You are visiting an island where everyone is either a knight or a knave. Knights always tell the truth and knaves always lie. They can only answer yes-no questions.
Single inhabitant
You come across a lone inhabitant. How can you tell if they are a knight or a knave?
Ask a question to which you both know the answer. For example, “Are you a mushroom?”
“We are both knaves”
You come across two inhabitants. One tells you “We are both knaves”.
Are they knights or knaves?
They can’t both be knaves, otherwise the inhabitant would have lied about it. Hence the statement was a lie, and the speaker was a knave. This means the other must be a knight.
Same or different
You come across two inhabitants. The first claims they are both of the same type (both knights or both knaves), the second says they are different.
What are they?
Since the statements are different their types must be different, hence the second person is speaking the truth and is a knight. The first must therefore be a knave.