In Search of Wisdom
The King called the three wisest men in the country to his court to decide who would become his new advisor. He showed the men five hats. Three of the hats were black and two of the hats were blue. He placed a hat on each of their heads, such that each wise man could see all of the other hats, but none of them could see their own. The two hats left over were hidden. The wise men were forbidden to speak to each other. The king declared that whichever man stood up first and announced correctly the color of his own hat would win and become his new advisor.
The wise men sat for a long time before one stood up and correctly announced the answer. Determine the color of the hats of the three wise men (the color of the winner's hat first, then the other two).
Details and assumptions :
All three men are extremely wise, therefore, they will reach any logical conclusion correctly.
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1 solution
Total number of hats blue-2 and black -3
There are five answer choices-
First choice is blue,blue ,black -In this case the third one will say the answer first, because, there are only two blue hats and already he saw it in other two's head.This fact contradict the answer because as per the answer the one with blue hat(first person) said the answer.
Second choice is black,blue,blue- in this case first person will say the answer suddenly, because there are only two blue hat and already he saw it in other two's head.This fact contradict the statement "The wise men sat for a long time before one stood up and correctly announced the answer" because in this case there is no need for sitting for a long time to think before telling the answer.
Third choice is Black,blue,black. In this case the first person with black hat will see other persons with blue and black hat and first person will think, if my hat is also blue then the third person with black hat will see this two persons with blue hat and he suddenly would have told that his hat is black, as there are only two blue hats. This third person did not told like that.So the first person can tell easily that his hat is black.This fact contradict the statement that "The wise men sat for a long time before one stood up and correctly announced the answer" because in this case there is no need for sitting for a long time to think before telling the answer.
Fourth choice is blue,black and black.In this case the first person who see the others two with black cant say his hat is blue because before he saying his hat is blue, one of the other two will say its black hat on his head.(can use the logic written for third choice above)
Fifth choice is black,black,black. In this case, first person will see the other two persons with black hats.The first person will think like"if my hat is blue and since the other two persons hats are black, the second person with black hat will think like "if my hat is blue then the third person will see the other two hats as blue and would have said his hat is black" ". Since this did not happen and all were thinking for a long time,the first with black come to a logical conclusion that his hat is also black.So this is the answer.