## Task 1 - 150731

The football teams of classes 7a, 7b, 8a, and 8b took the first four places at the school sports festival.

When asked which place each of the four teams had taken, the pioneers Antje, Benno, and Chris each gave two answers, one of which is true and one is false.

Antje: (1) The team of class 8a took second place.

(2) The team of class 8b took third place.

Benno: (1) The team of class 8a took first place.

(2) The team of class 7b took second place.

Chris: (1) The team of class 7a took second place.

(2) The team of class 8b took fourth place.

Investigate which distributions of the four teams 7a, 7b, 8a, and 8b on the four places correspond to the true answers of the pioneers!
Assume (1) is true. Then the team of class 8a would have taken second place, so (3) would be false and thus (4) true. This contradicts the assumption. Therefore, (1) is false and thus (2) is true, meaning the team of class 8b took third place.

From this, it follows that (6) is false and thus (5) is true. Therefore, the team of class 7a took second place.

From this, it follows that statement (4) is false and thus (3) is true, meaning the team of class 8a took first place.

For the fourth place, only the team of class 7b remains. Therefore, the following distribution is the only one that meets the conditions of the problem:

The team of class 8a took first place, the team of class 7a took second place, the team of class 8b took third place, and the team of class 7b took fourth place. This distribution indeed meets the conditions; for in it, statements (2), (3), and (5) are true, and (1), (4), and (6) are false.