20 different companies, each hires 15 new employees, 300 applicants
Source: Mathematics Regional Olympiad of Mexico West 2019 P6
September 9, 2022
combinatorics
Problem Statement
In Occidentalia there are different companies, each looking to hire new employees. A group of applicants interview each of the companies. Each company qualifies each applicant as suitable or not suitable to work in it, in such a way that each of them finds exactly suitable applicants, with . and each applicant is found suitable by at least one company. What is the smallest of f or which it is always possible to assign applicants to each company, given that each company is assigned only applicants that it considers appropriate, and that each of the applicants is assigned to a company?