Around a circular table, 18 girls are sitting, 11 dressed in blue and 7 dressed in red. Each of them is asked if the girl to their right is dressed in blue, and each one answers yes or no. It is known that a girl tells the truth only when her two neighbors, the one on the right and the one on the left, are wearing clothes of the same color. How many girls will answer yes? If there is more than one possibility, state all of them.
Solution

Let's analyze the possibilities. If the two neighbors of a certain girl are wearing blue, then she answers yes, and if they both wear red, she answers no, because in these cases she tells the truth. If the neighbor on the right is wearing red and the one on the left is wearing blue, the answer is yes, and if the one on the right is wearing blue and the one on the left is wearing red, the answer is no, because in these cases she lies. Observing the possibilities, we conclude that a girl answers yes when her left neighbor is wearing blue. Since there are 11 girls wearing blue, there are 11 girls who have their left neighbor wearing blue, and we can conclude that exactly 11 girls will answer yes.