Knaves and knights problem

Question

In a Island of knights and knaves..

Knights always says the truth knaves always says Lie.

You come across three Peaple(X,Y,Z) knave,knight and guest..identify knight,knave and guest..

X Says that Z is a knave

Y says that X is Knight

Z says that "I am the guest"

Answer 1

Sometimes the best way to do these questions is to start making assumptions.

We'll let X be the knight. If they are the knight, then what they say is true, and Z is a knave. If Z is a knave, then they are lying, and obviously they are not the guest. This leaves Y as the guest, with their statement being truthful (X is in fact, a knight).

There were no contradictions, but let's check other answers to be sure.

Let X be the knave. Then X's statement is false, and Z is not the knave. Since Z is not a knave, they can only be a guest (being a knight would make their statement false and contradict itself). This would leave Y as the knight, however, Y says that X is a knight which is false. This is a contradiction, so this is not the scenario, and X is not the knave.

Let X be the guest. They could be telling a lie or the truth, so let's look at some other statements. Y says that X is a knight, which is a lie, so Y must be the knave. This leaves Z to be the knight, however this is a contradiction as being a knight makes Z's statement false. Therefore X is not the guest.

Since X can't be a knave or guest, but we've shown that it can be a knight when Y is a guest, and Z is a knave, there is only one combination which works: X is a knight, Y is a guest, and Z is a knave.