Imagine three little girls sitting in a circle, each wearing either a red hat or a white hat (no girl can see the color of her own hat). Suppose that all the hats are red. When the teacher asks if any student can identify the color of her own hat, the answer is always negative, since nobody can see her own hat. But the teacher reveals that there is at least one red hat in the room, a fact which is known to every child (who can see two red hats in the room). Then the teacher asks if any student can identify the color of her own hat, and no one can. The teacher asks a second time if any student can identify the color of her own hat, and no one can. The teacher asks a third and last time if any student can identify the color of her own hat, and each little girl answers "red." Describe the reasoning that has led each little girl to the answer.