The Problem of the Cubs Caps
The problem is this: A teacher comes to class with a box and shows the contents of the box to the students. It contains three Cubs caps, two Cardinals caps, and nothing else: the Cubs caps are true blue (for goodness), the Cardinals ones fire red (for evil).
There are only three students in this class and the teacher tells them that she is going to blindfold each one of them and then place one of the five caps on each of their heads.
The remaining two caps will then be placed back in the box so no one can see them when the blindfolds are removed. The teacher then tells the students that if anyone can tell what color cap she has on her head, then the teacher will give her 10 extra credits points. However, the students are not allowed to guess the color of their hats, they must be able to prove they have that cap on.
The teacher removes the blindfold from the first student who is now able to see the color of the caps on the other two students' heads, but he cannot see his own cap. The first student looks carefully at the other two caps, thinks for a while, and says he does not know the color of his hat.
(The student does not say aloud the color of the hats he sees on the other two students' heads.) The teacher then removes the blindfold from the second student who looks at the other two students' caps, thinks for a while, and says he does not know the color of his cap either.
(As before, this student does not say aloud the color of the caps he sees on the other two students' heads.) Just as the teacher is about to remove the blindfold from the third student, the third student says that she knows exactly the color of the cap on her head, and she doesn't even need to see the caps of the other two students.
The information given regarding this problem is to be considered accurate. 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 the description of the problem.
There are three possibilities to consider. Which of the three is correct?
1. She cannot possibly know what color cap she has on her head.
2. She has a Cubs cap and can prove it.
3. She has a Cardinals cap and can prove it.
For the correct answer and a precise explanation (250-500 words