Problem 2.

Four boys - Alyosha, Borya, Vanya, and Grisha - competed in a running race. The next day, when asked who took which place, they answered as follows:

Alyosha: I was neither first nor last.

Borya: I was not last.

Vanya: I was first.

Grisha: I was last.

It is known that three of these answers are correct, and one is incorrect. Who lied? Who was first?
Answer: Vanya was the one who lied. Borya was the first.

Solution. If we assume that Alyosha was the one who lied, then it would mean that he was either first or last, which would imply that either Vanya or Grisha also lied, contradicting the condition that only one of the boys lied. The same consideration applies to all other possibilities.