A Hat of a Different Color

In This POW, our task was to find out how Carletta, a highly intelligent and very talkative student solved her wise teacher’s problem. She and two other students were complaining about the number of POW’s that they have had to complete throughout the semester. The teacher and the three students made a deal. The three complaining students would close their eyes and sit down in chairs. While they were sitting down, the teacher would take three hats out of a possible five, (3 blue hats and 2 red hats) and place one hat on each student’s head and then hide the other two. 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. The students had two options. They could either to guess what color of hat they had on their own head or pass. If a student guessed the correct color of hat on their own head they would be exempt from any POW’s the rest of the semester, but if they guess wrong they had to do all of the POW’s as well as grading all of the others students’ POW’s. The other option is to pass, if a student chose to pass then the workload stayed the same. The first student, Arturo, opened his eyes and looked at the other person’s heads. He couldn’t tell for sure what color of hat he had on, so he decided to pass. The next student, Belicia, looked up and saw that she couldn’t tell by looking at the other’s hats either so she decided to pass also. Carletta was third. She sat there, with her eyes still closed tightly and said, “I know what color hat I have on,” and she gave the correct answer. Our task is to find out how she did this. When I first looked at this problem I started to write out all of the possible combinations of hats. I figured out that there are only seven possible combinations of hats.

Possible Combinations

|Student One- Arturo |Student Two- Belicia |Student Three- Carletta |
|Blue