## Task 1 - 260521

At the GDR Mathematics Olympiad for Young Mathematicians, Andreas, Britta, Dirk, and Kerstin meet. Each comes from a different city, namely Berlin, Dresden, Halle, and Schwerin. We know the following about them:

(1) Andreas and the participant from Berlin are the only two of the four students who were already at the GDR Olympiad last year;

(2) the other two, namely Kerstin and the participant from Dresden, are attending the GDR Olympiad for the first time.

(3) Dirk is older than the participant from Berlin.

(4) Kerstin is younger than the participant from Schwerin.

Which participant comes from which city?

Who are the two who already participated in the GDR Olympiad last year?
From (2) and (4) it follows that Kerstin cannot be from Dresden, nor from Schwerin. Because of (1) and (2), Kerstin is also not from Berlin, so it follows: (5) Kerstin is from Halle.

From (1) and (2) it follows that Andreas is not from Berlin, nor from Dresden. From this and because of (5) it follows: (6) Andreas is from Schwerin.

From (3), (5), and (6) it follows: (7) Dirk is from Dresden.

Further, it follows: (8) Britta is from Berlin.

From (1) and (8) it follows: Andreas and Britta already participated in the GDR Olympiad last year.