Question 55
The people entitled to vote on the island of Cavalfurfandia number $5000$; each of them is either a knight, in which case they make only true statements, or a knave, in which case they make only false statements. Three thousand inhabitants declare that they will vote for Carla, two thousand that they will vote for Flavia. Each of the three thousand who declared they would vote for Carla makes the further statement: "Everyone who declares they will vote for Flavia is a knave". Knowing that every inhabitant votes for one of the two candidates, what is the minimum number of votes by which the winner will lead the loser?
(A) $5000$
(B) $4998$
(C) $1002$
(D) $1000$
(E) Carla and Flavia could tie.
(A) $5000$
(B) $4998$
(C) $1002$
(D) $1000$
(E) Carla and Flavia could tie.