Most Intelligent Student
Three college toppers are summoned by the inspecting faculty. To identify the best from them, the faculty takes them into a room and places one hat on each of their heads. Now all of them can see the hats on other’s heads but can’t see his own. There are two colored hats – green and red.
Now the faculty announces that he had made sure that the competition is extremely fair to all three of them. He also gives them a hint that at least one of them is wearing a red hat. Now the first one who is able to deduce his own hat color will be awarded the most intelligent student of all award. After a few minutes, one of them raises his hand and is able to deduce the color correctly.
3 conditions are possible-
2 Green and 1 Red hat-
Boy A will see other 2 are having green hats.
So, will understand that he is the only wearing Red Hat.
1 Green and 2 Red hat-
The Two boys A and B are wearing Red hat,
Boy A will see that boy B is wearing read hat but still not raising hand as per condition 1,
Hence, He will understand that B and he himself are wearing red hat.
3 Red hat-
Boy A,B,C are wearing red hat.
A will see boy B,C are wearing red hat but still not raising hand as per condition 2.
Hence, He will understand that B,C and he himself are wearing red hat.
There are two things to keep in mind:
Firstly there is at least one red hat. (There can be two or three as well)
Secondly the competition is fair enough for everyone. (As stated by the faculty)
Thus if there is only one red hat, that person will see two green hats on the other persons’ heads and will be able to deduce his own color as red. However the other students will see one red and one green hat and thus they can never be sure. In such a manner, the competition will prove to be partial for one student.
Suppose if there are two red hats. Then the students who are wearing red hats will see one red and one green hat on others. Now they must have deduced that there can’t be just one red hat. Thus they will know that they are also wearing a red hat. But the one who is wearing a green hat will see two red hats and can never be sure of his own color. In this case as well, the competition will not be fair.
Thus the only possible and fair means is if all of them are wearing a red hat. The one who is able to deduce the situation first, will raise his hand and will tell the correct answer.
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