6.1. A cross-country race was held in the forest. Discussing its results, one squirrel said: "The first place was taken by the hare, and the second was the fox." Another squirrel objected: "The hare took second place, and the elk was first." To which the owl remarked that in each squirrel's statement, one part was true, and the other was not. Who was first and who was second in the race? Justify your answer.
Solution: If the hare took first place, then there is no true statement in the second squirrel's statements. Therefore, the first part of the first squirrel's statement is false, which means the second part of her statement is true, that is, the fox was second. Then, in the second squirrel's statements, the first part is false, so the second part is true. Therefore, the moose took first place.

Note: Of course, the reasoning presented is not the only possible one.

Recommendations for checking:

| included in the work | points |
| :--- | :--- |
| at least one correct example is provided | 7 points |
| Only one of the winners is correctly identified, first or second  A correct answer is provided, and it is shown that it is possible, but it is not shown that other cases are impossible | 4 points |
| Answer without justification and/or incorrect answer | 0 points |