Saturday, February 11, 2017

What to Do in the Forest of Werewolves Part VII

Here is an elegantly simple one involving just two inhabitants, A and B. Just one of them is a werewolf. They make the following statements:
  1. The werewolf is a knight.
  2. The werewolf is a knave.
Which one would you select for your traveling companion?
(Source: What Is the Name of This Book? The Riddle of Dracula and Other Logical Puzzles by Raymond Smullyan)

If it is the case that A is the werewolf, then consider the two possibilities for him. If he is a knight, then the prior assumption checks out. If he is a knave, then, although this may sound a bit trivial, it is the case that the werewolf is a knave. But it still is possible for A to be the werewolf in either case.

Now, if it is the case that B is a werewolf, then consider the two possibilities for him. If B is a knight, then he would never say that he (the werewolf) is a knave. So he cannot be a knight. But he can't be a knave either because a knave would never report that he is a knave.

I don't believe it's possible to figure out who is a knight or a knave here, other than to say that if A is a knight, then B is a knave, and vice versa. Having said that, if not traveling with a werewolf is of the utmost importance, go with B.

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