# Re: S, B, and a puzzle by Boolos, Smullyan, McCarthy

`Bruno Marchal wrote:`

```As a Price, I give you the (known?) Smullyan McCarthy
puzzle. You are in front of three Gods: the God of Knights, the
God of Knaves, and the God of Knives. The God of Knight always
tells the truth. The God of Knaves always lies, and the God of Knives
always answers by "yes" or "no" randomly.
You must find which is which, through some questions.
(Each question must be asked to one God, but you can ask
more than one question to a God; only then there will be a
God you can no more ask a question).
```

Playing around with this for a while, I realized you can always trick the knave into giving the same answer as the knight to any question "X" by asking the more complicated question, "If I were to ask you question X, would you answer 'yes'?" The knight will always give the same answer to this question as he would to the question X itself, while the knave will always give the opposite answer that he would if you had actually asked him X, which means he will always answer the same as the knight!

With this trick, the problem reduces to a simpler one where you have three guys with different names--say, Huey, Dewey, and Louie--and you know Huey and Dewey always tell the truth while Louie always answers randomly, and you have to figure out each guy's name with only three questions. In this case, you could ask the first guy, "is the second guy Louie?" Then if he answers "yes", you know the third guy must be either Huey or Dewey, so you ask the third guy "are you Huey?" and then ask "is the first guy Louie?" and you're set. On the other hand, if the first guy answered "no" to your first question, then you know the second guy is either Huey or Dewey, so you can ask the second guy the same two questions.

```And (added McCarthy) I let you know that all the Gods, although
they understand English, will  answer the yes-know question by
either "JA" or "DA", and you are not supposed to know which
means "yes" and which means "no".
```

Ugh, I'll have to think about that some more...but again, this is equivalent to a problem where you have three guys named Huey, Dewey and Louie, and Huey and Dewey always tell the truth while Louie answers randomly, but they all answer with "JA" or "DA" and you don't know which word means yes and which means no. If anyone else can figure it out feel free to jump in.

`Jesse`

```

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