## Task 1 - 230731

Five girls, all older than 10 years and having their birthday on the same day, but no two of the same age, are asked about their age on their birthday. Each girl answers truthfully:

(1) Anja: "I am 5 years younger than Elke."

(2) Birgit: "I am younger than Carmen, but older than Dorit."

(3) Carmen: "I am 14 years old."

(4) Dorit: "I am neither the youngest nor the oldest of the five of us."

(5) Elke: "Birgit and Carmen are both younger than I am."

Determine whether it is possible to uniquely determine the age of each of these girls from these statements! If this is the case, then give the age for each of the girls!
If the age of each girl is denoted by the first letter of her first name as $A, B, C, D$, and $E$, then from (2) $D<B<C$ and further from (5) $D<B<C<E$.

Thus, $D$ is the smallest of the four numbers $B, C, D, E$. However, since $D$ cannot be the smallest of the five numbers $A, B, C, D, E$ according to (4), it follows that $A<D<B<C<E$.

From (3), $C=14$. Therefore, $A, D$, and $B$ are three natural numbers for which $10<A<D<B<14$ holds. This is only possible with $A=11, D=12, B=13$. According to (1), $E=16$.

Thus, from the information given in the problem statement, the ages of each of the five girls can be uniquely determined, and the result is: Anja is 11, Birgit 13, Carmen 14, Dorit 12, and Elke 16 years old.