9.6. Thirty girls - 13 in red dresses and 17 in blue dresses - were dancing in a circle around a Christmas tree. Later, each of them was asked if their right neighbor was in a blue dress. It turned out that those who answered correctly were only the girls standing between girls in dresses of the same color. How many girls could have answered affirmatively?

(R. Zhenodarov)
Answer: 17.

Solution: Consider any girl. The colors of the dresses of her left and right neighbors could have been: blue-blue, blue-red, red-blue, red-red. The girl answered "yes" in exactly the first two cases; therefore, she said "yes" exactly when her left neighbor was wearing a blue dress.

Thus, since exactly 17 girls had a left neighbor wearing a blue dress, the answer "yes" was given 17 times.

Remark: There are other (more complex) justifications for why exactly 17 girls in the circle answered "yes."

Comment: An answer alone (without justification, or obtained by considering specific cases of arrangement) -1 point.

For attempts at justification that do not consider all possible arrangements of the girls, no additional points are awarded.