Knights, knaves and vampires

The Game Room
1

In the land of Transylvania there are knights, knaves and vampires, all of whom are physically indistinguishable to non-natives. The only difference between them is that knights are upright and honourable, knaves are blackguards and scoundrels, and vampires are barking mad. What this means in effect is that when a knight says “Yes” he means “Yes”, and when he says “No” he means “No”, while a knave is just the other way round on principle, and a vampire will answer “Yes” or “No” at random without rhyme or reason.

You have had the ill-luck to fall into the hands of The Count, who unfortunately is the only sane vampire in all Transylvania and is pleased to meet some new blood. However, his one weakness is an admiration for logic, and he offers you the following chance for life:

You are to be shown into a cell where there are three Transylvanians. One of them is a vampire - you are not told whether the other two are knights, knaves or one of each, nor which one of the three is the vampire. You may ask any of them one question, which he or she will answer according to his/her predilections as noted above. You must then select one of them to leave the cell with you and if you are unfortunate enough to have picked the vampire, the Count will be having you for dinner.

All of the Transylvanians are flawlessly logical and each of them knows what the other two are, but none of them will be voluntarily helpful. How can you frame one single Yes/No question that will guarantee that you will not leave the cell with the vampire?

2

What does a knight or a knave do when presented with a yes or no question to which they can’t determine a certain answer?

3

Got it.

Naming them A, B, and C for convenience, and assuming that they are all male, ask A:

“If I were to ask you, would you tell me that that gentleman (B) is a vampire?”

If the answer is “No”, then you leave the room with B. If the answer is “Yes,” then you leave the room with C.

(If A is a knight, he will answer honestly; if he is a knave, he will still answer honestly because you phrased the question as a double-negative (that is, he WOULD lie to you, but then he lies about whether he would lie). If he is a vampire, then you’re all right as long as you don’t leave the room with him.)

4

Hmmm… What about… If the three Transylvanians are A, B and C, I go to (let’s say) A and ask him: “If I asked the vampire whether he is a vampire, would he say ‘yes’”?

If A is either a knight or a knave, he will be unable to answer – the knight cannot be sure of answering truthfully (because the vampire will say whatever the fuck he wants), and the knave cannot be sure of answering deceitfully (because idem).

However, if A is a vampire he will say whatever – he doesn’t care, he will answer without rhyme or reason with a “yes” or a “no”. His logical processes don’t work. He doesn’t have to worry about lying or saying the truth.

So – After the question, if the person is unable to answer, pick him. And if the person answers with either “yes” or “no”, pick any one of the other two.

What do you think?

5

Very creative! Looks like it works. ETA: As does Tom Scud’s. There is at least one other approach as well.

6

All I cam up with is that anyone admitting to being a knave is a Vampire.
Anyone who denies being a knight is a Vampire.

7

This also works: [spoiler]Point to one of the Transylvanians and ask another of them “Is it the case that either you are a knight or he is a vampire, but not both?”

  • If he is a knight and the other is a vampire, he will answer “No” (because “but not both” has not been satisfied)
  • If he is a knight and the other is not a vampire, he will answer “Yes”
  • If he is a knave and the other is a vampire, he will answer “No” (because “Yes” would be the correct answer since only of the conditions holds)
  • If he is a knave and the other is not a vampire, he will answer “Yes” (because “No” would be the correct answer)
  • If he is a vampire he will answer either “Yes” or “No” as he sees fit

So if you receive the answer “No” then either the person you asked has certified that the person you pointed to is a vampire, or else he is himself the vampire. This guarantees that the third person (neither questioned nor pointed to) is not a vampire. If instead you receive the answer “Yes” then either the person you asked has certified that the person you pointed to is not a vampire, or else he himself is the vampire. This guarantees that the person you pointed you is not a vampire.

This is quite elegant because it does not use a “meta-question” (“what would your answer be if I were to ask you…”)
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