2017 BMT Individual 11
Source:
January 9, 2022
combinatorics
Problem Statement
Naomi has a class of 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?