Knights and Knaves – Three People

discrete mathematicslogic

Knights and Knaves Problem: There are three people A, B, and C. One of them is a cop. They say the following:

A: I am not a cop

B: The cop is a knave

C: All three of us are knaves

Is the cop a knight or a knave?

My answer: the cop is a knave because that person is person A. If Person C is a knight, and everyone is a knave, then person A is lying. I am not sure if my reasoning or answer is correct and would really like some help please. Thank you.

Best Answer

$C$ cannot be a knight - he would be calling himself a knave.

  1. (from $C$): $C$ is a knave, and either $A$ or $B$ (or both) is a knight.
  2. (from $B$): $B$ is not a cop.
  3. (from $A$): $A$ is either a knave cop, or he is a knight non-cop meaning $C$ is a knave cop.

Which also incidentally shows that $B$ is a knight.

Related Question