## Task 1 - 140831

To test Peter's puzzle-solving skills, he is given seven statements about five students on a circle afternoon, and he is told that exactly one of these statements is false. He is to find the false statement and also order the students' names by age.

The statements are:

(1) Anton is older than Elvira.

(2) Berta is younger than Christine.

(3) Dieter is younger than Anton.

(4) Elvira is older than Christine.

(5) Anton is younger than Christine.

(6) Elvira is older than Dieter.

(7) Christine is younger than Dieter.

Determine the false statement, and order the students' names by age (starting with the youngest)!
The age of each student is denoted by the first letter of their first name. Assuming (5) were true. Then, first, it would follow that (1) and (4) could not both be true; second, it would also follow that (7) and (3) could not both be true.

Thus, among statements (1) to (7), there would be more than one false statement. This contradicts the assumption that (5) is true; hence, (5) is the false statement, and (1), (2), (3), (4), (6), and (7) are true.

From (2) it follows that $B<C$, from (7) it follows that $C<D$, from (6) it follows that $D<E$, and from (1) it follows that $E<A$.

The required order of the students is thus: Berta, Christine, Dieter, Elvira, Anton.