8.1. Olya, Oleg, and Pasha took the first three places in a competition. Each of them said they took first place. Olya, in addition to this, said that all odd places were taken by boys, and Oleg said that Olya was wrong. It is known that the children either always lie or always tell the truth. Who took which place?
Answer: I - Oleg, II - Pasha, III - Olya.

Solution: Olya could not have told the truth because according to her statement, she took the I place, which could only be occupied by a boy. Therefore, she is not first. Moreover, if she took the II place, her second statement would be true, which is not allowed. Therefore, Olya is third. Oleg's statement about Olya is correct, so he is telling the truth and took the I place. Pasha took the remaining II place.

Criterion: only the answer, answer with verification - 1 point; only proven that Olya is in the III place - 2 points. These points are summed!