Problem 811

Solution:

The answer is (A). Let $a, b, c$ be the number of turns in which, respectively, Annalisa, Bruna and Cecilia are in goal, while $A, B, C$ are the number of turns in which they are on the field. If $x$ is the total number of turns played, then we will have $a = x - 12$, $b = x - 21$, $c = 8$ and $A = 12$, $B = 21$, $C = x - 8$. At 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 gives $x = 25$. Since $a = 13$, there is only one way in which Annalisa could have played, namely if she starts in goal and returns there every two turns, thus never scoring a goal.