## Task 1 - 230511

Bernd, Peter, and Fred successfully participated in the School Olympics. Each of them received exactly one of the following three awards: 1st Prize, 2nd Prize, or Diploma. Furthermore, it is known:

(1) The student who received the 2nd Prize is older than Bernd.

(2) Fred did not receive the 1st Prize.

(3) Bernd is not a member of a mathematics working group.

(4) The student who won the 1st Prize is a member of a mathematics working group.

Who among them received the 1st Prize, who received the 2nd Prize, and who received the Diploma?

Justify your answer!
From (3) and (4) it follows that Bernd did not win the 1st prize. Since exactly one of the three students received the 1st prize, it follows from (2): Peter received the 1st prize. (5)

Due to (1), Bernd did not receive the 2nd prize; due to (5), Peter also did not receive the 2nd prize. Therefore, it follows: Fred received the 2nd prize. (6)

Since each of the three students received exactly one award, it follows: Bernd received the diploma.