Knights Knaves and Spies

There are inhabitants of an island on which there are three kinds of people:

Knights who always tell the truth Knaves who always lie Spies who can either lie or tell the truth. You encounter three people, A, B, and C.

You know one of these people is a knight, one is a knave, and one is a spy.

Each of the three people knows the type of person each of other two is.

For this situation, if possible, determine whether there is a unique solution and determine who the knave, knight, and spy is :

A says"I am the knave," B says "I am the knave," and C says "I am the knave."

• Is this your own puzzle? If not, you should mention the source in the post. – Ankoganit Aug 21 '17 at 5:54

This isn't possible.

First of all, there's no unique solution by symmetry.
Second, a knight could not say "I am the knave" because then they would be lying. A knave could not say "I am the knave" because then they would be telling the truth. Therefore all three of them are spies.

• It's difficult to conclude that they are spies, since spies must either tell a truth or lie. However, "this statement is false" is just paradoxically wrong, and can't really have truthiness. – greenturtle3141 Aug 22 '17 at 1:16
• @greenturtle3141 - if you're a spy, then "I am a knave" is a lie. (But it's not equivalent to "this statement is false", which is a paradox no matter who you are.) – Deusovi Aug 22 '17 at 1:57
• Ah right, that's true. – greenturtle3141 Aug 22 '17 at 2:19

Please correct me if I am wrong.

As I understand it, one of the three people must be a knight, and so must always tell the truth. However, as they all claim that they are knaves, then it follows that the knight claims he is a knave. However, this is a lie - and as the knight always tells the truth, we have a contradiction. Thus, there is no solution.

A, B and C cannot be one of a knight, one of a knave and one of a spy. Only a knave can say "I'm the knave" but then knave don't tell the truth. Hence the is no knave among A, B and C. Also this implies everyone is lying. Hence all of them are spies.

• A knave cannot say "I am the knave.", because that would be telling the truth. – LeppyR64 Aug 21 '17 at 10:57

Would this require

Asking a question like "If the other kind of person that starts with the letter "k" told the truth about their identity, what would they answer if I asked for their identity?".
The knight would answer "I am a knave", because he'd be answering about a knave telling the truth.
The knave would answer "I am a knave", because he'd be lying about the knight telling the truth.
I can't get the spy to work, since the spy is essentially random in this scenario.

As for a unique solution:

It's not unique unless we get context to the question we asked the three people.

• This puzzle does not involve asking questions at all. I've downvoted because the answer does not seem relevant to the question. – Deusovi Aug 21 '17 at 5:23
• Fair enough. From the (limited) information given in the puzzle, the biggest piece of information missing seems to be the prompt that made A, B and C give those statements. I've merely attempted to determine what the prompt was that could make the three statements true. Perhaps I should have posted this as a comment rather than as an answer. – Alpha Aug 21 '17 at 5:31