2. Dima, Sasha, Kolya, and Gleb participated in an olympiad and took the first four places. A year later, their classmates managed to recall only three facts: "Dima took first place or Gleb took third," "Gleb took second place or Kolya took first," "Sasha took third place or Dima took second." Who performed better - Dima or Sasha? (In each of the three statements, one part may be true while the other is false, or both parts may be true).
Answer: Dima.

Solution. If Dima took first place, then from the last statement it follows that Sasha took third place, which means Dima performed better. If it is not true that Dima is in first place, then Gleg must be in third place. Then from the second statement, we get that Kolya took first place. Sasha could not have been in third place, so from the third statement, we get that Dima is in second place. This means Sasha is in fourth place, and in this case, Dima performed better again.

Evaluation Criteria: If any case is missed in the solution (the criterion for enumeration can be different), no more than 2 points.

Correct answer with all necessary explanations - 7 points.