2. The eligible voters on the island of Cavalfurfandia are 5000; each one is either a knight, in which case they only make true statements, or a knave, in which case they only make false statements. Three thousand residents declare that they will vote for Carla, and two thousand that they will vote for Flavia. Each of the three thousand who have declared they will vote for Carla makes the additional statement: "All those who declare they will vote for Flavia are knaves." Knowing that each resident votes for one of the two candidates, what is the minimum number of votes by which the winner will surpass the loser?
(A) 5000
(B) 4998
(C) 1002
(D) 1000
(E) Carla and Flavia could tie.
2. The answer is (C). We observe that we have two distinct cases depending on whether the statement "All those who declare they will vote for Flavia are scoundrels" is true or false:

- if the statement is true, then all those who made it (who are the 3000 people who declared they would vote for Carla) are knights; therefore, these 3000 people will actually vote for Carla. On the other hand, since the statement is true, we know that all those who declared they would vote for Flavia are scoundrels, so they were lying when making this declaration and will therefore vote for Carla. In this case, all the islanders will vote for Carla, the election result will be 5000 to 0, and the winning margin for the winner (Carla) will be 5000 votes.
- if the statement is false, then all those who made it (who are the 3000 people who declared they would vote for Carla) are scoundrels and, therefore, will vote for Flavia.

Let $n$ (with $n \leq 2000$) be the number of knights who declared they would vote for Flavia (since in this case the above statement is false, we have $n \geq 1$): among these 2000 people, $n$ will vote for Flavia (because they were telling the truth when declaring who they would vote for) and 2000 - $n$ will vote for Carla (because they are scoundrels, they were lying when declaring who they would vote for). We thus obtain that Carla receives a total of $2000-n$ votes, while Flavia receives $3000+n$ votes. In this case, the winner (Flavia) will have

$$
(3000+n)-(2000-n)=1000+2n
$$

votes of advantage. Since $1 \leq n \leq 2000$, the winning margin is between 1002 and 5000.

Since the problem asks for the minimum number of votes of advantage that the winner will have, the answer is 1002.