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MathNet 2014 Question 28

Math Olympiad Vault · MathNet 2014

Question 28

The 60 inhabitants of a village can be of three types: farmers (who always tell the truth), werewolves (who always lie), and necromancers (who answer however they like). Apart from these behaviors, members of each faction are completely indistinguishable from those of the others. When a visitor arrives, they stand in a circle, and each declares that the inhabitant to their right is a werewolf. Which of these statements is necessarily true?

(A) There is at least one necromancer.
(B) There are at most 20 werewolves.
(C) There are at most 30 farmers.
(D) There are at most 40 necromancers.
(E) None of the above.