MathDB

14

Part of 2017 Harvard-MIT Mathematics Tournament

Problems(1)

2017 Guts #14: Unhappy classroom

Source:

2/21/2017
Mrs. Toad has a class of 20172017 students, with unhappiness levels 1,2,…,20171, 2, \dots, 2017 respectively. Today in class, there is a group project and Mrs. Toad wants to split the class in exactly 1515 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 1515 groups. What's the minimum unhappiness of the class Mrs. Toad can achieve by splitting the class into 1515 groups?
combinatorics