2. The board of directors, consisting of Ivanov, Petrov, Sidorov, and Kuznetsov, decided to remove one of the directors from their position. For this, each wrote down the surname of the candidate for dismissal (but not their own). The one against whom the majority voted is the one who leaves (the ballots were counted by an independent expert). In the end, Ivanov lost his position. Petrov consoled Ivanov: “I voted against Kuznetsov.” Ivanov concluded that Petrov was lying. Against whom did Ivanov vote? Justify your answer.
2. Answer: Against Kuznetsov.

Ivanov could have been removed from his position by a majority only in two cases of vote distribution: $3,1,0,0$ and $2,1,1$. Ivanov would have had no reason not to believe Petrov if he himself had voted against any of them except Kuznetsov: the second distribution of votes. But Ivanov did not believe Petrov, which means that he himself voted against Kuznetsov and understood that if Petrov were telling the truth, he could not be removed: the vote distribution would be $2,2,0,0$.

Grading criteria:

Correct answer with justification provided: 7 points.

Only the answer provided: 1 point.