Be Clever with Logic This is a logic puzzle from the book Logic by Stan Baronett

Question

Be Clever with Logic This is a logic puzzle from the book Logic by Stan Baronett Scientists, philosophers, mathematicians, detectives, logicians, and physicians all face logical problems. How do they go about solving them? For insights, try your own hand at a challenge, the problem of the hats Once you are given the facts of the case, be aware of how you attack the problem, how you take it apart, what you place emphasis on, your avenues of pursuit, and plausible conjectures. The answer requires "seeing" a key move. Here is the challenge: A teacher comes to class with a box and shows the contents of the box to the students. contains three white hats, two red hats, and nothing else. There happen to be only three students in this class, and the teacher tells them that he is going to blindfold each one and then place one of the five hats on each of their heads. The remaining two hats will then be placed back in the box, so no one can see them once the blindfolds are removed. anyone can tell what color hat they have on their heads, then the teacher will give that student an A. But the students are not allowed to guess: They must be able to prove they have that color hat. The teacher removes the blindfold from the first student, who is now able to see the color of the hats on the other two students but not his own. The first student looks carefully at the other two hats, thinks silently for a while, and says he does not know the color of his hat. The teacher then removes the blindfold from the second student. He, too, looks at the hats on the other two students, thinks for a while, and says he does not know the color of his hat. (As before, this student does not say aloud the color of the hats he sees on the other two students' heads.) Now, just as the teacher is about to remove the blindfold from the third student, she says that she knows exactly the color of the hat on her head. In fact, she doesn't even need to see the hats of the other two students to know this Can you see how she did it? No information is being held back, no tricks are being played, and no word games are used. All the information necessary to solve the problem is contained in its description. There are three possibilities for you to consider. Which is correct?

Explanation / Answer

The answer is obviously 3 :

Person 1 looks at the other 2 and sees a red on person 2 and white hat on person 3. he says nothing

person 2 sees red on person 1 and white on person 3. he says nothing

person 3 realizes that person 2 and 1 saw the same thing and saw that since there are 2 red hats they have to be worn by the person 1 and 2.

Thus, Person 3 is wearing white

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