## Task 1 - 290621

Jana wants to report on Christians, Alexander's, and Martin's successes in extracurricular activities in the wall newspaper. She interviews the three students and notes down the following:

(1) All three students participated in the Mathematics Olympiad. One of these students won a first prize, another one of them a second prize, and the remaining student a third prize.

(2) Martin and the winner of the second prize enjoy track and field. Both won a silver medal at the last sports festival.

(3) In the competition of young reciters, the winner of the second prize in the Mathematics Olympiad performed better than Christian.

(4) The winner of the first prize in the Mathematics Olympiad enjoys playing chess in his free time; his most frequent opponent is Martin.

When Jana reads through her notes, she realizes that she didn't write down which of the three students won which of the three prizes in the Mathematics Olympiad.

Determine whether this can still be uniquely determined from Jana's notes!

If this is the case, state the distribution of the three prizes!
From the notes it follows:

According to (2), Martin and the winner of the second prize are two different students, which means Martin did not win the second prize. According to (3), Christian also did not win the second prize. Therefore, from (1): (5) Alexander won the second prize.

According to (4), Martin is not the winner of the first prize. From this and (5), (1) it follows: (6) Christian won the first prize, (7) Martin won the third prize.

Thus, it is shown that this distribution (5), (6), (7) can be uniquely determined from Jana's notes.