8. Annalisa, Bruna, and Cecilia are playing soccer: one of them is in goal and the others are on the field. Whoever scores a goal stays on the field, while the one who doesn't score switches places with the goalkeeper. Knowing that Annalisa was on the field for 12 turns and Bruna for 21 turns, while Cecilia was in goal 8 times, who started in goal?
(A) Annalisa
(B) Bruna
(C) Cecilia
(D) Annalisa or Bruna (but definitely not Cecilia)
(E) It could be any of the three friends.
8. The answer is (A). Let $a, b, c$ be the number of turns in which Annalisa, Bruna, and Cecilia are in goal, respectively, and $A, B, C$ be the number of turns in which they are on the field. If $x$ is the total number of turns played, then we have $a=x-12, b=x-21, c=8$ and $A=12, B=21, C=x-8$. In each turn, one of $a, b, c$ increases by one, while two of $A, B, C$ increase by one, so $A+B+C=2(a+b+c)$, and substituting the previously found values, we get $x=25$. Since $a=13$, there is only one way Annalisa could have played, and that is if she starts in goal and returns every two turns, thus never scoring a goal.