Least swaps to get any labeling of a regular 99-gon
Source: 2024 China MO, Day 2, Problem 6
November 29, 2023
combinatorics
Problem Statement
Let be a regular -gon. Assign integers between and to the vertices of such that each integer appears exactly once. (If two assignments coincide under rotation, treat them as the same. ) An operation is a swap of the integers assigned to a pair of adjacent vertices of . Find the smallest integer such that one can achieve every other assignment from a given one with no more than operations.Proposed by Zhenhua Qu