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Seating in a round table for each day...

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February 13, 2011
combinatorics unsolvedcombinatorics

Problem Statement

Merlin summons the nn knights of Camelot for a conference. Each day, he assigns them to the nn seats at the Round Table. From the second day on, any two neighbours may interchange their seats if they were not neighbours on the first day. The knights try to sit in some cyclic order which has already occurred before on an earlier day. If they succeed, then the conference comes to an end when the day is over. What is the maximum number of days for which Merlin can guarantee that the conference will last?