Knights and Knaves 2 Puzzle - Solution
The Puzzle:
The knight always tells the truth, the knave always lies, and the spy can either lie or tell the truth.
They are brought before a judge who wants to identify the spy.
Alex says: "I am not a spy."
Brook says: "I am a spy."
Now Cody is in fact the spy. The judge asks him: "Is Brook really a spy?"
Can Cody give an answer so that he doesn't convict himself as a spy?
Our Solution:Cody should answer "No".
Brook is either a knave or a spy. If Brook is a spy, then Alex is truthful and is therefore the knight.
Alex is a Knight
Brook is a Spy
Cody is a Knave
On the other hand, if Brook is the knave, there are two possibilities:
Alex is a Spy
Brook is a Knave
Cody is a Knight
or
Alex is a Knight
Brook is a Knave
Cody is a Spy
If Cody is either the knave or the knight, his answer to the question will be "No", and so the judge will not be able to draw a conclusion. On the other hand, Cody can answer "Yes" only if he is the spy.
Brook is either a knave or a spy. If Brook is a spy, then Alex is truthful and is therefore the knight.
Alex is a Knight
Brook is a Spy
Cody is a Knave
On the other hand, if Brook is the knave, there are two possibilities:
Alex is a Spy
Brook is a Knave
Cody is a Knight
or
Alex is a Knight
Brook is a Knave
Cody is a Spy
If Cody is either the knave or the knight, his answer to the question will be "No", and so the judge will not be able to draw a conclusion. On the other hand, Cody can answer "Yes" only if he is the spy.