Problem 2. Misha, Anton, Katya, and Natasha organized a table tennis tournament. When asked who took which place, they answered:

Misha: - I was neither first nor last.

Anton: - I was not last.

Katya: - I was first.

Natasha: - I was last.

It is known that one of the kids lied, while the other three told the truth. Who took the third place, given that it was a boy?
Answer: Misha took third place.

Solution. First, let's find out who among the children lied. If Katya and Natasha told the truth, then they took the first and last places, so Misha and Anton cannot have taken these places, which means they also told the truth and no one lied, which is impossible. Therefore, either Katya or Natasha lied. If Natasha lied, then no one was last, which is impossible. Therefore, Katya lied. From this, we can see that Anton took the first place, Natasha the last, and Misha and Katya the second and third places. Remembering that a boy took third place, we conclude that it was Misha.