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Hat Of Different Color.

A Hat of a Different Color

Once there was a teacher who offered his three students a deal. He will place a hat on each of the student’s head and the student then have to guess what color hat he or she is wearing. If he or she guess it right he/she won’t have to do writing problems for the rest of the semester. But any student guessed wrong he/she would have to do the problems and help grade everyone else’s work. First, all will have to close their eyes, then the student will take turn to open their eyes to guess what color hat they have. There are five hats in total, two in red and three in blue. While three of the hat are place on the students head, the other two hat will be hidden, but their colors are unknown.
The first student to go is Arturo. He open his eyes, look at other’s head and couldn’t tell for sure what color hat he has, so he pass. The second student is Belicia. She open her eyes, look around and also pass. The last to go is Carletta, she sat there with her eyes close and said she know what color she got. In the end she give the right answer.
So now the problem is how does Carletta know what color her hat is, without even opening her eyes?
To solve this problem, first I drew a sketch of the possibilities of the hat color each student has. My hypothesis is there are two red hat and one blue hat are on each of the students head. The first to guess is Arturo, it might be possible that he saw a red and a blue and couldn’t guess what his is. Then it was Belicia’s turn, she   also saw the same as Arturo and couldn’t guess what her color is. That leave Carletta with the answer. Since both Arturo and Belicia see red when taking turns, which means red appear two times.

There’s only two red hat, so that means the two hidden hat are blue and Carlleta had the third blue hat.
At first I didn’t how to do this problem, because the information didn’t give any clue about what Arturo and Belicia saw. So I start to put examples by putting two red and...