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Nine IITians and a Professor

The puzzle is that Nine IIT students were sitting in a classroom. Their professor wanted them to test. Next day the professor told all of his 9 students that he has 9 hats, the hats either red or black color. He also added that he has at least one hat with red color and the no. of black hats is greater than the no. of red hats. The professor keeps those hats on their heads and ask them tell me how many red and black hats the professor have? Obviously students can not talk to each other or no written communication, or looking into each other eyes; no such stupid options and no tricks. Professor goes out and comes back after 20 minutes but nobody was able to answer the question. So he gave them 10 more minuets but the result was the same. So he decides to give them final 5 minutes. When he comes everybody was able to answer him correctly. What can be the answer and how did you reach the answer?

SOLUTION : After first interval, if there are 8 black hats and 1 red hat, the student with Red Hat can tell the answer as he can see 8 black hats, and there is at least 1 red hat. But nobody answers after this interval, so this is not the case.

After second interval, if there are 7 black hats and 2 red hats, the student with Red Hats can tell the answer as they can see7 black hats, and 1 red hat. But nobody answers after this interval, so this is not the case.

After third interval, if there are 6 black hats and 3 red hats, the student with Red Hats can tell the answer as they can see 6 black hats, and 2 red hats. Also, this time professor said these were the final 5 minutes that means the professor is expecting the answer after this. And they gave the answer after this interval, so this is the correct possibility. So there are 3 red hats and 6 black hats.

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