Peter Bradley

TTh 11:40-1:10 (hill 005)

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!