Problem 2. Andrei, Maksim, Igor, and Kolya competed in a cycling race. When asked who took which place, they answered:

Andrei: - I was neither first nor last.

Maksim: - I was not last.

Igor: - I was first.

Kolya: - I was last.

It is known that three boys answered honestly and only one lied. Which of the boys lied?
Answer: Igor lied.

Solution. If Igor and Kolya told the truth, then they took the first and last place, so Andrey and Maksim could not have taken these places, which means they also told the truth and no one lied, which is impossible. Therefore, either Igor or Kolya lied. If Kolya lied, then the last place was not taken by Kolya, Igor, Maksim, or Andrey, which is impossible. Therefore, Igor lied.