3. On an island, there live two types of people: knights who always tell the truth and scoundrels who always lie. During a birthday party, attended by 450 people, each of the attendees states: "all those present at the party, besides me, are scoundrels." How many scoundrels are at the party?
(A) none
(B) 450
(C) 449
(D) 224
(E) 225
Problem 3. The answer is (C).

If there is at least one rogue at the party, it is false that all the other attendees are rogues, and therefore at least one of the attendees is a knight; this naturally happens even when there are no rogues at the party. On the other hand, if there is at least one knight at the party, then all the other attendees are rogues, and thus the rogues present are exactly 449.

(Problem proposed by P. Francini)