IMO 2024 Shortlist C3
Let n be a positive integer. There are 2n knights sitting at a round table. They consist of n pairs of partners, each pa...
Category: Combinatorics
Problem
Let n be a positive integer. There are 2n knights sitting at a round table. They consist of n 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. (Belarus)