A Hat of a Different Color
The wise teacher offered the three noisiest students a deal. He showed them that he had two red hats and three blue hats.
The deal worked like this:
The three students would close their eyes, and while their eyes were closed, the teacher would put a hat on each of their heads (and hide the other two hats). Then, one at a time, the students would open their eyes, look at the other two students' heads, and try to guess which color hat was on their own head.
Any students that guessed correctly would have no homework to do the rest of the semester. But any students that guessed wrong would not only have to do their own homework, but they would have to help grade everyone else's work also. The students drew numbers to see who would guess first. Then they closed their eyes and the wise teacher put a hat on each one's head. Arturo, who was to go first, opened his eyes, looked at the others' heads, and said he didn't really want to play. He couldn't tell for sure and he didn't want to guess in case he was wrong. Next, Belicia opened her eyes and looked at the others' heads. She also thought about the fact that Arturo had said he couldn't tell. Then she said she didn't want to risk it either. She couldn't tell for sure.
Carletta was third. She just stood there with her eyes still closed tightly and a big grin on her face. "I know what color hat I have on," she said. And she gave the right answer.
Your problem is to figure out what color hat Carletta had on and how she knew for sure. Remember: Carletta didn't even look!
1. is it practical?
2. is the imagery memorable?
3. can it be interpreted in more than one way?
4. can it be solved with the given information?
5. would kids be able to interpret it as intended or not?
6. is there anything strange about it?
7. how would you rewrite it, expand it, use it?
1. Yes, this question seems practical to me because it is easily applicable to any students in a classroom.
2. Since this situation is easy to set up, yet the answer to this question is tricky, students would remember this question's imagery easily (especially since the reward and penalty are at such high stakes).
3. I do not think that it is possible to find this word problem to be ambiguous in any other way... it is quite straight forward.
4. Yes, this question can be solved with the given information! There is a simple solution and a more complex solution as well, if you are interested, you can check this question out at the following link: http://mathforum.org/library/drmath/view/55638.html
5. Students should be able to interpret this question easily. If not, then the teacher can always do a quick and easy demo in class to demonstrate.
6. There is nothing strange about this question at all, except that I can see students wondering why the first two students could not guess the color of their own hats, but if you take this information as a hint, then you can solve this question easily!
7. I would not rewrite this question in anyway as it is already a well structured and logical word problem (at least for me), I would expand this question to adding more hats or more students or more hats of different colors to make this question more interesting. This is a great question to lead into the topic of probability or logical reasoning.
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