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 as they wish). Except for these behaviors, the members of each faction are completely indistinguishable from those of the others. Upon the arrival of a visitor they arrange themselves in a circle and each one declares that the inhabitant to his right is a werewolf. Which of these statements is necessarily true?
Problem 796
Pick one
Official solution
Solution:
The answer is . One of the possibilities is that there are werewolves and farmers, alternating. This arrangement falsifies (A) and (B). Another possible situation is that the inhabitants of the village are all necromancers and they are all lying, which falsifies (D).
Let us now consider (C). If there are farmers, there must be at least inhabitants who are not farmers (but werewolves or necromancers), since the farmers cannot lie. Therefore the farmers can be at most half of the total inhabitants, that is, at most .