MathDB
2017 BMT Individual 11

Source:

January 9, 2022
combinatorics

Problem Statement

Naomi has a class of 100100 students who will compete with each other in five teams. Once the teams are made, each student will shake hands with every other student, except the students in his or her own team. Naomi chooses to partition the students into teams so as to maximize the number of handshakes. How many handshakes will there be?