Problem 2. Anna, Vera, Katya, and Natasha competed in the long jump. When asked who took which place, they answered:

Anna: - I was neither first nor last.

Vera: - I was not last.

Katya: - I was first.

Natasha: - I was last.

It is known that one of the girls lied, while the other three told the truth. Which of the girls took first place?
Answer: Vера took the first place.

Solution. If Katya and Natasha told the truth, then they took the first and last places, so Anna and Vера could not 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 could have taken the last place, which is impossible. Therefore, Katya lied. Then the first place was not taken by Anna, Katya, or Natasha, so it must have been Vера.