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February 4, 2015
combinatorics

Problem Statement

Along a round table are arranged 1111 cards with the names ( all distinct ) of the 1111 members of the 16th16^{th} JBMO Problem Selection Committee . The cards are arranged in a regular polygon manner . Assume that in the first meeting of the Committee none of its 1111 members sits in front of the card with his name . Is it possible to rotate the table by some angle so that at the end at least two members sit in front of the card with their names ?