IMO 2021 Shortlist C3
A thimblerigger has 2021 thimbles numbered from 1 through 2021. The thimbles are arranged in a circle in arbitrary order...
Category: Combinatorics
Problem
A thimblerigger has 2021 thimbles numbered from 1 through 2021. The thimbles are arranged in a circle in arbitrary order. The thimblerigger performs a sequence of 2021 moves; in the kth move, he swaps the positions of the two thimbles adjacent to thimble k. Prove that there exists a value of k such that, in the kth move, the thimblerigger swaps some thimbles a and b such that a ăk ăb.