On the island of Knights and Knaves, everyone is either a knight or a knave (but not both). Knights always speak the truth, and knaves always lie. It is rumored that there is buried treasure on the island. You ask one of the people on the island if the rumor is true: is there really buried treasure on the island? The person replies, "there is buried treasure on this island if and only if I am a knight." Can you determine whether this person was a knight or a knave? And if so, which are they? Can you determine if there is buried treasure on the island?

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