2017 Guts #14: Unhappy classroom
Source:
February 21, 2017
combinatorics
Problem Statement
Mrs. Toad has a class of students, with unhappiness levels respectively. Today in class, there is a group project and Mrs. Toad wants to split the class in exactly groups. The unhappiness level of a group is the average unhappiness of its members, and the unhappiness of the class is the sum of the unhappiness of all groups. What's the minimum unhappiness of the class Mrs. Toad can achieve by splitting the class into groups?