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IT-CESENATICO 2003 Problem 4

    There are two sorts of people on an island: knights, who always talk truth, and scoundrels, who always lie. One day, the people establish a council consisting of 20032003 members. They sit around a round table, and during the council each member said: "Both my neighbors are scoundrels". In a later day, the council meets again, but one member could not come due to illness, so only 20022002 members were present. They sit around the round table, and everybody said: "Both my neighbors belong to the sort different from mine". Is the absent member a knight or a scoundrel?

    Dataset text AI-MO AoPS. Quoted with source.

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