Question 2
On an island there are two categories of people: the knights, who always tell the truth, and the villains, who always lie. On a certain day the Grand Council meets, consisting of 2003 members. They sit randomly around a round table, and during the meeting each of them declares: "Both of them $i$ My neighbors are rogues. "The next day the council meets again, but one of the members is sick, so there are only 2002 members present. They re-arrange themselves at random again around the round table and each of them says:" Both of my neighbors belong to the category opposite to mine ". Was the patient a villain or a knight?