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Five in a circle, each says the person on the left is a knave

knights-and-knavesparityimpossibility

Five islanders, each a knight or a knave, sit in a circle. Each one says: "The person on my left is a knave."

Is this situation possible? If so, who is what; if not, why not? What changes if there are six islanders instead of five?

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Start from any one person, assume a type, and follow the statements around the circle. What happens when you get back to where you started?

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