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This problem relates to Smullyan's puzzle about knights and knaves, where knights always tell the truth and knaves always lie. Every person is either a knight or a knave.

You encounter 3 people, each guarding a door. You know that one door has treasure behind it, while the other two lead to empty rooms.

  • A says "B and C are both knaves."

  • A says "The treasure is behind my door."

  • B says "The treasure is behind C's door."

  • C says "The treasure is behind A's door."

Which door has the treasure and what are the roles of the three people?

So with this question I am a little confused. My thought process was: make A the knight and then evaluate his statements. I see that when C talks it's a contradiction for A being a knight.

Now my issue is when I evaluate B and C being knights I can't seem to arrive at any contradiction.

If I say B is a knight I see that when I ask C he tells me A, which would be true if C was also a knight.

I want to say C is a knight because of this, but I am not confident in my reasoning. I would like to know of a good approach to this problem.

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How could B as C possibly both be knights when they disagree on where the treasure is? They can't both be speaking the truth.

A and C agree on where the treasure is. So either they are both knights, or they are both knaves.

They can't both be knights, because then the first statement would be problematic. So they are both knaves.

The first statement is a lie, but C is a knave. Therefore B must be a knight. C has the treasure.

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