PMs can move to a group if it increases his relative rating
Source: Romanian TST 2002
February 5, 2011
ratioinvariantcombinatorics proposedcombinatorics
Problem Statement
After elections, every parliament member (PM), has his own absolute rating. When the parliament set up, he enters in a group and gets a relative rating. The relative rating is the ratio of its own absolute rating to the sum of all absolute ratings of the PMs in the group. A PM can move from one group to another only if in his new group his relative rating is greater. In a given day, only one PM can change the group. Show that only a finite number of group moves is possible.(A rating is positive real number.)