n + 1 pawns on n sectors of a circle
Source: TOT 329 1992 Spring Α J6 - Tournament of Towns
June 9, 2024
combinatoricscombinatorial geometry
Problem Statement
A circle is divided into sectors. Pawns stand on some of the sectors; the total number of pawns equals . This configuration is changed as follows. Any two of the pawns standing on the same sector move simultaneously to the neighbouring sectors in different directions. Prove that after several such transformations a configuration in which no less than half of the sectors are occupied by pawns, will inevitably appear.(D. Fomin, St Petersburg)