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Minimum Swaps for All Pairs to Meet

Logic · IMO Shortlist 2024 1750
There are 200 knights sitting at a round table. They consist of 100 pairs of partners, each pair of which wishes to shake hands. A pair can shake hands only when next to each other. Every minute, one pair of adjacent knights swaps places. Find the minimum number of exchanges of adjacent knights such that, regardless of the initial arrangement, every knight can meet her partner and shake hands at some time.