A circle is divided into n sectors. Pawns stand on some of the sectors; the total number of pawns equals n+1. 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) combinatoricscombinatorial geometry