,I know what colour my hat is". What colour is his hat?
Answer by ikleyn(52887)   (Show Source):
You can put this solution on YOUR website! .
Inside a dark closet are 5 hats; 3 blue and 2 red. Knowing this 3 men go into the closet and each select a hat in the dark
and places it unseen upon his head. Once outside the closet, no men can see his hat.
The first man looks at other 2 and 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 3rd man is blind and says, "well, I know what color my hat is". What color is his hat?
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I analysed this problem and got a conclusion that it is posed incorrectly.
To show it, I will construct a contradicting counter-example.
Consider these two configurations:
a) (1b, 2b, 3r) // (first is blue; second is blue; third is red) and
b) (1b, 2r, 3b) // (first is blue; second is red; third is blue).
In case a) the first sees (b,r) and can not determine the color of his hat.
the second sees (b,r) and can not determine the color of his hat.
in case b) the first sees (r,b) and can not determine the color of his hat.
the second sees (b,b) and can not determine the color of his hat.
Thus in cases a) and b) the reaction of the first and the second men is the same;
but the color of the hat on the third man is different.
Therefore, in this situation the blind man can not recognize the color of his hat correctly.
This counter-example shows that the problem is posed incorrectly.
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