Friday, 18 August 2017

Four men in hats puzzle

Question



As shown in picture above there are 4 men looking forward. None of them can see back. There is a opaque wall between man number 3 and man 4 (1,2,3 cannot see pass the wall). Two of the men are wearing a black hat and two of them are wearing a white hat. Each man can see the color of the hat wore by the men in front of him. (1 can see 2,3 and 2 can see 3) but each person does not know the color of the hat he is wearing.

Now one of the man needs to call out the color of his hat else they all die in 10 mins. Which man will callout the color of his hat correctly and why?


Solution

Answer is Man no 2.

Reasoning


 Lets start by eliminating men. Man number 4 is at the other end of opaque wall facing other side. There is no way he can see any men or the color of their hat. So he is eliminated. Now man no 3 also cannot see anyone else - he cannot look back and he cannot see beyond wall. So he is eliminated too. Now man number 1 knows the color of man 2 and 3. Now lets say they (2 and 3) were wearing same color hat then man no 1 would know the color of his hat since there are 2 white and 2 black hat. But he keeps mum which means man 2 and 3 are wearing different hat. S0 man number 2 waits for sometime if he does not hear man 1 calling out that means man 2 and 3 are wearing different color hats. Since man 2 knows the color of hat wore by man 3 he know the color of his hat and calls it out.

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