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I was working my way through some Knight and Knave Puzzles in Discrete Maths by Rosen, when I came across the following question:

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 "C is the knave,” B says, “A is the knight,” and C says “I am the spy"

My Solution:

A is the Knight, B is the Spy, and C is the Knave

Doubt:

Am I correct in saying my answer will work?

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3 Answers 3

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Yes. Your answer is correct.

A is the Knight
B is the Spy
and C is the Knave

To get the solution, First assume, A is knight and will always tells the truth.

Then as per his statement, C is the knave and so what he said will be false. That means he is not a spy. B is the spy and his statement A is the knight is random (true here). This is the only case in which the statements didn't contradict.

Now assume, A is the Knave.

Then as per his statement "C is the knave", it's clear that C is definitely not the knave. Which doesn't contradict since A is the knave already. That means, either B or C is Knight. If B is Knight his statement "A is knight" is false and it contradicts. If C is Knight his statement "I am the spy" is wrong and it contradicts. So this combination A is Knave, B is knight/Spy, C is Knight/Spy is wrong.

Continue this assumptions for other chances of combinations.

You will understand that all other combination except the first one (A is knight, B is Spy and C is knave) is wrong since the statements contradicts.

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Simpler explanation:

First, notice that B cannot be the knight, because then for their statement to be true, A would also have to be a knight, and we know there is only one knight.

Second, notice that C cannot be the knight, because then their statement would be false.

Therefore, A is the knight. By their statement, C is the Knave. By elimination, B is the spy.

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  • $\begingroup$ One could add a sentence that assuming this assignement the statement by C is indeed a lie. B's statement could be either. So this is a solution. $\endgroup$
    – quarague
    Nov 8, 2022 at 9:42
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Just logical if a is the night then he is telling the truth but if B is the night then he's telling the truth and be can't be the night because that would mean there would be two nights so B has to be false which doesn't mean that he is the knave I just means he's lying so he could be the Spy so if he's telling the truth than a is the night but if he's lying is not the Knight then see you would c telling the truth and if c was telling the truth he would have to be the night which is statement is false so he has to be lying and if B and C or both lying that means a is telling the truth so we know the a is the night and that night is telling the truth so therefore she has to be the knave and last but not least B has to be the Spy only thing that makes sense

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    $\begingroup$ You... might want to break this up into sentences, with punctuation, and read it back to make sure it is understandable. This torrent of words is, as it stands, possibly a correct (though redundant) explanation, but after three tries at reading through it I gave up trying to follow what you are saying. See some of the other answers for examples of how to write and format an answer for clarity. $\endgroup$
    – Rubio ♦
    Jul 9, 2018 at 2:01

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