Saturday, February 11, 2017

What to Do in the Forest of Werewolves Part III

In this and the next two problems there are again three inhabitants A, B, C, each of whom is either a knight or a knave. However only two of them, A, B, make statements. But in these statements, the word "us" refers to the three people A, B, C—not to just A and B.

Suppose A, B make the following statements:
  1. At least one of the three of us is a knight.
  2. At least one of the three of us is a knave.
Given that at least one of them is a werewolf, and that none of them is both a knight and a werewolf, which ones are werewolves?
(Source: What Is the Name of This Book? The Riddle of Dracula and Other Logical Puzzles by Raymond Smullyan)

Thinking about this a little, I think it makes sense to fix attention first on B's claim and whether he can be a knave. If he is a knave then what he's saying is true, but knaves always lie. So B is necessarily a knight. Now we turn our attention to A. If he is a knave then there are in fact no knights among the whole lot of them. But it's already established that one is a knight. A is a knight too then. Because one of them has to be a werewolf, and any werewolves in this scenario can't be knights, C is a werewolf and a knave. A dangerous combination!

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