Saturday, February 11, 2017

What to Do in the Forest of Werewolves Part II

Again, each of A, B, C is a knight or a knave and exactly one of them is a werewolf. They make the following statements:
  1. I am a werewolf.
  2. I am a werewolf.
  3. At most one of us is a knight.
Give a complete classification of A, B and C.
(Source: What Is the Name of This Book? The Riddle of Dracula and Other Logical Puzzles by Raymond Smullyan)

The same approach as before will be used. If A is the werewolf, then A is a knight, B is a knave and C cannot be classified. This should be familiar now. If C is a knight, then there are two knights, and so his statement false. If, however, he is a knave, then what he's saying is true. This rules out A being the werewolf. Virtually identical reasoning rules out B. This leaves only the possibility that C is the werewolf. Accordingly, A is a knave and so is B. C is the werewolf, but he is at least honest: if he were not a knight and instead a knave, there would be at least two knights and there are not. So he is a knight.

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