Problem 2. Misha, Anton, Petya, and Fyodor competed in parallel bars exercises. When asked who took which place, they answered:

Misha: - I was neither first nor last.

Anton: - I was not last.

Petya: - I was first.

Fyodor: - I was last.

It is known that one of the boys lied, while the other three told the truth. Which of the boys took the last place?
Answer: Fedia took the last place.

Solution. Suppose Fedia lied. Then no one of the boys could take the last place, which is impossible. Therefore, Fedia told the truth and was the last.