Talk:Puzzles/Logic puzzles/Knights, Knaves & Spies II

If C answers, "No", then there is no contradiction in saying that A is the spy, B is the knave, and C is the knight. Therefore, it will not be possible to prove C is the spy.

If, however, C answers, "Yes," C can be proved the spy:

If C is telling the truth, then B is the spy. Then A and C would have to both be the knight, since they both tell the truth. But only one can be the knight. So C must then be lying.

B cannot in any case be the knight, since he would be lying. Since C is lying, too, B is not the spy, and so B is the knave. Thus C herself cannot be the knave, but neither can she be the knight, since she is lying. Therefore, if C answers, "Yes", C is the spy.

Am I right?

Eric119 22:33, 7 Oct 2003 (UTC)


 * Perfect, Eric! Great explantation. Thomas

Almost. Unfortunately, those are not the only two possible answers. C knows that he/she is the spy. The knight and knave do not necessarily know which of the others is. Therefore, C may answer "I don't know," and the judge will be unsure whether A or C is the spy. Avery

Another possibility would be A: Knight, B: Spy, C: Knave. Cyp 13:59, 18 Oct 2003 (UTC)

This is incorrect, as is the given answer to this logic problem.

The statement above says "Then A and C would have to both be the knight, since they both tell the truth." You forgot that the spy can tell the truth or lie. Look at it this way:

A: I am not the spy.

B: I am the spy.

C: I am not the spy.

We know that B is the knave, because the knave will always say he is the spy (he must lie). We cannot distinguish A from C, since a truth-telling knight, in this instance, looks exactly like a lying spy.

Now, let's try the other:

A: I am not the spy.

B: I am the spy.

C: I am the spy.

In this instance, we know that A is the knight, since the knight must always say he is not the spy (he must tell the truth), We cannot distinguish B from C, since a lying knave, in this instance, looks exactly like a truth-telling spy.

Eric B.


 * I think the puzzle intends C to answer either "yes" or "no", not "I am the spy" or "I am not the spy". In this case, "yes" or "no" is a statement of whether or not B is the spy, not C, and the given solution remains correct.  If C can say whatever he wants, he could say something like "I don't know" or "Go jump in the lake" or just remain silent and whether or not he was the spy would be trivially undecidable...  Perhaps the puzzle could be revised to reflect this?
 * Joe Lee 19:27, 31 May 2005 (UTC)