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 “I am the knight,” B says “I am the knave,” and C says “B is the knight.”
I am not able to understand why this is the case .
- For A it is fine
- For C it is fine
- But for B , if B is the Spy and B says "I am the knave" -- does that mean B is a Spy who lies ?