## Task 3 - 280613

Mario, Petra, Rigo, and Tanja are discussing which places they will likely achieve in the school olympiad. They express the following opinions:

(1) Tanja will achieve the first place and Petra the second.

(2) Tanja will come in second and Rigo in third.

(3) Mario will take the second place and Rigo the fourth.

(4) No two students will come in the same place.

After the school olympiad, it turns out that statement (4) is true and that in opinions (1), (2), and (3), exactly one of the two statements is true and the other is false. State which student took which place in the school olympiad! Show that the place distribution you have named meets the conditions of the task!
A possible distribution is:

Tanja - 1st place; Mario - 2nd place; Rigo - 3rd place; Petra - 4th place.

In this distribution, statement (4) is true. In (1), "Tanja reaches the first place" is true and "Petra the second" is false. In (2), "Tanja will be second" is false and "Rigo third" is true.

In (3), "Mario takes the second place" is true and "Rigo the fourth" is false. Thus, in opinions (1) to (3), exactly one of the two statements is true and the other is false.