TOT 375 1993 Spring A S3 dividing an inheritance
Source:
June 10, 2024
combinatorics
Problem Statement
A fixed number of people are dividing an inheritance among themselves. An heir will be called poor if he gets less than and rich if he gets more than (some heirs may be neither rich nor poor). The total inheritance and the number of heirs are such that the total income of the rich heirs will be no less than that of the poor ones no matter how the inheritance is divided. Prove that the total income of the rich heirs is no less than times that of the poor ones. (F Nazarov)